FLUID TRANSIENTS AND PIPELINE OPTIMIZATION€¦ · Fluid Transient and Pibel ïne Obtimization...
235
FLUID TRANSIENTS AND PIPELINE OPTIMIZATION USING GENETIC ALGORITHMS A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Civil and Environmental Engineering University of Toronto O Copyright by Zhiqiang Zhang 1999
Transcript of FLUID TRANSIENTS AND PIPELINE OPTIMIZATION€¦ · Fluid Transient and Pibel ïne Obtimization...
FLUID TRANSIENTS AND PIPELINE OPTIMIZATION
USING GENETIC ALGORITHMS
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Civil and Environmental Engineering
University of Toronto
O Copyright by Zhiqiang Zhang 1999
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Fluid Transient and Pibel ïne Obtimization Usiniz Genetic AInorithms I
ABSTRACT
Millions of dollars are spent each year on water distribution systems. Pipe
optimùation techniques provide an oppomuùty for potentid savîngs in costs for water
- mear supply systems. These optimization techniques include linear programming, non 1'
programming, dynamic programming, enurnerative approaches, and genetic algorithms.
The former four techniques have been applied to pipe network optimization in the
research literature over the last 20 years or so. Genetic algorithms provide a new
approach to pipe network optimization. Details of this method are considered in this
thesis. A global cost analysis of each component in a water supply system is carried out
of the genetic algorithm in order to assess the fonn of the objective bction.
Traditionally, the analysis on pipeline systems has focused on the steady state. In the
current work, a genetic aigorithm optimhtion model, which uses a probabilistic search
procedure that emulates Damhian natural selection, is coupled with a transient hydraulic
simulation model to generate and evaluate trial pipe network designs in search of an
optimal solution. A new and powerful penalty hc t ion is also developed for pressure
violations disthguishing steady state and transient conditions. The genetic algorithm
search is applied to a case study which demonstrates its flexibility and the opportunity for
significant cost saving offered by this method.
Fluid Transient and PiwIine *tïmiza!ion Usine Genetic Alnorithms ii
ACKNOWLEDGEMENTS
I would like to express my profound appreciation to rny supervisor Dr. B. W. Kamey,
for his continuous and enthusiastic assistance and encouragement, as well as his patience
and invaluable advice throughout this research work. I feel fortmate to have been his
student.
My thanks also go to Dr. C. A. K e ~ e d y for his helpful comments as the second
reader. Also, a speciai thanks to Kai-Wah Tang for his assistance with the cornputer
p=ogram-
1 would also like to thank my parents for providing love and support. Throughout my
graduate years at the University of Toronto, 1 have been fortunate to share fnendships
with many outstanding individuals. In particular, 1 would Iike to thank Darko Joksimovic,
Pradeep Kumar Behera, Susan Hansler, Martin Pendlebury, and Yves Filion for their
interest in my work, advice, and always wann-hearted encouragement.
Additional gratitude is extended to my wife Yingzhen (lanice) Guo, for her
understanding, patience and attention.
Finally, 1 would like to thank my good friend Cristovao Fernandes, a 'cray'
Brazilian, his sweet wife Marcia and their lovely daughter Victoria Cristovao not only
gives me academic help, but aiso, the most important, a brother's love!
Many thanks to you dl!
Forrest Z. Zhmg
... Fluid Transient and Piwline %tirnMon Usinn Genetic Al~orithms 111
CONTENTS
A bstract i
Acknowledgements u
Contents üi
List of Tables u
List of Figures xi
Notation xii
1 Introduction 1
1.1 Overview .................................................................................... 1
1.2 Modeling Approaches and Development . . . . . . . . . . . . . . .... . . . . . . . . . . . . . . . . . -. . . .. . . . . . . ... 2
1 -3 Thesis Organization . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . - . . . . . . . . . -. - 4
2 Transient Anaîysis 7
2.1 Fluid Transients . . . ... . . -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . 7
2.2 Mode1 for Transient Analysis - TransAM . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . . . . . . . . . . . . .. 10
2.3 Design Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Alternative Design for Fluid Trsnsients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. 13
2.3.2 Alternatives Considered in Thesis . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . -. . - . . . . . . . . . . . . 15
2.4 Summary ......................................................................... . . 18
3 Pipeline Optimizrition 19
3.1 Introduction . .. . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Problem Formulation .. . . . . . .. . . . .. . . . . . . . . .. . .. .. . .. . . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Solution Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 23
Fluid Transient and Pibtline ODtimization Usinn Genctic Alnonthms iv
............................................................... 3.3.1 Linear Programming 24
3.3.2 Non-Linear Programming ......................................................... 25
............................................................ 3.3.3 Dynamic Programming 28
............................................................ 3.3.4 Enuneration Appmach 29
........................................................................ 3.4 Design Components 31
3.4.1 Pipes .................................................................................. 31
................................................................................. 3.42 b p s 33
3-43 Vaives ............................................................................... -35
3.4.4 Reservoirs/Tanks .................................................................... 36
3.5 Pipeline Optimization including Transients ............................................ 37
.................................................................................... 3.6 Summary 40
Review of Genetic Algorithms 41
................................................................................. 4.1 Introduction 41
4.2 Genetic Algonthms for Optimization ................................................ 42
4.3 Genetic Algorithms for Pipeline S ystem Optimization .............................. - 4 5
4.4 Summary ............................................................................. 48
Genetic Algorithms for Pipeline Optimization 49
5.1 Introduction ................................................................................. 49
..................................................................... 5.2 Overview of Approach 50
............................................................................. 5.3 Implementation 52
....................................................................................... 5.4 Coding 56
.....*................. ...........................................................-. 5 -5 Fitness .. 56
................................................................................ 5.6 Reproduction 58
Fluid Transient and Piwline O&nization Usinn Genctic Alnorithms v
.................................................................................... 5 -7 Crossover 60
..................................................................................... 5.8 Mutation 62
.................................................................................... 5.9 Summary 63
6 Cost Objective Function 65
.......................................... 6.1 Pipeline Optimization in Transient Condition 65
.................................................................... 6.2 Input Data of TransAM 67
........................................................................ 6.3 System Cost Factors 68
6.3.1 PipeCosts ........................................................................... 69
.......................................................................... 6.3.2 Pump COSU 72
................................................ 6.3.3 Protection Measure Device Costs 73
..................................... .................. 6.3.3.1 Cost of Nodal Devices .. 75
......................................................... 6.3.3.2 Cost of In-Line Devices 76
........................................................... 6.3 -3 -3 Cost of A u Chamber 78
.................................. .............................. 6.3.4 Resewou Costs ... 80
6.3.5 Electricity Cost ...................................................................... 85
6.3.6 O&MCost .......................................................................... 86
................................................................. 6.4 Performance Cost Factors 87
............................................................ 6.4.1 Hydradic Performance 88
........................................................... 6.4.2 Operathg Cost Function 88
........................................................................ 6.5 Objective Function -90
....................................................................... 6.5.1 Operating Life 91
.................................... ............................ 6.5.2 Inflation Rate .. 9 1
..................................................................... 6.5.3 Discount Rate 9 1
Fluid Transient and Pipeline Obtimization Usina - Genetic Aleorithms vi
6.5.4 Objective Function ................... .. .....................-.............-.... 93
6.6 Summary ................................................................................... 95
7 Description of Case Study %
........................................................................ 7.1 System Description 96
.......................................... ........................... 7.2 Design Variables .. LOO
................................................. 7.3 Economic Consideration 105
................................................................................. 7.4 Computing 107
........................................ ................... 7.4.1 Master Program .... 107
................................................... 7.4.2 Transient Simulation Pmgram 1 1 1
.......................................... 7.4.3 Run Procedure ...................... ... 112
7.5 Summary .................................................................................. 113
8 Outcomes and Aoalysis 114
8.1 Previous Case Study ...................................................................... 114
....................... ..........*-.... 8.2 Performance of GA Including Transient .. 120
........................................................................ 8.3 Least-Cost Design 127
........................................................... ................... 8.4 Summary ... 130
9 Conclusion 131
10 Future Work 135
Reference 137
Appendixes 152
A Input Data for User 152
............................................................................. . A 1 Description 152
Fluid Transient and Piwline Obtimizatïon Usine Genetic Aieorithms vii
......................................................................... A.2 Pipe Cost Data 154
....................................................................... A.3 Pump Cost Data 155
..................................................................... A.4 DeviceCost Data 156
............................................................ A S Reservoir/Tank cost Data 158
.................................................................. A.6 Electrïcity Cost Data 159
A.7 O & M Cost Data ....................................................... 160
...................... ...............................- A.8 Performance Cost Data .. .. .. 161
......................................................................... A.9 Opetating Life 162
.......................................................................... A . 10 Inflation Rate 163
................................. .....*.............*.............. A . 1 1 Discount Rate .. 164
A.12 Summary .............................................................................. 164
. ...........................*.... .................... A 1 2.1 TransAM Data File .... 164
....................................... A . 12.2 Data File Cornpleted From TransAM 164
A.12.3 input Data File .................................. ...... ........... 165
...................... A.12.3.1 Cost Data File .. .................................. 165
A . 12.3.2 Parameters and Constants File .......................................... 165
......................................................... A . 13 Example of Input Data File 166
................................................................... A.13.1 Cost Data File 166
................................................ A . 13.2 Parameters and Constants File 166
B Important Events in The Genetic Algorithms Community 168
........................................................ . B 1 Books on Genetic Algorithms 168
......................................................... B.2 Conferences and Workshops 173
............................... 8.3 Journals and Special Issues on Genetic Algorithms 179
... FI uid Transient and Pipeline Ostirniauion Usinn Genetic A lnorithms -11
.............................................................................. B.4 References 180
C Input Data for TransAM program 192
D Input Data for TrinsAM program 210
D . 1 Data File of PIPEDATA-DBD ....................................................... 210
D.2 Data File of NEWORK.TDF ................................... ... ........... 210
D.3 Data File ofNEWORK-CAD ....................................................... 212
Fluid Transient and Piwline Optimization Usinv Genetic Aleonthms ix
LIST OF TABLES
................................................. Table 3.1 Literatures of Linear Progmmmhg 24
Table 3 -2 Literatures of Non-Linear Prognimming ................... .... ....... -. ......... 2 6
Table 3.3 Literatures of Dynamic Programming .............................. .. ......... 2 8
............................................... Table 3.4 Literatures of Complete Enurneration 30
Table 6.1 Parameters of Some In-Line Devices ............................................... 75
Table 7.1 Node Data for the New York Tunnels Project ...................................... 97
Table 7.2 Pipe Profile Data for the New York Tunnels Project ............................ -99
..................................................... Table 7.3 Design Options for Case Study 103
................................................ Table 7.4 Parameters of Genetic Algorithms 104
................................... ........*.......... Table 7.5 Pipe Costs of Case Shdy .. 106
.................... ................ Table 7.6 Computer Platforni for case Smdy .... 107
Table 8.1 Comparative Designs for the New York Tunnels Problem ..................... 115
................................... Table 8.2 HGL of Case Smdy in Steady State Condition 122
Table 8.3 Cornparison of Nodal Min . Head with and w/o Cavitation ..................... 123
Table 8.4 Cornparison of Nodal Min . Head for Different Valve Closure Duration ..... 125
................................................... Table 8.5 Optimal Solution of Case Study 126
.............................................. Table 8.6 Results of GA Runs (60 sec . closure) 127
................................ Table 8.7 Resuits of GA Runs (300 sec . closure) ... .......... 128
Table 8.8 Hydraulic Analysis for GA Designs (60 sec . closure) ........................... 129
.......................... Table 8.9 Hydraulic Analysis for GA Designs (300 sec . closure) 129
FI u id Transien t and Piwl ine mtim ization Usinn Gcnetic A lnorithms x
...................................................... Table B . 1 Books on Genetic Algorithms 170
..................................................... Table 13.2 Papers on Genetic Algorithms 172
.............................................. Table B . 3 Conferences on Genetic Aigorithms 174
............................... Table B.4 International Confècence on Genetic Algorithms 175
Table 8.5 international Conference on Parallel Problem Solving h m Nature ......... 175
...................... Table 8.6 Workshop on Foundation of Genetic Algorithms .. ....... 176
............................. Table 8.7 Annual Conference on Evolutionary Pmgramming 177
Table B.8 international Conference on Artificial Neural Nets and
.............................. ......................... Genetic Algorithms .... 177
Table B.9 IEEE International Conference on Evolutionary Computations ............... 178
Fiuid Transient and P i d i n e Outim ization Usinn Genetic A leorithms xi
LIST OF FIGURES
Figure 6.1 Generalized Air Chamber and Input Variables .................................... 84
Figure 7.1 New York City water supply tunnels ............................................... 98
Figure 7.2 Flowchart Representation of Genetic Ngorithms Mode1 .................... .. 110
Figure 7.3 Flowchart Repmsentation of TransAM .......................................... Il1
Figure C . 1 . 1 Extreme Head Summary Plot .................................................. 200
Figure C.1.2 Extreme Head Summary Plot ................................................... 201
Figure C.2.1 Extreme Head Summary Plot ................................................... 202
Figure C.2.2 Extreme Head Summary Plot .............................................. 203
Figure C.2.3 Extreme Head Summary Plot ............................................... 204
Figure C.2.4 Extreme Head Summary Plot .................................................. 205
Figure C.2.5 Extreme Head Surnmq Plot ................................................ 206
Figure C.3.1 Extreme Head Summary Plot ................................................... 207
Figure C.3.2 Extreme Head Summary Plot ................................................... 208
Figure C.3.3 Extreme Head Summary Plot ................................................... 209
Figure D . 1 - 1 Extreme Head Summary Plot .................................................. 213
Figure D . 1 -2 Extreme Head Summary Plot .................... .. ............................. 214
................................................... Figure D.1.3 Extreme Head Summary Plot 215
Figure D . 1 -4 Bxtreme Head Summary Plot ................................................... 216
Fluid Transient and Piwline atimization U s i n ~ G e n ~ c - Aborithms xii
NOTATION
Symbol Meaning
a = exponential constant, in this thesis, usuaiiy assumed to be 1.0
At = ACAWAREA) = actuai tabulateci ta& cross sectionai areas (in mZ or ft2)
starting h m the bottom of the tank
A, = annual value
A, = area o f the valve opening
b~ = exponentiai constant for steady state condition, assurned 1.0
= exponential constant for transient condition, assumed 1 .O
= time coefficient, changing with year (assumed to be 1.14 in 1999)
= cost coefficient o f perfomance for steady state conditions
($/m2 or $/P)
Cht = cost coefficient of performance for transient conditions
($/m2 or $/AL)
CC = cost coefficient depending on the air chamber size ($/m4 or
$0.00863/ffJ)
= discharge coefficient which accounts for real vaive losses
(dimensiodess)
= cost constant depending on the pipe material ($/kg or $ 0.454Ab)
= cost of purnp ($)
Fluid Transient and Piwline Obtimization Usinn Genetic Alnorithms xiii
ESVi
ES*
ha
h b
H
Ha
Ho
He
Hm,
Hrnins
Hmwi
Hmin,t
HP
= cost constant assumed equal to $300,000
= unit exchange and cost coefficient, assumed to be $690,000
(sO-'/m2' or $3 5,390 sO-'/ftLS)
= unit exchange and cost coefficient = $ 140/m3 (or $3.96/ft')
= cost coefficient for valves ($)
= inner diameter of pipe (m or ft)
= pipe diameter
= price of energy ($/kWehr)
= valve size parameter determineci by the energy dissipation
potential of the valve (= Cd A" (2@lR), mSR/s or PR/s
= effective discharge coefficient of valves
= e f f d v e discharge coefficient of reference valve
= ailowable pressure head for pipe (m or ft)
= length parameter for pipe (m or fi)
= total dynamic head of pump (m or ft)
= initial maximum water head inside air chamber (m or fi)
= pressure head at valve or head loss across valve (m or ft)
= average head of pump (m or ft)
= allowable maximum pressure in pipeline for steady state (m or fi)
= allowable minimum pressure in pipeline for steady state (m or ft)
= ailowable maximum transient pressure in pipeline (m or A)
= allowable minimum transient pressure in pipeline (m or A)
= pressure head in pipeline (m or ft)
Fluid Transient and Piwline mtimization Usinn Genetic Altzorithrns xiv
HP
i = NSA
= required head of pump (m or fi)
= index of cuttïng plane which marks the beghning of Segment 2
= discount rate
= the index of cutting plane which marks the end of Segment 2
= parameter (experirnentally chosen to be 0.8)
= unit conversion factor, 1/550 in imperid units
or 1/75 in SI uoits
= cost conversion coefficient for pipes ($/m2 or $/f??)
= cost constant for pipes ($/m2 or $/!AL)
= cost constant for pumps
= length of pipeline (m or fi)
= length of pipe (Iink) (m or ft)
= 1engt.h of pipeline which does not satis@ the pressure
requirements under transient conditions (m or fi).
= length of pipeline which does not satisQ the pressure
requirements under steady state conditions (m or A).
= chromosome length (m or fi)
= capital cost of air chamber (%)
= electrïcity cost ($/y)
= penalty constant for hydraulic violation ($)
= cost of system components ($)
= cost of maintenance and operathg (S)
= capital cost of pipeline ($)
Fluid Transient and Piwline Obtimization Usinn Genen'c Alnorithms xv
n, n l ,
na = NAREA
NLXNK
N P W
NSTOR
= capital cost of pump station (S)
= capital cost of elevated storage tanks (S)
= capital cost of in-line valves (S)
= exponent coefficient to pipe diameter and pump respectively
= total number of tabulated cross sectional areas describing
both segment 1 and segment 2
= generation number
= operating life (yr)
= maximum nurnber of generations
= popuiation size
= number of station 53+16 fi device options in case study
= number of station 63+21 fi device options in case study
= number of station 69+57 fi device options in case study
= number of station 86+61 A device options in case study
= number of station 9 1+82 fi device options in case study
= nurnber of station 97+14 fi device options in case study
= number of pipe diameter options
= number of pipe material options
= number of purnping station device options
= total nurnber of designs
= number of ptential links in the network
= number of pumps in the network
= number of elevated storage resmroirs in the system
Fluid Transient and Piwline O~timization Usinp Genetic Alporithms xvi
= penalty multiplier
= power requirement (kW)
= cost h c t i o n for pipes (S)
= cost fiinction for pumps ($)
= cost function for storage (S)
= present worth
= steady state discharge for valve (m3/s or ~ / s )
= average discharge of pump (m3/s or PIS)
= pipe (link) diameter (m or ft)
= maximum discharge of pump (m3/s or PIS)
= rated discharge of pump (m3/s or PIS)
= flow capacity of pump (m3/s or P/s)
= inflation rate (%)
= predefined system storage requirement (m3 or &)
= nurnber of hours per year for pump operation, hours.
(a fûnction of demand, with a maximum value is 8760 hours)
= minimum volume of tank j (m3 or d)
= total air chamber volume (m3 or fr')
= maximum capacity of the tank (m3 or A-')
= mass of wall materid of pipe (kglm or 1bM)
= head lie of pump (m or ft}
= head lift of storage (m or fi)
= flow capacity of storage (m3/s or f i s )
Fluid Tmsient and P i d i n e ODtimization UsinnGenetic Altzorithms xvii
GREEK SYMBOLS
Symbol
6Zik = ZS1
Symbol
{...-..)
[*.....]
C
I
a
Meaniag
= height of air chamber in meters or feet comsponding to
Segment 1
= height of air chamber in meters or feet corresponding to
Segment 2
= constant penalty multiplier
= unit weight o f the fluid (kWrn3 or lblft')
= alIowable level of circumferentid stress of pipe (MPa or psi)
= pipe matenal density (kg/m3 or lb/ft3)
= pump efficiency
MATH SYMBOLS
Meaning
= set of
= set of
= summation
= integral
= partial differential
FIuid Transient and Piwline ODtimization Usinn Genetic Akorithrns 1
CHAPTER 1
INTRODUCTION
Water distribution systems are usually designed to adequately satis@ the water
requirements for a combination of domestic, commercial, public and fire fighting
purposes (El-Bahrawy and Smith, 1987). The construction and maintenance of pipeiïnes
for water supply systems in North Amencan costs millions of dollars every year. As a
vital part of water supply systems, water distribution networks represent one of largest
inf'rastmcture assets of industrial society. There is a growing desire to achieve the
highest level of effectiveness for each dollar spent-
Traditionally, the cost effectiveness of the distribution system is determined during
the design and construction stage. Although the economicai design of hydraulic networks
has long been an area of interest for researchers in hydraulics, the subject has received
particular emphasis since the 1960s because of the emergence of digital cornputers. The
magnitude of the investment would seem to dictate that care be taken to ensure a cost
effective distribution scheme is implemented.
Fluid Transient and Pipeline Obtimization Usine Genetk Algonthms 2
Pipeline system optimization is not new. A large number of optirnization models for
water distribution systems have k e n reporteci in the literature. The general problem of
the least-cost design of hydraulic networks can be summarised as the optimization of an
objective function subject to a set of topologk, geometric, and hydraulic (pressure and
velocity) constraints. The objective fiinction consists of fixed costs (e.g., invesbnents in
piping, valves, accessories, and assembly) and operating costs (e-g., due to energy and
maintenance).
1.2 MODELLING APPROACHES AND DEVELOPMENT
Over the years, many techniques such as linear programming (LP), non-linear
programming, dynamic programming (DP) and enurnerative approaches have been
applied to optimization of both the design and operation problem. Optimization is a
mathematical procedure for fïnding the best decision in design: pipes or pipe diameters,
existing pipes to be duplicated or cleaned, pump locations and sizes, etc. and in operation
-- which purnps should be odoff in each t h e period, valve sethgs, tank operation, etc.
The goal is " ... to achieve economy of design, construction, operation and maintenance of
these systems." (Karney and Mcinnis, 1990).
Although the LP approach has advantages over other methods in terms of
computational requirements and simplicity, its application to large systems may be
awkward and may impse unrealistic constraints on the formulation. For this ceason,
many researchers have chosen non-liriear foda t ions . However, non-Iinear
programming bas a number of limitations: (1) because the pipe diameters are generally
Fluid Transient and Pipe fine Optimitation Usine Genetic A lnorithms 3
assumed to be continuous variables, the optimal values will not necessarily conforni to
the available pipe sizes; thus, rounding of the final solution is required; (2) only a local
optimum may be obtained; and (3) there is a limitation on the number of constraints and
hence the size of network that can be handled (Simpson et al., 1994).
The validity of dynamic programming (DP) can be extended by increasing the
number of States, but this extension is achieved at the cost of increased computation. Its
usefulness is Iimited by the so-called "dimensionality" of the problem which is a strong
fwiction of the number of state variables (Yeh, 1985). The enurnerative approach,
however, can obtain global solution, but requires large amounts of cornputer memory and
operation tirne even for moderately-sized networks.
Most of these methods have applied deterministic optimization techniques to the
network design. In recent years, genetic aigorithms (GAs), involving the application of
stochastic optimization techniques, have k e n successfully applied to the optimization of
pipe networks. A challenge in using genetic algorithms is that there are many variables
and many decisions to make about the details of implementations. However, GAs are a
powerful, population-orientated optimization technique based on the mechanics of naturai
selection and genetics (Simpson and Goldberg, 1994).
Furthemore, ûaditionally, the optimization process for distribution systems has
focused on steady state conditions. Although steady state conditions are cornmon in most
of water suppl y projects, transient phenomena are unavoidable. Unfomuiately , "despite
their intrinsic importance, transient considerations are frequently relegated to a secondary
role when pipeline systems are designed or constnicted. That is only d e r the pipelines
profile, diameter and design discharge have k e n chosen is any thought given to transient
Fluid Transient and Pidine Obtimization us in^ Genetic Alnorithms 4
conditions" (Kamey, 1993). So, to ensure a global minimum cost, dl variables of design,
including the eEects of transients, should be considered.
The organisation of this thesis is as follows:
First, this thesis considers, in chapter 2, the properties of the fluid transient tesponse.
The transient analysis mode1 (TransAM) is introduced in this chapter, as are its
advantages compared to the other models and approaches.
Mer this, chapter 3 compara and reviews a series of programrning approaches that
have been developed to assist in the optimal design of pipe distribution networks,
including linear programming, non-linear programming, dynamic programming and
enume rat ive approaches.
Next, a relatively new approach, genetic algorithms (GAs), is introduced in chapter 4.
This chapter overviews the genetic algorithm technique and its application to pipe
network optimization. During the 1s t 20 years, many methods have been applied to
optimise both the design and operation of pipeline systems. However, because of the
processing associated with the genetic approach, this method has a more global
orientation than many methods encountered in engineering optimization practice
(Goldberg, 1983).
The numerical and conceptuai characteristics of the GAs are described in chapter 5.
In this thesis, the genetic algorithms with their characteristics are examined in detail.
FIuid Transient and Pibeline ODtimization us in^ Genetic Alnorithms 5
The next step is to formulate the cost objective fiinction for the optimization using
genetic algorithrns (in chapter 6). This comprehensive objective function includes
"standard" components, such as pumps and pipes and also "non-standard" components,
such as valves, in-line devices, protection devices, and reservoirs.
The objective of this study is to apply genetic aigorithms to the optimization of
pipeline system including transient considerations and apply this method to a detailed
case study. Thus, the thesis discusses the advances in GA theory and tests them on the
practical optimization of pumping pipeline systems with a reservoir at the terminus. The
details of simulation variables are discussed, including pipe diameters, pipe materials,
and valves etc. A master program that utilizes the program TransAM is developed to
determine the optimum design (in chapter 7).
A previous case study conducted by Simpson, et ai., (1994) is described in chapter 8.
Also, the performance of GA programs (Tang, 1999) is shown with the solution obtained
fiom case study (in chapter 8). The results compare the optimal solution considering both
steady state alone and combined steady state/transient considerations. In addition, the
sensitivity and outcome of the GA program (Tang, 1999) is analysed. In this chapter, the
mechanics and effectiveness of the genetic algorithm are examined. Cornputer results in
the pipeIine problem show that the genetic algorithm obtains near-optimal solutions after
expIoring a small number of the operation alternatives. Also, the results considered
transient phenornena are compared to results which account for steady state evaiuations
alone. The case study shows that the system will become safer, even though the system
cost increases a littie. These conclusions are summarised in chapter 9.
Fluid Transient and Pipeline Obtimitation Usinn Genetic Alaorithms 6
The model to be fonnulated, although representing a rather simple situation, has,
nevertheless, considerable practîcal importance because many distribution systerns are, at
present, designed under the same operating conditions. Furthemore, the model forms the
foundation upon which more complex f o d a t i o a s may be constructed. Some
recommendations on an approach to take so as to apply a GA to the pipe network
optirnization problem, and the parameter values that are likely to lead to a faster
convergence to the near-optimaf solution, This fbture work is considered in chapter 10.
Fluid Transient and Pibeline Obtimization Usinn Genetic Alnorithms 7
CHAPTER 2
TRANSIENT ANALYSIS
Fluid transients play an essential role in the operation of pipeline systems. Transient
conditions represent potential problems for many distribution systems and should not be
ignored. Transient analysis is a fiuidamental and challenging part of rational pipeline
design.
in most water distribution systems, hydrauiic conditions are subjected to an almost
continuai state of change. When conditions in a pipeline are adjusted, such as by closing
a valve or starting a pump, large-%ale conversions of mechanical energy ofien occur.
From this perspective, it is difficult to consider systems to be dominated by steady state.
Actually, unsteady flow or fluid transient conditions occur continually in al1 water and
wastewater engineering systems.
Despite the importance of transient conditions, Karney and McInnis (1990) point out
that unsteady flow is ofien poorly accounted for:
The cornplexity of transient phenornena has, at times, induced many analysts to adopt simpfified
FIuid Transient and Piwline Obtimization Usine Genetic Alnorithms 8
design pmcedures. ... These simplifications are rationalized on the grounds of necessity (the
actuai physical system can not be analyzed) and conservatism (the analyzed system perfonns
worse than the real one). Unfortunately, the assumption that some rudimeniary and conservaîive
system can be found is questionable. It is difficuit to simplify a pipeline systern to enswe worst-
case performance under ail transient conditions, particularly if the simplifications are made before
any analysis has k e n performed.
The following causes of water distribution transients are identified by Karney (1 994):
Changes in valve settings (accidental or planned; manuai or automatic);
Starting or stopping of either supply or boosîer purnps;
Changes in the demand conditions (e.g., starting or stopping a fire flow;
changes in industrial demands);
Changes in reservoir level (e-g., waves on a water surface or the slow
accumulation of fiuid in a finite reservoir with time);
Unstable device characteristics (this may include unstable pump or fan or
charactenstics, valve instabilities, the hunting of a turbine, etc.);
Changes in transmission conditions (e.g., if a pipe breaks or buckles);
Changes in thermal conditions (e.g., if the fluid fkezes o r as a result of
property changes caused by temperature fluctuations);
Air release, accumulation, e n t e m e n t or expulsion can cause ciramatic
disturbances (e.g., a sudden release of air h m a relief valve at a high point in
the profile triggered by a passing vehicle; pressure changes in air chambers;
rapid air expulsion during filling operations, etc .);
Transitions h m open channel to pressure flow, such as duhg filling
Fluid Transient and Piwline ODtimimtion Usine Genetic Alnorithms 9
operations in pressure conduits or during storm events in sewers; and
AdditionaI transient events may be initiated by changes in turbine power
Io& in hydroelectric projects, draft-tube instabilities due to voriexing, the
action of reciprocating pumps and vibration of impellers or guide vanes in
pumps, fans or turbines.
It is well knuwn that pipe mdacturers often characterise the mechanical strengh of
a pipeline by its pressure rating. So, the interna1 pressure requirement is of particular
importance. Often, designers relate the intemal pressure experienced by a pipe to steady
state conditions alone. However, if the rate of flow is changed rapidly, e-g., closing a
valve or stopping a pump, transient pressures will be unavoidable. This kind of pressure,
whether caused by design or accident, is superimposed on steady state values to produce
the total pressure load on a pipeline at the time the transient occurs. The pressure
generated by transient condition in pipe systems is frequently three or more times the
value of normal operating pressures. Thus, it may cause problems if transient pressures in
pi pet ines are negiected.
Transients are associated with changes in fluid velocity, gradua1 or sudden. If
transient waves were srnall, research into transient conditions would be of little interest to
pipeline engineers. Udortunately, it is not tnie. As h e y (1998) sumarises, when
sudden changes occw, the results can be dramatic since pressure waves of large
magnitude can occur:
Water hammer waves are capable of breaking pipes, darnaguig equipment and have caused some
spectacular pipeline failures. Rational design, particularly of large pipelines, requires reliable
Fluid Transient and Piwline ODtimization Usina Genetic Aleorithms 10
transient analysis. There are several reasons why transient conditions are o f particular concern for
large conduits, Not only is the cost of large pipes greater, but the required wall thickness is more
sensitive to the pipe's pressure rathg Thus, poor design - whether resulting in pipeline failure or
the hidden costs of overdesign - can be very expensive for large pipes.
2.2 MODEL FOR TRANSIENT ANALYSIS - TRANSAM
Fluid transients refer to the unsteady flow of water in pressure pipes. Pressure puises
are generated when the "flow conditions are changed h m one steady state to another .,."
(Chaudhry, 1987). These pressure variations are important in the design of a water
distribution system because they can "... threaten the integrity of the system ..." (Betamio
de Almeida and Koelle, 1992). in practice, however, analysts fkquently neglect transient
conditions, particularly in cornplex systems such as distribution networks. With modem
cornputer techniques, it is possible to analyse distribution systems under a wide range of
flow conditions and with relatively few restrictions.
This thesis uses a powerçiil transient analysis program, TransAM, created by Mçi~ i s ,
Karney and Axworthy (1997; originally in 1988). TransAM is a general-purpose
simulation mode1 for cdculating hybui ic conditions in pipeline systems. This program
calculates both steady state and transient flow in pipe networks. It has the ability to
perform transient analyses of virtually any water distribution system, fiom a simple
pipeline to !arge, cornpiex pipe networks.
TransAM is capable of simdating cavity formation which is essential for the analysis
given the transient source included pump start-ups or shutdowns and the existence of
Fluid Transient and Piwline Obtimization Usinn Genetic Alnorithrns 11
hi& points, which constitute a recipe for vapour cavity collapse. The model efficiently
represents the entire pipe network - simple series systems with only a few pipes, or large
branc hed and looped networks. The program provides considerable power and flexibility
in the detailed specification and operation of system components; as McInnis et al. (1997)
state:
nie program simulation uses the rnethod of charactcristics which is based on an established tirne
increment and calculations are continued for a specified time interval. Initial conditions are
defmed by a steady state description supplied by the user. ... In addition, the standard solution by
the method o f characteristics has been improved to allow flexible 6ktion term linearkation.
TransAM formulates a unified set of boundary conditions to efficiently represent the
majority of valve and orifice devices found in water distribution systems. A particularly
usehl combination of mathematical components results when a lurnped inertia model is
Iinked with a thronling device. This combination of elements, termed a pipe replacement
element/vaive-in-line (PREVIL), has been constmcted to permit a wide range of control-
vaive/short-pipe combinations to be conveniently modeUed with the method of
characteristics (McInnis et al., 1997a). The solution is quadratic in form and explicit,
regardless of the number of pipes that are connected to the boundary condition. This
model can accurately hancile a variety of on-off and modulating valves.
As is mentioned in more detail in chapter 6, the cost of valves is only related to the
valve setting or valve discharge constant (i.e., the valve size), regardless of motion
duration and the pressure setpoints. However, based on the discussion above, it is known
that the other parameters are not only important, but their interactions are as well. This
FIuid Transient and Piwline Omimization Usinn Genetic Alnonthms 12
means that researchers can not omit one of them and still optimize the selection of a
valve. In fact TransAM considers ail the key physical properties of vaives. These
properties include the initial valve setthg. the final valve setting. the duration of the valve
motion and the number of points input to represent the valve motion and the tabulateci t
values. So, even though this thesis only uses the valve discharge constant in the capital
cost objective h c t i o n to calculate the cost of valves, the approach realisticaily takes into
account the pecformance o f the pipe system, including the key aspects of valve
performance.
In this thesis, the pipe matenal is aiso considered in the cost of pipe. It makes the
objective fùnction more comprehensive. Pipe material used has a signifiant impact on
dynamic behavior of the systern. Many materials are suitable for use in water distribution
systems, ranging fiom flexible plastic pipes to more rigid rnaterials, such as steel or
concrete.
23 DESIGN ALTERNATIVES
Although it is possible to design a pipeline to withstand any pressure, such a design
would generally be uneconocnical. Therefore, provision of various control devices or
appurtenances should usually be investigated to reduce the pressure requirements and
thus to obtain an overall economic design.
The following are some of the cornmon appurtenances ofien employed to bit
transient pressures (Chaudhry, 1987):
Air chambers;
Fluid Transient and Pibcline Obtim ization us in^ Genetic Alnorithms 13
Surge tanks;
One-way surge tanks;
FI ywheels;
Air-inlet valves; and
Pressure-relief or pressure regulating valves.
2.3.1 ALTERNATIVE DESIGN ALTERNATTVES FOR TRANSIENTS
The elements or components considered in a transient design include some of the
cornponents considered above. They also extend beyond the common components.
Alternative techniques and devices, although they are not coosidered directly in this
thesis, can be used to address transients including the following (Laine, 1996):
1. Profile Changes
Changing the pipeline route can be achieved either by going around obstacles
or through them. Betamio de Almeida and Koelle (1992) suggested that for
preliminary design, %orne of the critical points can be removed by choosing
another system lay-out or pipe profile or by placing the pump station in
another site." Sometimes a transient analysis can suggest an alternative design
solution with regard to the layout of a system.
2. Lowering the Static Head
Since the pressure load is made up of both steady and transient loads, Kamey
(1993) States that "anything that might lower the static heads in the system
(such as low reservoir levels or large head losses due to fiction) will tend to
Fluid Transient and Pimline Obtimizatian us in^ Genetic Alizonthrns 14
lower the total head (static plus dynamic) a pipe system must withstand."
3. Changing Valve Movements
By extending the valve closure over a time much longer than the pipeline
period, the amplitude of the pressure fluctuations in the pipeline will be
reduced. So, the operation of any control valves should be considered. As
Thorley (1 99 1) states, "too fast a closure can lead to colurnn separation, whilst
a slow c tosure c m pennit reservoirs to drain down or tanks to over-fill.. ."
4. Flywheels
An option (Thorley, 1991) for controlling transients is to increase the inertia
of the pump since "for a given pump the run-down time is govemed mainiy by
the back pressure (which can be considered fixed) and the inertia of the
rotating parts." Thus, increasing pump inertia can lessen the impact of a
pumP-trip-
5. By-pass Lines
A bypass line around a pump offers a means whereby the pressure &op
following a pump-trip can be reduced. For some installations, a by-pass line
around the pumps may be an inexpensive and satisfactory control device.
The methods presented above represent a diverse group of options for addressing
fluid transients in a pipeline. In a pipe network, such approaches may be fiequently
employed. However, their integrated performance should be snidied carefully. in addition
to the technical motivation and capital cost of the available options, other factors will also
influence the choice. These additional factors include rel iability , space and power
Fluid Transient and Piwline Omimitation Usinn Genetic Alnon'thrns 15
requirements, the amount of maintenance and supervision needed, and the availability of
suitably skilled labour.
Al1 of these issues can in some way be considered in TransAM and could be included
by the economic evaluatioa However, to make the appmach manageabie, several
important devices are considered in greater detail. The devices receiving special
consideration are common in water distribution engineering and are discussed in more
detail next,
2.3.2 ALTERNATIVES CONSIDERED IN THESIS
Although not exhaustive, a wide variety of protection strategies are explicitly
considered in this thesis.
A number of popular devices are addressed in this thesis and are taken into account in
the cost objective function. Nine specific options for transient and steady state
optimization are included.
1. Changes in the Pipe Diameter
"The transient performance of a piping system may be improved, in general,
by increasing piping diameter. Since head change is directly proportional to
velocity change, doubling the diameter reduces pressure fluctuations by a
factor of about 4." (Wylie et al., 1993).
2. Check Valves
Even though check valves are sometimes selected without proper thought to
their response under transient fiow conditions, "in some situations the
FIuid Transient and Pidine ODtimizatïon Usine Genetic AIeorithms 16
strategic location of a non-retum valve, or check valve or reflux valve, is
sufficient to prevent al1 or at least d u c e water hammer overpressures."
(Stephenson, 1984).
3. Air Vessels and Air Cushion Surge Chambers
An air vessel is one of the most common devices used to suppress transients,
particularly to guard against the adverse effects of a complete pump stoppage.
As stated by Sovern and Poole (1990): "Air chambers are normdly located in
the pumping facility. When power to the pumps is de-energized, the air
chamber supplies water to the system at the pressure in the tank. The main
criterion is to have sunicient water in the air chamber for continuous supply
of water to the system until the pressure wave fiom the end of the system is
reflected back to the pumping facility."
4. SurgeTanks/Shafls
A surge tank is suitable in large, low-pressure applications, or where the
hydradic grade line is close to the pipeline profile- A surge tank consists of a
vessel or chamber that is connected to the pipe and open to the atmosphere. it
acts to "fùmish or store the necessary liquid volume in order to impose total or
partial wave reflection and a gradua1 flow variation in the nearby pipes ..."
(Chaudhry, 1987).
5. One Way Surge Tanks/ Feed Tanks
One way surge tanks c m make a useful and economical contribution to the
surge suppression strategy (Thorley, 1991). This is particularly hue for
systems in which the principal hazards to a part of a riskg main are sub-
FI uid Transien t and Piw line Outimization Usin= Genetic A lporithms 17
atmospheric pressures following a pump trip a feed tank.
6. Air Releasd Vacuum Breaking Valves
The majority of "... vacuum air valves installed on water mains are reaily
combination air valves. These devices contain both a large orifice air vacuum
valve for draining the pipeline and a mal1 air valve for the continuous release
of small amounts of accumulateci air h m the pipeline. In the context of
transient analysis, ody the large orifice portion is of concern since it permis
the rapid admission and expulsion of significant amounts of air during the low
pressure phase of the transient." (McInnis and Karney, 1992).
7. Pressure Relief Valves
The pressure relief valves can reduce the transient effect on the upstream side
of the valve where the flow in a line is interrupted by a control valve or
similar device at the end, or at some distance h m the source. Pressure relief
valves are valves that open to facilitate the release of excess pressure. "The
valve closes when the pipeline pressure drops and is fully closed when the
pressure is below the limit set on the valve." (Chaudhry, 1987).
8. Pipe Strength
Adjusting the pipe thickness to withstand transient condition is one approach
to deal with the excess pressure associated with transients. This method is
essential in some cases, such as to protect the pipeline and tunnels in the high-
pressure region immediately upstream of the check valves as well as for
pipelines conveying corrosive and toxic chemicals.
Fluid Transient and Piwline Obtirnimtion Usina Genetic Alvorithms 18
Transient control actions can be important and these actions have implications for
other aspects of system design and operation. This chapter reviews a variety of usehl and
popular strategies to control transient conditions. A variety of these approaches are
considered by the economic fiinction in this thesis.
mer considering transient analysis, the topic of pipeline optunization is considered
in the next chapter. Thus, the next cbapter reviews traditional pipeline optimization
techniques, including linear programming, non-linear programming, dynamic
programming and complete enurneration. Theu advantages and disadvantages are briefly
compared,
Fluid Transient and Pipeline ODtimization Usiw Genetic Aiaorithms 19
CHAPTER 3
PIPELINE OPTIMIZATION
3.1 INTRODUCTION
Traditionally, the design of water distribution networks has been baseci on experience
and relatively simple analysis. However, there is now a significant body of literahve
devoted to the optimization of pipe networks. Much of the research to date has appiied
deteministic optimization techniques, including linear programming, non-linear
programming, dynamic programming and enumeration, shulated anneaiing and, more
recentl y, genetic algorithms (Lansey and Mays, 1 989).
This chapter overviews conventional pipeline optimization. Various constraints,
including hydraulics, water demand, energy and economy, etc., are introduced. Then, the
traditionai optimization techniques are summarised, dong with theu advantages and
di sadvantages .
Steady state design variables for pipeline optimization are particularly introduced,
with a larger emphasis on transient optimization reserved for later chaptea.
Fluid Transient and Pi~eline Obtimizarion Usinp Genetic Aleonthms 20
3.2 PROBLEM FORMULATION
Water supply systems cornponents include the water supply or source and the
transmission/distribution system. Optimization of pipelines focuses primarily on the
second component, with the goal of assuring that enough water is distributed to sat ise
the demand without interruptions and at adequate pressures. The overall optimization
problem for water distribution network design c m be stated rnathematÎcalIy in t e m of
minimishg an objective h c t i o n subject to the constraints related to the performance of
the system.
As stated by El-Bahrawy and Smith (1987), 'optimization' problems (for watet
distribution systems) arise when it is desired to solve the design problem at minimum
total cost (usuaily discounted present value), subject to a set of practicai constraints such
as maximum and (or) minimum operathg pressures, minimum pipe diameters, and use of
a discrete set of comrnercially available pipe sires. The design or optimization problem
can be stated as:
Minimise: Capital Investment Cost + Operating Costs (e. g., energy,
maintenance, etc.)
Subject to:
1. Hydraulic constraints
2. Meeting a minimum ievel of water demand
3. Maintaining reasonable pressures
4. SatisSing the conservation of flow and energy constraints
Fluid Transient and Piwline Obtirnization Usine - Genetic Akorithrns 21
5. Budget consttaints
6. General constraints
The objective function comprises both decision variables and cost fiinctions. The
decision variables define the characteristics of each hydradic component in the design
such as diameters of the pipes, pump sizes, valve settings, pipe thicknesses, and tank
volumes or elevations, The objective hction may be either linear or non-Iuiear, aiiowing
for various types of components to be designed. Each component to be designed will
have a term associated with it in the objective; so, the formulation allows for variation of
cost equations to account for site-specific costs such as material and installation costs. in
addition, the operating costs, maintenance and replacement cos& should be "...converted
into present value ..." (Shamir, 1974) for inclusion into the cost function.
Lansey and Mays (1 989) proposed a typical objective h c t i o n as follows:
Objective:
.VPUMP ACWaR
min ['x P ( L , , D . ) + c PU ( ~ . . P P . ) + C PS ( m . . ~ . ) n - 1 n r l
where:
NLlNK = number of potential links in the network.
P(Lk , Dk) = cost fûnction for pipes (link) as a fùnction of the length of link k, Lk and
the diameter, &.
NPUMP = number of purnps in the network.
PU(XP, , QP,) = cost h c t i o n for pumps as a function of the head lift XPm for pump
rn and the flow capacity QP,.
Fluid Transient and Pid ine Obtirnization Usinn Genetic Al~iorithrns 22
STOR = number of elevated storage reservoirs in the system.
PS(XS, , XV,) = cost function for storage as a fùnction of the head lift XS, for
storage n and the flow capacity XV,.
Subject to: (AWWA, 1989)
Quality of Service
( 1 ) Satisfaction of various demands (e.g., hourly peak, fire flow, etc.).
(2) Maintaining adequate pressures (under al1 demand conditions).
(3) Each node in the system is c o ~ e c t e d by a minimum of two pipes.
Physical Laws
(1) Continuity of flows at nodes.
(2) Continuity of the hydraulic grade line.
(3) Head discharge relationships of various components.
Practicai
use of comrnercially available components.
Optimization models are created "...by finding the values of the decision variables ...
that minimise (or maximise) the value of the given objective function ... while s a t i s w g
a given set of constraints, expressed as equalities or inequalities" (AWWA, 1989). The
design constraints are usually simple bounds, typically set by physical limitations or the
availability of the components, but are shown as functions for the general formulation.
Ideally, an optimization mode1 for a proper design should do the following (Lansey
and Mays, 1989).
Fiuid Transient and Pimlinc ODtirnization Usinn Genetic Alnorithms 23
1. Determine optimal pipe layout and sizes;
2. Design both new systems and extensions to existing networks;
3. Select existing pipes for cleaning and relining as part of an optimal solution;
4. Analyse the network under one or more demand pattern;
5. Allow for variability in the objective function so as to represent construction
staging and site variation of components;
6. Handle al1 types of networks and network complexities;
7. Determine the location, size, and height of tanks and their operation;
8. Assist in the selection and operation of pumps and pump stations;
9. include valves, both pressure reducing and control, in the design and determine
their optimal settings in the operation of the system; and,
10. Determine optimal designs and operations of networks containhg a large number
of pipes, pumps, valves and tanks.
In generai, existing models do not meet al1 these requirements.
3 3 SOLUTION METHODOLOGY
Traditionally, mathematicai programniing techniques in conjunction with hydraulic
simuiations, and techiques incorporating the hydraulics into optimization models have
been used in the past. Many models have been developed in the literatwe to solve at least
a part of the opthkition mode1 descnbed by L a w y and Mays (1 989).
Fluid Transient and Pidine Omimization Usinn Genetic Alnorithm 24
3 -3.1 L W A R PROGRAMMTNG
The use of linear programrning (LP) for the optimization of water distribution
systems was first described by Labye (1966). The basic concept has since been
incorporated into standard textbooks, and has been used by other authors in developing
M e r applications. For linear programming, a brief tabulation of the previous literatures
are shown in foUowing table (Table 32-1 in Lansey and Mays, 1989)-
Calhoun D P B Extension of Gupta-Karmeli formulation
K a l l ~ D P L Unknowns are the change of lenghs of given diameter in a
Kanneli Gupta
Lai & Schaake
Case & White 1 D 1 P 1 L 1 Varvinn dernands over time Gupta 1 D 1 G 1 Multiple sources
DIAM. D D
C
Alperovits & Shamir
Table 3.1 Literature of Lincar Programming AUTHOR [ PIPE Gmity, 1 Bmched, 1 COMMENTS
- d
-
-
-
- - r(
-
-
LP with heuristics, one source
Only single source networks Only for single source networks With assumeci pressure surface
purnpod 1 b ~ e d
Two level Hierarchial scherne-LP with gradient correction
P G
P
Bhave D
B B
L
Bhave
B With heuristics to develop critical path and limit candidate pipe sizes
P B Multiple sources, extension of Gupta and Kanneli
G L 1 Morgan & D G L LP with change of lengths as Goulter the unknowns, heuristic to
determine optimal layout Fujiwara, et D G L Modified LPG method of
( al. 1 1 1 Aiperovits & Shamir - Discrete; P - Pumped; G - Gravity; L - Looped; B - Btanched; C - Continuous
Fluid Transient and Pibel ine Obtim ization Usinn Genetic Alnorithrns 25
LP is a powerful and easy-to-use form of optimization, but can only be adopted for
problems which can be expressed in linear terms, or c m be transformeci into a linear
problem. Hence the complete optimi;ration problem is linear and a standard LP package
can be used for its solution.
Despite these drawbacks, the LP method remains useful for many simple network
pipe optimization problems.
Non-linear programming (NLP) was originally applied to pipeline problems by
Jacoby (1968) and has shce been adopted by other authors. A number of non-linear
optimization packages have been applied to the network design problem. They include
MINOS (Murtagh and Saunders, 1987; El-Bahrawy and Smith, 1987), GIN0 (Liebman et
al., 1986), and GAMS (Brwke et al., 1988), to name but a few. Al1 these packages use a
constrained generalised reduced gradient technique to identiQ a local optimum for the
network problem. For non-linear programming, some previous work is shown in
following table (Table 3 .S. 1 in Lansey and Mays, 1989).
Fluid Transient and Pimline Optimization Usinn Genetic Alnmirns 26
Table 33 Literature of Non-Liaear Programming
1 1973 1 Cembrowicz 1 C 1 G 1 B 1 Decomposition with Non-
1 1 1 1 1 1 Unconstrained by Lagrangian
Gmvity, Pumped P
PIPE DIAM. C
YEAR
1968
1973
1 I I I I I of flow constraints
AUTHOR
Jacoby
1 19741 Sw I C I P I formulation as / km; but extendeci for
Brnnchd, b p c d
L
et al. Watanatada
) Kher, et ai.
COMMENTS
Unconstrained coastraints in
C
L
P
other components Optimal water distribution
L systems Non-linear Pmg. Solved by
Pipeline
L
Univariate method Non-linear solved using Maximum Principle modifieci
1981
hear programming Design and layout,
1988
Researchers have also repoaed a number of applications of non-linear optimization to
Omsbee &
1 Mays
pipe network problems (El-Bahrawy and Smith, 1985, 1987; Su et al., 1987; Lansey et
Contractor
Lansey & 1 non-linear optimization
al., 1989; Lansey and Mays, 1989a; Duan et al., 1990).
D
D - Discrete; P - Pumped; G - Gravity; L - Lwped; B - Branched; C - Continuous
ECBahrawy and Smith (1985) applied MINOS to the design of water collection and
C
distribution systems. Their model included a preprocessor to set up the data files and a
P
postprocessor to round off the pipe sizes to commercial diameters.
P
Su et al. (1987) w d NLP to optimise looped pipe networks. In addition, they
L
included reliability constraints. The basis of the optimization model was the generalized
for integer con&nts Non-linear solved by Box-
L
reduced gradient (GRG) technique.
Cornplex, pump flows prefixed Linked simulation mold with
Fluid Transient and Piwline Obtimization Usinn Genctiç Aleorithms 27
Lansey et al. (1989) considered the op- design of pipe networks where there is
uncertainty in the nodal demands, Hazen-Williams coefficients and the minimum nodal
heads. Lansey and Mays (1989a) used NLP to h d the optimum design and layout of pipe
networks. Their model was able to simulate purnps, tanks, and multiple loading cases.
Duan et al. (1990) fUrther extended the earlier work of Lansey and Mays (1989a). They
develop a general optimization model that can include pumps and tanks (and the
locations of these) as well as multipie loading conditions.
However, the non-linear programming approach is uniikely to achieve an overall
(global) optimum solution, since there are a multitude of local optima correspondhg to
the feasible networks that can be formed within the original systems- Most NLP
approaches halt at the £ k t local optimum they encounter in their search, and this will
depend on the starting values (Simpson, et al., 1994).
Simpson, et al., (1994) aiso stated the limitations of the technique are as follows:
1. Because the pipe diameters are continuous variables the optimal values will
not necessarily conform to the available pipe sizes; thus, rounding of the finaI
solution is required;
2. Only a local optimum is obtained; and
3. There is a limitation on the number of constraints and hence the size of
network that can be handied.
Fluid Transient and Piwl ine Omimization Usine Genetic Alporithms 28
3.3 -3 DYNAMIC PROGRAMMiNG
As an alternative to LP, dynamic programming @P) has both advantages and
disadvantages. It benefits h m k i n g able to handle a more general f o m of cost function,
but is ofien more computationally demanding.
Because dynamic programming is robust, it is unlikely that numerical problems will
occur during the wmputation, Large networks can be handled with only a lhear increase
in execution time with network size, and o d y a small increase in memory over that
required for small networks. A brief summary of the previous DP literahue is shown in
following table (Table 3.2.1 in Lansey and Mays, 1989).
Table 3 3 Litenture of Dynamic Progrrimming
YEAR AUTHOR -7- DIAM. 1 Pumped
1 - Discrete; P - Pumped; B - Branched
1 phasing with varying loads
1 over time
B I DP for networks with single
Pipeline DP with water lost cost
B
source
Decomposes multiple tank
system, solves subproblem
by LP of Gupta, DP to Iink
together and add other costs
Fluid Transient and Piueiine Obtimization Usinv Genetic Al~orithms 29
However, the basic memory requirement for DP is quite large, and d i k e LP, there is
no general-purpose package available for users. It is necessary to use soAware specially
developed for pipe system optimization.
DP can only be applied to systems that can be arranged in a series of "stages". Each
stage is related to past stages only by the "input state" of a stage, which is the "output
state" of the previous stage. At each stage, some "decisions" are made which produce a
" r e W or cost, and it is the cumulative s u m of these retunis o r costs that is minimiseci
(or maximised).
This method is described in detail by Walters and McKechnie (1985). It is guaranteed
to find the global optimum solution for the problem, but c m only be used for networks of
a smail to medium size, due to large memory requirements and computational t h e .
3.3.4 ENUMERATION APPROACH
The enurneration approach involves an exploration of al1 of the possible system
configurations. To ensure a complete optimization result is found, ail-important elements
that affect system performance and cost should be considered. So, a global set of design
components, including transient suppression devices, must be explored.
As Laine (1 996) stated, the enurneration process involves the following steps:
Development of al1 feasible designs for the given components mder
consideration;
Sirnulate the performance of the different designs;
Evaluate their performance;
Fluid Transient and P i d i n e Optimization Using Genetic Alnorithms 30
If the desigm are viable determine their costs; and
Selecting the least cost designs h m the population of viable designs.
For the enumeration approach, some previous literature is summarised in the
following table (Table 32.1 in Lansey and Mays, 1989).
Table 3.4 Literature of Complete Enumeration
' YEAR AUTHOR PIPE
I 1 I
D - Discrete; P - mimped; L -
1973
1982
a two level scheme with implicit l Artina
Gessler
DIAM.
D
D P
Looped
Pipeline
However, due to large memory requirements and computational time, this method
L
Enumeration with pumps given
by discrete values
severely limïts the scale of the water distribution system thaî can be considered. For large
enumeration seiecting pipes
Enurneration
networks, this approach seems infiible. Gessler (1985) has proposed the use of
selective enurneration of a severely pruned search space to optimise the design of a pipe
network. Unfominately, the global optimum may be eliminated in the process of pruning.
Fluid Transient and Piwline Omirnizatïon us in^ Genetic Alnorithms 3 1
Loubser and Gessler (1990) suggested guidelines for pninuig the search space to reduce
the amount of cornputational effort involved in enmeration, including:
1. Grouping sets of pipes and assuming that a single diameter will be used for each
group;
2. progressively storing the lowest cost solution which satisfies the constraints and
eliminating al1 other solutions of higher cos; and
3. checking on combinations that violate the constraints.
Despite these aids, Loubser and Gessler (1990) point out that this technique requires a
considerable amount of computer time for large networks and there is no guarantee that
the optimal solution will remain in the pruned search space after applying these
heuristics.
3.4 DESIGN COMPONE3NTS
Traditionally, optimization research has focused on the steady state. The components
that are concemed include the following: pumps, pipes, valves, and tanks, etc. These
cornponents are discussed in more detail in this section.
3 -4.1 PIPES
A pipe is a length or segment of conduit having specifïed physical properties, which
is connected into the system in a specific way. Pipes are the principle elements of a water
Fluid Transient and Piwline Omîmization Usina Genetic Akorithms 32
distribution system, and often comprise up to 70% of its initial cost ( M c h ï s et ai.,
1997).
For both new and existing pipes, a continuous function is conventionaliy used for the
cost for the pipes as follows:
where:
& = cost constant ($Id or $le) L = pipe length (m or ft)
n = constant exponent, assumed to be 1.0
Dp = pipe diameter (m or fi)
For the pipe diameter, either continuous or discrete pipe sizes may be considered. The
optimal continuous diameter can be considered as the equivalent diameter for two
commerciaily available sizes (referred to as a split pipe).
A typical example of pipe cost is described by Swamee and Sharme (1990a,b).
Analysis of the capitalised cost of pipelines yielded the following hctional form for the
pipe cost Cm :
Cm = km (l+h./W LDm
where:
km = cost conversion coefficient ($lm2 or $/ft!)
FIuid Transient and Pi~eline ODtimization Usinn Genetic Algorithms 33
ha = allowable pressure head (m or fi)
hb = pressure head cost datum (m or fi)
L = pipe length (m or fi)
D = pipe diameter (m or ft)
However, the methods above always ignore the relatioaship between pipe thickness
and pressure. b e y and McInnis (1990) proposed a more complete equation,
considering not only pipe length and diameters, but also pipe material and thickness.
Details of this approach are addresseci in chapter 6.
3.4.2 PUMPS
The complexity of the design and operation of pumping systems is dependent upon
the network hydraulic requirements and other components in the system. Pumps operate
accordïng to head-discharge curves and may be in or out of service during a given
demand pattern depending on their efficiency, availability and storage tank levels.
The moa basic reason for employing a pump is to achieve a desired or required
hydraulic condition in the water or wastewater system. As long as power is supplied to
the pump motor, the pump impeller will do work on the fluid, and thereby increase the
elevation of the hydraulic and energy grade lines (Mcuinis, et al., 1997).
Pump costs have been shown to be a hction of the design discharge and head. Costs
for pumping stations can be related to the maximum discharge of the installation and the
Fluid Transient and Piwline Obtimization us in^ Genetic Aleotithms 34
pressure corresponding to this flow in the following fonn (U.S. Army Corps of
Engineers, 1980).
C p = Kpu ( ~ m n ) " ' c ~ ( ~ n i a ) l ~
where:
C, = cost of pump ($)
Kp" = cost coefficient
Qma = maximum discharge of pump (m3/s or A-'/s)
H = head of pump (m or fi)
nl = exponent coefficient
n2 = exponent coefficient
Walski (1986) proposeci specinc coefficients for an equation of the form above. This
thesis adopts this equation, but with a few simplifications (discussed in section 6.3.2).
The cost considered to this point is a capital cost, However, the energy cost of
operating the pumps must aiso be included in the objective function. This cost is a
function of the pump power used to supply the system during defined loads which make
up the average or weighted average of the demand patterns during the design life of the
network,
Because of the complexities of networks, no single formulation is best for al1 types of
pump design problems. Various alternatives are acceptable for the different types of
FI u id Transient and Pimline Optim ization us in^ - Genetic AI~orithms 35
systerns. For the case of a network with one pump under one load and fixeci tank levels,
the equation above is certainly practical.
Lansey and Mays (1989) stated an advantage of this formulation: '?he discharge and
head required, as detennined by the model, are bown and can be substituted into the cost
equation. . . . Another advantage of using pump head as the unknown is that for the loads
considered there is no restriction on the head value." The goal is for the model to select
the optimum rhedules while king forced onto a specific head-discharge curve. After the
optimization mode1 bas detennined the heads, pumps would be extemally fit to best
match these points.
3.4.3 VALVES
Three main types of valves are commonly used in water distribution systems: air
valves installed to prevent vapour cavity in a pipe, check valves (typically following
pumps) whose purpose is to prevent backflows, and regulating valves such as pressure
reducing valves (PRV) or pressure sustaining valves which are designed to maintain a
specified pressure in the system. The target of an in-üne valve is to regulate flow by
adjusthg the valve's setting to increase or decrease head losses (created by fictional
dissipation of energy) for a particuiar pipe system.
High or low pressures can ofien be avoided under steady conditions by correctiy
selecting and setting the valves in a pipe system. The related design considerations are to
determine the location and operation of the system's valves. The existence of the valve
must ofien be assumed and the pressure setting can be determineci for the prelocated
Fluid Transient and Piwline Obtimization Usine Genetic Aleorithms 36
valves since their cost is only a h c t i o n of the valve setting. For a valve discharging to
the atmosphere uuder steady fiow condition, the valve operation can be detetmined using
an orifice discharge dation:
where:
Qo = steady state discharge (m3/s or tt.'/s);
Cd = discharge coefficient which accounts for real valve losses (dimensionless);
A v = area of the valve opening (m2 or fl?);
E, = valve size parameter determined by the energy dissipation potential of the
vaive (= Cd A,, (2g)1n), m5% or A%; and,
Ho = pressure head at valve or head loss across valve (m or ft).
3.4.4 RESERVOIRS / TANKS
Surprisingly, one of the most difficdt components to optimize in a pipe network is a
reservoir or tank. "Tanks store water for daily operations to smwth the purnpage
demands through the day, making the system more cost effective, and store water for
emergency conditions so that the amount of emergency storage is d e h e d for the system
by fire regulatioas." (Lansey and Mays, 1989).
Fluid Transient and Piwline ODtimization us in^ Genetic Alnorithms 37
The design question is to determine the size and the location of individual tanks in
order to accommodate the daiiy fluctuations. The controi variable for the cost of tanks is
the total volume of storage, based on area, height and tank elevation. For the system, the
following constraints is used in the model:
TVmin 2 SV
where:
TVmib = minimum volume of tank j (m3 or fk?)
SV = predefined system storage requirement (m3 or ft').
The required size of the tank is then the maximum volume containeci in it during the
cycle, and is the required model input In addition, flow restriction of tanks can be
accomplished by adding a valve into the comecting pipe and using the valve coefficient
as an unknown, which increases the head loss in either direction reducing the amount of
flow. The optimum valve coefficient can also be used to provide guidance for the
operating of tanks.
3.5 PIPELINE OPTIMIZATION INCLUDING TRANSIENTS
Severai steady state optimization models have been reported in the literature for the
optimal (minimum cost) design of water distribution systems. Some of these models,
developed before 1989, were summarized by Lansey and Mays (1989). None of these
previous models has achieved al1 the goals that should ideaiiy be accomplished in a
Fluid Transient and Pipeline Obtimization Usinn Gcnetic Alnorithm 38
comprehensive mode1 for the design of a water distF.bution system. Most of the effort in
previous models has dealt with the steady state pipe design and has not considered the
transient component Karney's statement (1993) appears to be vdid still: "Despite their
intrinsic importance, transient considerations are frequently relegated to a secondary role
when pipeline systems are designeci or constructed. That is only after the pipelines
profile, diameter and design discharge have been chosen is any thought given to transient
conditions."
It was suggested by A W A (1989) that "the designer should ... never overlook the
effect of water hammer or surge pressures in designn So, naturally, transient analysis
should be included in the optimization process. However, as Sharp (1981) points out:
in many cases, pmper consideration of water hammer only occurs after something calamitous has
happened. In this event tme economy can no longer be satist'actoriiy achieved and the form of
protection may be seriously testrictai. I f a system has been constructed such that is pmne to bad
effects of water hammer because of inadequate design or unusual site conditions, considerable
expenise is necessary to solve the problem.
The reason that transient analysis is other ignored in the optimization process is the
complexity of the phenornenon. The lack of optimization methods that consider the
existence of transient events contradicts the significance of fluid transients in the design
process. However, a few optimization approaches considered water hammer are
discussed in the followùig.
Karney and McInnis (1990) addressed an optimization study with a simple pipeline
system consisting a single non-branching pipe c o ~ e c t i n g a fluid source at the upstream
Fluid Transient and Pid ine Omimization Usinp Genetic Algorithms 39
end to a fluid sink at the downstream end, Their constraints take into account transient
flow conditions.
Papanikas et al. (1992) applied a simulation framework to the optimization of gas and
oil systems including transient requirements. Although the method is of lirnited value for
application to water distribution networks. it has demonstrateci that fluid transients could
and should be included in the optimi7irtion process in the distribution systems.
An alternative procedure has been devetoped by Xu et al. (1994). They successfirlly
applied dynamic programming to hi&-pressure valve-cy linder s ystem. Their
mathematical mode1 of fluid systems is "...baseci upon the state-space method, with the
method of characteristics used to simulate the dynamic transient process." This work
showed that the optimization process with transient analysis is feasible and worthwhile.
Pasha and Contractor (1990) applied an optimization scheme to a "...simple pipeline
with a constant head reservoir at the upstream end and a valve at the downstream end."
They applied "the method of chatacteristics ... to simulate fluid transients in a pipe and the
simplex method ... to optimise the objective fiuiction." At the same the, they considered a
valve closure policy to avoid the column separation.
A successhil approach of transient analysis to simple pipelines was developed by
Laine (1996). A complete enurneration scheme that incorporates both transient and
steady state concerns was developed. This comprehensive opti-tion approach is
explored through a case study involvhg a simple pipeline connecting a pump and a
storage reservoir. In addition, a sampling method that reduced the simulation burden or
workload without constraining the solution space was developed and applied to a case
sîudy.
Fluid Transient and Pipeline %timization us in^ - Genetic Alnorithms 40
This chapter introduces the basic concept of optimization for water distribution
systems. It reviews traditionai foms of objective fiuiction and coIlStraints. Typical
methods of solving these fomulatioas are also briefly reviewed, including linear
programming, non-linear programming, dynarnic programmhg and the enurneration
approach. Their advantages and disadvantages are briefly discussed
The design alternatives that are of prime concem when addressing the steady state
design of a water distribution system are reviewed. Although literature addressing
transient phenomenon is m e , some key contributions are reviewed. This work sets the
stage for the next chapter, which provides an introduction to optimization ushg genetic
algorithms.
Fluid Transient and Piwline Obtimization us in^ Genetic Al~orithms 41
CHAPTER 4
REVIEW OF GENETIC ALGORITHMS
4.1 INTRODUCTION
Genetic algorithms (GAs) are receiving increasing application in a variety of search
and optimization problems. These efforts have been greatly aided by the existence of
theory that explains what GAs are processing and how they are processing it, The theory
Iargel y rests on Holland's exposition of schemata (HoIland, 1968, 1 979, his bdamenta l
theorem of genetic dgorithms (HoIland, 1973, 1979, and tater work by several of his
students.
Many optimization problems fiom the hydrauiic engineering world, in particular for
large pipeline systems, are complex in nature and difficuit to solve by conventional
optimization techniques. Since the 1 96Os, there has been an increasing interest in
imitating living beings to solve such kinds of hard optimization problems. Simulating the
natural evolutionary process of human beings results in stochastic optimization
techniques called evolutionary algorithms, which can oflen outperfonn conventional
optimization methods when applied to difficult d - w o r l d problems (Back, 1996;
Schwefel, 1994; Back and Schwefel, 1996; Michalewicz, 1996).
Fluid Transient and Piwline ODtimization Usinn Genetic Alnorithrns 42
There are three main avenues of this research: genetic algorithms (GAs), evolutionary
programming (EP), and evolution strategies (ESs). Among them, genetic algorithms are
perhaps the most widely known types of evolutionary algorithtus today.
Recently, genetic algorithms have received considerable attention regarding their
potentiai as an optimization technique for complex problems and have been successfully
applied in the area of pipeline system. Weil-kwwn applications include pipeline
optimization, p m p operatng, sysystem reliability design, and many others. These topics
are reviewed briefly in this chapter.
4.2 GENETIC ALGORITHMS FOR OPTLMIZATION
A genetic algorithm is a search algorithm based on natural selection and the
mechanisrns of population genetics (Holland, 1975; Goldberg, 1989). Originally, GAs
were developed by John Holland (1975) and his graduate students at the University of
Michigan. The basic idea of the GA is borrowed fiom the biological process of survival
and adaptation. The result is an efficient algorithm with the flexibility to search complex
spaces such as the solution space for the design of a pipe network.
The genetic algorithm technique requires that the set of decision variables should be
represented by a coded sûing of finite length (Goldberg and Kuo, 1987). To implernent a
GA, one codes the decision variable set describing a trial solution as a binary or dual
string or "chromosome". Usually, a binary alphabet is used for the coding. The genetic
aigorithm evaluates the trial solution and cornputes a measure of worth or "fitness" for
the string. The GA successively evaluates and regenerates a collection of trial solutions
FIuid Transient and Piwline mtimization Usine Genetic Alnorithms 43
called a "population". New generations of the population are created based on the
survival of the fittest among the string structures h m the previous generation (Goldberg,
1989).
A simple, but powerfitl GA comprises three operators: reproduction, crossover, and
mutation. Reproduction is a survival-of-the-fittest selection process. Crossover is the
partial exchange of comsponding segments of bits between two parent strings to produce
two offspring. Mutation is the occasional £lipping of bit values and helps to prevent
missing a potentially useful genetic trait.
GAs can broadly and efficiently solve difficult optùnization problems. Researchers
have applied GAs to a diverse range of scientific, engineering, economic, and also artistic
search problems including:
1. Structural optimization (Goldberg and Saantani, 1986; Saed et al., 1991 ;
Koumousis and Georgiou, 1994);
2. Water distribution system optimization (Goldberg and Kuo, 1987; Dandy et al.,
1996);
3. Control systern optimization for aerospace applications (Krishnakumar and
Goldberg, 1990);
4. Musical composition (Homer and Goldberg, 199 1); and
5. Layout for a sewer system (Cembrowicz and b u t e r , 1987).
Gen and Cheng (1997) surnmarix recent resdts related to genetic aigorithms ( h m
early 1992 to 1997). As they indicate, genetic algorithms can be used for many problems
FIuid Transient and Piwline Outimization Usinn Genetic Aleorithms 44
including reliability optimïzation, flow-s hop sequencing, jo b-shop schedding, machine
scheduling, transpomtion, and faciiity layout design.
Genetic algorithms are highl y dimensional, stochastic, non-linear algorithms
(Goldberg, 1993). GAs are robust and have been proven theorptically and empirically to
be able to eficiently search complex solution spaces. Goldberg et al. (1992) proposeci the
following decomposition into subproblems or pieces of the GA puale includhg:
Knowing what the GA is processing: understanding the concept of building
blocks. (That is, the population structures or states enable one to determine the
fiiture without additionai idonnation about the past of the system.)
Ensuring an adequate supply of building blocks-
Guaranteeing that the individual building blocks grow or develop.
Making buildiug block decisions well.
Solving problems that are not tw difficult in establishing the building blocks
Ensuring that building blocks exchange or mix to f o m better solutions.
Substantial progress has been made on the fim five parts. Some attempts have been made
to tackle the sixth part (Goldberg et al., 1993 ; Thierens and Goldberg, 1993).
Genetic algorithms differ fiom conventional optimizaîion and search procedures in
severai fundamental ways- Goldberg (1 989) has summarised this as follows:
1. Genetic algorithms work with a coding of solution set, not the solutions
themselves.
2. Genetic algorithms search fiom a population of solutions, not a single solution.
Fluid Transient and Piwline OMimizatim us in^ Gcnctic Alnwidims 45
3. Genetic algorithms use payoff information (fitness ~ c t i o n ) , not derivatives or
other awiliary knowledge.
4. Genetic algorithms use probabilistic transition des, not deterministic d e s .
Some important events relaîing to the development of genetic algorithms as well as
more detailed information on the history of GAs has been summarised in Appendix B.
4 3 GENETIC GLGORITHMS FOR PCPELiNE SYSTEM OPTIMIZATION
A relatively comprehensive appmach for the use of genetic algorithms for steady state
pipe network optimization has been developed over the last ten years (Goldberg and Kuo,
1987; Hadji and Murphy, 1990; Murphy and Simpson, 1992; WaIters and Lohbeck, 1993;
Dandy et al., 1993; Walters and Cembrowicz, 1993; Simpson et al., 1993; Murphy et al.,
1993; Simpson et al., 1994; Davison and Goulter, 1995; Dandy et al., 1996; Halhal et al.,
1997; Savic and Walters, 1997).
Goldberg and Kuo (1987) applied GAs to the steady state optimization of a serial
liquid pipeline. The system consisted of 10 pipes and 10 cornpressor stations each
containing four pumps in series. nie objective was to minimise the power requirements,
while supplying a specified flow and maintainhg allowable pressures. The three
operators found near-optimal pump operation alternatives after evaluathg a fraction of
the total possible number of solutions (a total of about 3,500 h m 1.10 * 1012 possible
combinations).
FI uid Transient and Piw line %timization Usinn Genetic Alnorithms 46
Murphy and Simpson (1992) used SGA (Stnictured Genetic Algorithm) to find the
optimal solution of the Gessler (1985) network. The methai chooses the optimal
combination among the eight alternative decisions possible for each of the eight decision
variables (pipes).
Walters and Cembrowicz (1993) extended these concepts using linear programming
for the optimal selection of pipe sizes for branched pipe networks generated by a genetic
algorithm. The combination of GAs, graph theory, and hear programming was found by
the authors to be the basis for an effective search for near-optimal branched pipe network
designs.
Walters and Lohbeck (1993) studied the case of pipe networks with one demand
pattern and no constraints on minimum pipe diameters. They showed that the GA
effectively converges to near-optimal branched network layouts, as selected from a
directed base graph which defines a set of possible layouts.
Davison and Goulter (1995) used GAs to optimise the layout of a rectilinear
branched distribution network, such as a rural nahiral gas or water distribution system.
Their algorithm uses a binary solution-coding scheme that is similar to the type
comrnoniy used in genetic algorithms but employs two new operators, recombination and
perturbation, instead of the cornmon genetic aigorithm operators of crossover and
mutation; which, in the case of the layout design of rectilinear branched networks,
generate infeasible solutions at an unacceptably high rate.
Savic and Waltets (1995a,b) applied GAs within the framework of an evolution
program, integrating it with the hydraulic analysis of water distribution networks to
detemine the optimal location of isolating valves. They demomtrated that the
Fluid Transient and Piwline ODtimization Usinn - Genetic Aleonthms 47
evolutionary process considerably accelerates the search for an optuna1 solution, reducing
the number of hyâraulic analyses of a distribution network. Fuaher. it ailows infeasible
solutions to stay and help guide the search.
Dandy et al. (1996) developed an improved genetic algorithm (GA) formulation for
pipe network optùnization. The new GA uses variable power raling of the titness
function. The exponent introduced into the fitness hct ion is i n c d in magnitude as
the GA cornputer nm proceeds. In addition to the more commonly used bitwise mutation
operator, an adjacency or creeping mutation operator is intmduced. New codes (gray
codes) rather than binary codes are used to represent the set of decision variables which
make up the pipe network design.
Genetic algonthms have a number of advantages over other mathematical
programming techniques (Goldberg, 1989). in the context of optimization of pipe
network design some advantages include the fotlowing: (Simpson et al., 1994)
GAs deal directly with a population of solutions at any one the. These are spread
throughout the solution space, so the chance of reaching the global optimum is
increased significantly.
Each solution consists of a set of discrete pipe sizes. One does not have to round
diameters up or down to obtain the final solution.
GAs identiQ a set of solutions of pipe network configurations that are close to the
minimum cost solution. These configurations may correspond to quite different
designs that can be then compared in terms of other important but non-quantifiable
objectives.
Fluid Transient and Piwline ODn'mization Usinn Genetic Aborithms 48
4. GAs use objective fûnction or fitness information only, compared with the more
traditional metbods that rely on existence and continuity of derivatives or other
auxiliary information.
In addition, the GA approach can be easily applied to other system models that need
to be optimised without changing variables or codes inside the model. GAs simply
require a suitable interface with the other program. nius, GAs can be conveaiently
combined with other models.
Genetic algorithms do not necessarily guarantee that the global optimum solution will
be reached, although experience indicates that they wül give near-optimal solutions d e r
a reasonable number of evaluations (Simpson et al., 1994).
4.4 SUMMARY
This chapter reviews recent works related to genetic aigorithms, focusing on the
application of genetic algorithrns to pipeline system. First, an overview of genetic
algorithms is presented. However, given its importance to the current work, papers
relating to pipeline optimization using genetic algorithms are particuiarly emphasized.
Based on this information, it is natural to consider the inclusion of transient analysis
in the pipeline optirnization using genetic algoritbms. This thesis shows that genetic
algorithms are a promising method of reducing the execution time without limiting the
design options or the solution space. The next chapter develops the topic of pipeline
optimization including transients using genetic algorithms in more detail.
Fluid Transient and Pi-wline ûmirnization Usina Genetic Alnonthms 49
CHAPTER 5
GENETIC ALGORITHMS FOR PIPELINE
OPTIMIZATION
5.1 INTRODUCTION
Chapter 3 introduced conventionai appmaches and formulations for pipeline
optimization, including linear programming, non-linear programming, dynamic
programming, enurneration and briefly discussed genetic algorithms. Although each
method has advantages and disadvantages, an effective method for fmding a near optimal
solution for large networks is still required.
Using mie-based procedures to update and irnprove the previous best design, various
models have obtained good rather than tme optimal solutions to network layout problems
(Barlow, 1972 and Rothf'atb et ai., 1970). In fact, with d l such techniques, it is quite
possible that any optimum reached will be a local, rather than a global value.
Genetic Algonthms (GAs) are used in this thesis to optimise water distribution
systems. GAs have been ~mposed as a pract id means of giobd optimization for a
variety of water distribution systerns but, to date, littie consideration has been given to
transient conditions. Although genetic algorithms do not necessarily guarantee that the
Fluid Transient and P i d i n e Obtimization Usinn Genetic Alnorithms 50
global optimum solution will be reached (Simpson et ai., 1994), this method has proven
its usefulness in other contexts and is worthy of M e r investigation.
Chapter 4 reviews the literature relating to genetic aigorithms. This chapter, by
contrast, describes the genetic algorithm approach itself in greater detail. Fundamentals
of genetic algorithm are well described by Gotdberg (1989).
5.2 OVERVLEW OF APPROACH
Goldberg and Kuo (1 987) summariseâ several differences between genetic algorithms
and conventional search methods:
1. GAs work with a coding of the parameter set, not with the parameters
themselves.
2. GAs search h m a population of points, not fiom a single point.
3. GAs require oniy payoff (objective hct ion) information, not trend,
derivative, or other auxiliary data.
4. GAs use probabilistic transition rules, not deterministic transition des.
Genetic algorithms require the natural parameter set of the optimization problem to be
coded as a finite length string. Because GAs work directly with the underlying code, they
are dificult to fool, since they are not dependent upon continuity of the parameter space
and derivative existence. Genetic algorithms work iteration by itemtion, successively
generating and testing a population of strings. They work nom a database of points
Fluid Transient and Pimline Optimization Usinn Genetic Al~orithms 51
simuItaneousIy (a population of strings) climbing many peaks in parallel, thus reducing
the probability of finding a false peak (GoIdberg and Kuo, 1987).
A genetic algorithm oniy requires payoff (objective function value) information for
each of the structures it generates and tests Later, in this chapter, the fiuidamental
operators of genetic algorithms are addressed
It has been assumed that decision variables may be coded as some finite length string
over a finite alphabet, &en the binary alphabet The GA is applied generation by
generation using payoff information and randomised operators to guide the creation of
new string populations. With this background, the mechanics of the GA operations will
be executed to enable GAs to generate a new and improved population of strings h m an
old population.
A simple genetic algorithm is composed of three operators: reproduction, crossover
and mutation. These three operations are briefly introduced here, with a more detailed
discussion in later sections.
Reproduction is an operator which copies an old string into the new population
according to that string's fitness. Here, fitness is defiwd as the nonnegative evaluation of
ment (objective function value) king maximiseci. Thus, under reproduction, more highly
fit strings (those with better objective function values) give rise to higher numbers of
offspring (copies) in the mating pool.
M e r reproduction, simple crossover may proceed in two seps. F h t , newly
reproduced strings in the mating pool are rnated at random. Second, each pair of strings
interacts using cross-overs. The crossover operator is the partial exchange of
corresponding segments of bits between two parent strings to produce two children. in its
Fluid Transient and Pi~etinc Omimization Usinn Genetic Algorithms 52
simplest form, a single point dong the coded string is selected at random, and the code
strings from two parents are broken at this point. The tail ends are switched and the
strings recombined to form the codes for two offspring.
Mutation is needed in a genetic aigorithm search because even though reproduction
and crossover are effective search operations, occasionally they may arbitrarily eliminate
(or miss) some potentially usehl genetic materiai. The mutation operator helps to pmtect
against such an irrecoverable loss. Mutation is a p e s s that certain parts of the
chromosome are altered randomly such that the children chromosome differs in minor
ways fiom both parents. Mutation rates are sirnilarly small in naturai populations, which
leads to the conclusion that mutation is appropriately considered a secondary mechanism.
5.3 IMPLEMENTATION
The following steps sumurise an irnplementation of a genetic algorithm to optimise
a pipe neîwork (Simpson and Goldberg, 1994; Simpson et al., 1993; Simpson et al.,
f 994):
1. Randomty generate the initial popuIation. The initial population of solutions
(or say, size N=lOO) is produced using a random nurnber generator. Each bit
position in the string takes on a value of either 1 or O. Every string represents a
different configuration of a pipe network. In this process, a recurrence relation
called a linear congruential generator can be used to produce sequences of random
numbers (Barnard and Skillicom, 1988). Details of coding network components
into strings are indicated in section 5.4.
2. Decode each string to the correspondhg decision variables.
Fluid Transient and Piwline ODtim-on us in^ Genetic Alnorithms 53
3. Compute the capital cost of each neîwork component in the generation. The
GA decodes each &string into the correspondhg pipe size and cornputes the
total cost, including construction, maintenance and operation costs. This step
detemiines the costs of each network in the initial population.
4. Analyse each network hy&aulically. Each network in the population is
analysed for heads and discharges under the specified demand(s). The actual
heads are compareci with the minimum (or maximum) allowable pressure heads
and any pressure deficits are noted.
5. Cornpufe penaky cost for euch network The GA assigns a penalty cost for each
loading case if pressure constraints are violated. The penalty cost should be such
that near-optimal infeasible solutions are highly fit so that the optimum solution
will be approached fiom both above and below. The optimum solution often lies
on the boundary between feasible and infèasible solutions (Richardson et al.,
1989). Traditionaily, the penalty multiplier is given an absolute penalty to each
infeasible installation equal to the maximum value allowed. in this thesis, we use
pressure violation deficits in the system to formulate the cost hction. It builds a
practical relationship between penaity cost and the pressure violation. Details are
introduced in chapter 6.
6. Compute cost for the total network. The total cost of each network in the
population is the sum of the network cost (3) plus the p e d t y cost (5).
7. Compufe thefitness. For each network in the population, the fitness is taken to
be a function of its total cost in (6), for exarnple,
Fluid Transient and Pipeline ODtimization Usine Genetic Al~orithms 54
1 Fitness =
Details of fitness are addressed in section 5.5.
8 . Generate a new popdation of networks in the next generation using genetic
algorithm operators including:
- selection or a reproduction scheme, as stated in section 5.6.
- crossover, as stated in section 5.7.
- mutation, as stated in section 5.8.
9. Repeat steps (2) to (8) tu produce successive generations. Goldberg (1989)
refen to the application of the three operators of reproduction, crossover, and
mutation as a standard genetic algorithm. The process is repeated to produce
successive generations. The least cost strings are stored and updated as cheaper
cost alternatives are generated.
Some additional steps are also recommended including:
1. Check if any of the decision variables have been selected at the upper bound
of the possible choices. If so the number of choices should be expanded to
provide a larger range of choices and the GA re-m.
2. Select a minimum likeiy population size and run the GA for say 10 different
random number seeâs. Progressively increase the population size and r e m
the GA. When there is no improvement as the population size is increased the
analysis can be terminated.
Fluid Transient and Pimline Obtimization Usinn Genetic Alnorithms - 55
To successfûily implement the genetic aigorithm a number of basic decisions need to
be made including:
1. Sizing of the population, n.
2. Esthating the penalty cost for violation of pressure constraïnts, K (e-g., $1 m).
3. Selecting a method for computing the fitness of the network.
4. Choosing the type of selection scheme to be used.
5. Selecting the type of crossover operator to be used and the probabilities associated
with the crossover scheme.
6. Identifjing the type of mutation operator(s) to be used and the probabilities associated
with the mutation scheme or schemes.
Simpson et al- (1994) pmposed experiential parameters for genetic aigorithms, as
summarised in the following:
Population size (n) - usually 30-200.
Probability of crossover @,) - usually 0.7-1 .O.
Probability of mutation (p,,,) - usually 0.01-0.05. Guidelines for computing pm
are: p, 2 i/n and p, I l/m where n = population size and m = length of string
(Goldberg and Koza, 1990).
The following sections discuss details of the GA process, including the three
operators of reproduction, crossover and mutation.
Fluid Transient and Pid ine O~timization Usinn Genetic Alnoriuirns - 56
5.4 CODLNC
The genetic algorithm requires that the decision variables describing trial solutions of
the pipe network design problem be represented by a unique coded string of finite length.
This coded string is similar to the structure of a chromosome associateci with the genetic
code of a biologicai species.
The coding of the variables that describe the pmblem is an essential characteristic of a
genetic algorithm. The most common coding method is to transfonn the variables into a
binary string of a specific length. This string represents the chromosome of the problem
(Koumousis and Georgiou, 1994).
5 J FITNESS
The evaluation fûnction detennines the total cost of a solution by sumrning the cost of
the network components. Simulation of the network flows and pressure heads is then
carried out to assess the feasibility of a solution. The network solver used in this work is
based on the TransAM (McInnis, et al, 1997) cornputer program. This program empioys
the method of characteristics for hydraulically simulating pipe system under a variety of
constraints.
The minimum (or maximum) pressure constra.int discriminates between feasible and
infeasible solutions. Rather than ignoring infeasible solutions, and concentrating only on
feasible ones, infeasible solutions are ailowed to join the population and help guide the
search, but for a certain penalty. A penalty terni incorporateci in the fitness fwiction is
activated for a pressure-infeasible solution, thus reducing its strength relative to the other
strings in the population.
As stated by Savic and Walters (1 997), the penalty fiuiction used is gracie4 i.e., the
penalty is a fùnction of the distance from feasibility qd(~~'" -Hj)]. A penalty function
which considers the system performance is introduced in the next chapter.
The general form of the evaluation fùnction used is as follow:
where:
Mi = cost of system components (S)
p = penalty multiplier, and
term in braces() = maximum violation of the pressure constraint in pipeline;
term in brackets[ 1 = maximum violation of the pressure constra.int in each pipe.
The penalty multiplier is chosen to normalise nominal values of the penalties to the
sarne scde as the basic cost of the network. The multiplier is a fhction of the generation
number, which allows a gradua1 increase in the penalty tenn (Savic and Walters, 1997):
where:
q = constant penalty multiplier;
n, = generation number;
Fluid Transient and Piwl ine ODtimization Usinn Genetic Alnorithms 58
nPmn = maximum number of generations; and
k = parameter (experimentally chosen to be 0.8).
At the end of a GA run, the mdtiplier p should take a value that will not allow the
best infeasible solution to be ktter &&n any feasible solution in the population.
5.6 REPRODUCTION
Genetic algorithms strive to find solutions to optimal problems, but usually settle for
near optimal ones. In fact, absolute best solutions may not always be practical. So, a
substitute solution that is very close to the absolute best solution is ofien nasonable. Such
near-optimal solutions are often praaically identical in physical form, having only more
variables of components relative to the global optimum.
The GA generates new members of the generation by a selection scheme. A
proportionate method is used for this purpose in this thesis [ a h referred to as weighted
roulette wheel (Goldberg, 198911. A weighted roulette wheel has slots that are sized
according to the fitness of each member in the population. The selection operator assigns
each string in the population to a segment of the roulette wheel. The size of the segment
is proportiond to the fimess of the string,
Successive generations of new strings are results of a selective "survival" scheme.
Reis, et al. (1994) had proposed an implementation utilizing a "hybrid" method for
reproduction in two steps. Firstly, the number of copies, No(i), of a particular string i in
the population to be reproduced is calculated as follow:
Fluid Transient and Piwiine Obtimization Usinn Genetic Alnorithms - 59
In the case of the total number of copies is less than the nurnber in the population (n),
the second step is then used to identifl the additionai strings needed to maintain the
population level. The additional nr strings are selected h m those excluded k m the f k t
selection process, submitting h e m to a weighted roulette wheel, with the probability of
selection:
The "hybrid" method guarantees "survivai" of the best string h m one generation to
the next and, at the same time, permits that certain features of the strings excluded in the
first step are maintaineci during reproduction.
Even though many methods are used to evaluate the fitness, dl of them are b d on
the roulette wheel technique. Michalewics (1992) summarised the basic algorithms of the
roulette wheel parent selection techniques as follow:
1. For each generation, evaluate the fitness of ail n member of the population
2. Place al1 the members of the population in an imaginary queue, the queue
need not be in any particular order.
3. For each member in the queue assign a nurnber, which is the sum of its fitness
and the fimess of every mernber before it, cal1 this value the 'hinning total".
Fluid Transient and Pimline O~timization Usine: Genetic Alwonthrns 60
The "ninniag total" of the Iast member in the queue is assigned the speciai
name of "total fitness".
4. Generate x, a random number between O and total fitness.
5. Return the first population member whose correspondhg ninaing total is
greater than or equal to x.
6 Repeat steps 4 and 5 for as many times as required for the coming generation.
7. Repeat steps 1 through 6 as many times as there are generations required.
5.7 CROSSOVER
The crossover operator is the partial exchange of bits between two parent strings to
two offspring strings. It describes the process by which the parent's coded data strings are
combined to foxm new coded strings for their offspring.
The standard crossover operator does not take into account the individual structure of
a chromosome, but rather it is considered in a linear way. So, a crossover operator is
necessary which will take into account this underlying structure of the chromosome.
Unfortunately, it is difficult to find an operator which is able to maintain the feasibility of
a network.
A number of crossover operators have ken proposed. The current discussion focuses
on the one and two-point crossover rnethods, and uniforrn crossover technique.
Crossover between two strings occurs with a crossover probability of p,. If two
strings are crossed, a crossover point is randornly chosen and the bits following the
crossover point are exchanged between the strings.
Fhid Transient and P i d i n e Obtimization us in^ Genetic Alnorithm 61
The one point crossover method was inspireci by biological professes. In its simplest
form, a single point dong the coded string is selected at random, and the code strings
from two parents are broken at this point. The tail ends are mvitched and the strings
recombined to fonn the codes for two offspring. The greatest advantage of the one-point
crossover is its simplicity. However, it has the disadvantage in that it can not combine
certain combinations of features encoded on chromosomes (Davis, 1991). Sometirnes, it
is slow to converge.
Two-point crossover is by far the most popular crossover technique (Davis, 1991 ). It
has two randomly chosen cut points instead of one. The chromosome material is swapped
between the two cut points between the two strings. Again there are still some schemata
that two point crossover c m not combine (Simpson and Goldberg, 1994).
Uniform crossover is a third method. For each bit position on the first cchild, a parent
is selected with probability fi. The bit fiom the parent that is not selected goes to the
second child, The location of the encoding of a feature on a chromosome is kIevan t to
uniform crossover. So, it has the distinct ability to combine al1 combinations of
schemata However, the method is quite 'violent' in the sense that it c m cause a great
deal of hami to whatever is good in a chromosome (Michalewicz, 1992). In one and two-
point crossover the more bits that intervene in a scheme then the less likely it will remain
intact in one of the children.
For uniform mixing, Thierens & Goldberg (1993) and Goldberg, Deb & Thierents
(1 993) developed a control map of crossover probability p, versus selection pressure S.
These control maps show that various combinations of s and p, can be selected to provide
successfbl results h m the GA run as long as the population is adequately sized. The
Fluid Transient and Piwline %timization Usinp Genetic Alnorithm 62
larger the selection pressure, the fewer evaluatioos that are necessary before convergence
to the lowest cost solution occurs.
Simpson and Goldberg (1994) statd the permissible combination of s and p, as
follows:
1. A minimum s to prevent stochanic variations ovexwhelming selection (i.e.,
prevention of genetic drift).
2. A maximum s above which selection wiil be o v e d o u s and cause competing
aileles to go head to head with one another (i.e., cross cornpetition occurs).
3. A minimum pc to ensure good mOUng occurs (Le., otherwise a W i n g failure
occurs). The minimum value of p, increases as s increases (a logarithmic
variation).
5.8 MUTATION
Occasional random alteration of digits protects the genetic algorithm process against
premature loss of potentially useftl genetic material. A mutation in a chromosome should
be a minimum change of configuration. The mutation operator should ensure that when
applied to feasible installations, it maintains their feasibility. However, it is difficult to
find such an operator, because the critical nature of a network is too strong and any
change in its chatacteristics can make it ideasible.
A priori, it is not possible to determine whether or not the new state wiil be more
economical than the previous one, so we can not say in which direction the mutation
Fluid Transient and Piw line ODtimizdon Usinn Gcnetic Alnorithm 63
should be made. Thetefore, the mutation is chosen randomly (Castille and Gonzalez,
1998).
Mutation can be applied in two ways, The £irst is a bit-wise mutation where with a
small probability b, the mutation operator changes the value of the bit to the opposite
value (i.e., a O to a 1 or a 1 to a O). One of the most cornmon methods of bit mutation is to
generate uniformly distributeci random numbers for ail bits, and if the random nurnber is
below the mutation probability, then the bit is altered @avis, 1991 ).
The second type is refened to adjacency or creeping mutation where with a small
probability p. the randomly chosen pipe variable is altered to the next adjacent pipe size.
In adjacency mutation, the probability of movhg to the smaller pipe diameter is assigned
as Pd-
Usually, the mutation probability is selected to be in the range as follow:
Un, -+ l/m
where:
n, = population size, and
m = chromosome length
The research cornmunity involved in optimization of water distribution networks has
started to become aware of the shortcomings of the methods which are oflen able to find
Fluid Transient and Pi~eline mtimization Usinn Genetic Algorithms 64
only local minima Although GAs c m not guarantee that the global optimum is found,
there have been successfûi applications of these techniques to the design of water
distribution networks,
This chapter presents the fundamental mechanics and techuiques of genetic
dgorithms. A simple GA consists of three basic operators: reproduction, crossover and
mutation.
The current investigations demonstrate that GAs are particularly suited to the
optimization of large water distribution systems. Because the procedure works with a
coding of decision variables instead of the decision variables themselves, it is dficult to
fool. The method does not depend upon underlying continuity of the search space and
requires no information other than payoff values. Furthemore, GAs work from a
population of points and have a more global perspective than many optimization
procedures.
It is now natural to move on to implement pipeline optimization using genetic
dgorithms. The next chapter formulates a complete objective fünction for the genetic
algorithm. The objective fimction not only considers the capital cost, but also includes
operating cost The performance evolution considers transients and this is attempting to
ensure a more complete optimal solution.
Fluid Transient and Pipeline Optimization Usinn Genetic Alnorithms 65
CHAPTER 6
COST OBJECTIVE FUNCTION
Having addressed pipeline optimization in chapter 4, and transient d y s i s in chapter
3, these subjects must now be combined with the material of chapter 5 on genetic
algorithms to focus on pipeline optimization including transient conditions-
6.1 PIPELINE OPTIMIZATION IN TRANSIENT CONDITION
There are a few recent papers which explore the inclusion of m i e n t analysis in the
optimization of water distribution systems. Fluid transients play a significant role in
determining the design cntena for distribution system and optimization procedures.
Unfomuüitely, though, "consideration of transients ofien takes place after the fact (if it is
done at dl) by assurning that the cost of controlling transients represents a small portion
of the overall pipeline cost." (Kamey and McInnis, 1990)
Yet pipe costs constitute a large portion of the total pipeline price. The components of
pipe seiections, such as diameter, material, thickness and length, are greatly influenced by
pipe1 ine transient responses and performances of the water distri bution system. So, any
optimized design that fails to account for transient influence wiU be incomptete. "The
Fluid Ttansient and Pipeline Optimization Usinn Genetic Al~orithrns 66
basic proposition is that if a rapidly occurring control operation is a significant design
consideration, then cost optimization should include the system transient response(s)"
(Kamey and McInnis, 1990). Even if one perfomis a qualitative analysis of transient
phenomena and the likely impact of transients on the system, exactly how aad to what
extent the occurrence and treatment of shock wave phenornena in the system will
impinge on the cost of the system is less obvious and tequires a broder understanding.
There is no analytical solution to the water harnmer problem. So, we have to adapt
numerical, typically deterministic, simulation procedures. One simulation approach is
surnrnarized in the program TransAM (Transient Anaiysis Model), as has been mentioued
before. Thus, we focus here on an optimization methodology that models transient
conditions as a key part of its simulation. in this thesis, such a simulation mode1
(TransAM) is combined with a genetic algorithm (GA) to optimize water distribution
systems under transient and steady state conditions.
Clearly, the cost of the system should be considered in this evolution. Since, models
can be operated with different parameter values, procedures for acquiring response
information m u t be provided. For the purpose of current optimization problem, it is
reasonable to provide cost factors associated with TransAM's input data This is the
purpose of the current chapter.
Due to the complexity of transient phenomena, it is very difficult to analyze transients
without a computer and the run time required to fïnd a solution are still significant,
especially for large water distribution systems. However, if we restrict our attention to
simpler, but still redistic, water supply systems, a defined comection between transient
Flu id Transien t and Piwl ine Obtirnization us in^ Genetic Al~orithms 67
performance and optimal design is easy to demonstrate. For this reason, the research here
is limited to relatively simple pipeline systems.
6.2 INPUT DATA OF TransAM
In TransAM, there are two kinds of input files. The £kt file contains al1 the physical
system information. The other file is the tabulated values of the pump head and torque
characteristics.
The physicd description of the system includes the length, diameter, wavespeed and
friction coefficient of each pipe, and ail hydraulic devices in the system, as well as the
initial conditions at the beginniig of the transient run. Head losses at pipe junction are
usually considered negligible in a manner analogous to most steady state modeb.
The input data in TransAM is split into several categones (Mcinnis, Kamey and
AxwolThy, 1997):
1. General System Data;
2. Node Data;
3. Pipe Data;
4. Pipe Profile Data;
5 , Device (Boundary Condition) Data:
0 Airvalves;
0 Valves, surge tanks, reservoirs;
Air chambers;
In-line eiements (PRVs, PSVs, ROFs, etc.);
Fluid Transient and Pibcline Optimimtion Usina Genetic Alnorithms 68
Junction losses.
6. Pump Station Data;
7. Output Data:
Graphic Path;
Energy Path;
Nodai traces;
Pump Station valve Traces.
In this thesis, we use the input &ta for the pipes, nodes, and devices (boundary
conditions) in the system. These input data are al1 dîrectly physical and thus are usenil for
evaluating system costs. Since the input data varies considerably fkom one component of
system to another, specinc details for the appropriate devices are discussed below.
6.3 SYSTEM COST FACTORS
The variables that are assumed to primarily determine the cost of the water suppiy
system are the cost of:
Pipes;
Pumps;
Control devices same as reiief valves and air valves;
Reservoirs or tanks;
The cost of electricity;
Operating and maintenance costs; and
Fluid Transient and Piwline ODtimization Usine Genetic Aleorithms 69
a The cost of system performance.
The cost hct ions for the pipes, pumps, transient suppression devices, reservou and
O & M are presented in the next six sections. The cost hction for system performance,
which relates to appropriate penalty fiuictions for violating constraints, is presented in
section 6.4.
6.3.1 PIPE COSTS
Due to the complexity of the cost of the pipeline installation, b e y and Mclimis
(1 990) proposai two simplifjhg assumptions:
Pipes are available only in commercial sues and pressure classes.
Structurai, service or other considerations fk the type of pipe material needed
for a pariicular installation. In other words, the optimization algorithm does
not directly contml the selection of the pipe material or the selection of non-
standard pipe size.
nie f h t assumption reflects the practicality of workhg with commercial pipe sues
while the second is a convenience which reduces the number of variables (and the
mathematical clutter) in the illustrative optirnization problem fomulation.
Factors that influence the cost of pipe include: - Construction cost:
FIuid Transient and P i d i n e Outimization Usinp Genetic Alnorithms 70
diameter, material, thickness, length, depth of excavation, type of protective
coating, etc.
Maintenance costs:
cleaning, repair, etc.
Operation and performance costs are considered separately.
Athough the cost of a pipeline is a fhction of many factors, as Kamey and McInnis
(1990) indicated, most of these items are correlated with the amount of material used to
manufacture the pipe. So, they assumed that the mass of wall matenal needed per unit
length of pipe, W , is a good indicator of the relationship between the system hydraulic
variables, the material strength, the pipe size and the cost of pipe. Ultimately, they
concluded that a satisfactory cost b c t i o n could be obtained by sïmply multiplying the
mass expression (shown below) by a constant that converts mass Wp to coa C,. The
expression of W, is as follow:
where:
D = inner diameter of pipe (m or fi).
y =unit weight ofthe fluid(kN/m3 orlblft)).
HP = fluid pressure head of pipe (m or R).
-1 = allowable level of circumferential stress of pipe (MPa or psi).
p, = pipe material density (kg/m3 or lb/£t?).
Fluid Transient and Piwline Wmitation Usinn Genetic Alnonthms 71
For many systems which the ratio y/adl cc 1, the second order head term may be
neglected. Then, we can say that the requued wall mas is almost linearly related to the
design static pressure. However, pipe diameter plays an important role in detennuiing the
pipe cost.
Based on the above analysis, the cost of pipe, M , is qua1 to following:
where:
Mp = the capital cost of pipeline (S).
Cm = a cost constant depending on the pipe material ($/kg or â0.454Ab).
W, = the mass of wall material of pipe &g/m or Ib/ft).
L = the length of pipeline (m or fi).
This thesis explicitly considers two kinds of pipe material, steel and PVC.
The TransAM program also considers pipe and node data. The pipe data is split into
three groups. The information includes generai parameters for pipes in the system,
hydraulic parameters for al1 individual pipes, and pipe topology. The hydraulic
parameters for individual pipes contain the initial pipe flow rate, the approximate pipe
length, L, the intemal pipe diameter, D, the wavespeed of the pipe, a, and its fiction
factor, f, or conveyance, etc. The node data includes nodal hydraulic grade Iine, HGL,
and the nodal demand.
Fluid Transient and Pipeline Outimitation Using Genetic Ainorithms 72
6.3.2 PUMP COSTS
The cost of pumping capacity depends on the rated discharge and required head of the
pumping station. Walski, et ai. (1987) had proposeci that the cost of new pumping
equipment be given by :
where:
M, = capital cost of pump station, ($).
Qps = rated discharge of pump, (m3/s).
H, = rated head of pump, (m).
The equation shows a moderate economy of scaie with respect to the discharge
capacity that varies in the search for the optimal system. However, this equation was
formdated in 1987. So, the constant 690,000 needs to be updatd We introduce a time
coefficient Ca to make this adjusmient Then, the equation become as follow:
where:
Q, = rated discharge of pump, (m3/s or P/s).
H, = rated head of pump, (m or fi).
Ca = time coefficient, it changes with year (assumed to be 1.14 in 1999).
C, = unit conversion and cost coefficient. It equals to $690,000 in so-'/mlm2-' or
Fluid Transient and Picteline ODtimization us in^ Genetic Alaorithms 73
$35,390 so-'/AU.
In Tfafl~AM, two types of pump stations are distinguished: e x t e d pumping stations
and booster pumping stations. Any pump station can include check valves, control
valves, surge anticipating or pressure relief valves, a bypass line with check valve and
may also include air chambers. h generai, the input data for pump station contains
virtuaily ail the information necessary for descrï'bing the pump station and its
components.
Thus the pump data describes the pump operation and pump physical characteristics.
It first tells how many parallel pumps there are in the station. Then, the integer code
refemng to the dimensionless pump characteristics for each pump is listed. The
remaining input data describes a single parameter for each pump in the established
sequence. These variables include rated discharge, QR, and rated head, HR. However,
there is also an auxiliary &ta file containing the actuai non-dimensional pump
characteristics. Based on the data descnbed above, it is possible to approxirnate the cost
of the pump system.
6.3.3 PROTECTION MEASURE DEVICE COSTS
Another important cost factor in the simple series pipeline under consideration is the
cost of the control devices. There are three components for the devices: the valve body
and chamber, the valve actuator, and the controller. For simple valve systems, the
controller rnay be absent and only the valve and driver need be considered.
Ftuid Tmsient and Piwline Obtimization Usinn Genetk Akorithrns 74
The costs of devices can be easily lumped together. In this thesis, we focus on the
essential device parameters that interact hydraulically with the pipeline and affect the
system cost, Karney and Mcinnis (1990) assumed that valves are available only in
specific sizes and pressure classes and with restrictive o p e r a ~ g constraints. This
assumption is not as arbitrary as it might appear. Azoury (1986) bas shown that, for
standard valve closure schedules, the linear closure provides the best performance (with
respect to transient peak pressures) over a wide range of physical system parameters.
Although the cost terni hct ion for system devices is difficult to develop, Laine
(1996) had partially addressed the costs and design lives for six devices. In addition, he
assumed that additional buildings and chambers are not requkd for the various devices.
Since neglect by operators canwt be predicted, he also assumed that al1 devices are
properly maintaineci. The assumed costs and design lives for these devices are given in
Table 6.1 ; variations in these assumptions are simply accommodated.
It is emphasized that the proper performance of a given design hinges on the
performance of ail facets of a design. So, in the next part, we also introduce the cost of
performance.
It is clearly impossible for any transient mode1 to handle ail sets of system devices.
TransAM is no exception. New devices are continuously king developed and applied in
water distribution systems to solve many control-related problems. This makes it difficult
for an analyst to stay abreast of every development. However, the basic huictions of new
devices are generally similar to the original control devices. Fortunately, TransAM can
handle in a reasonable way most common devices in water supply, transmission and
distribution networks.
Fluid Transient and Pimline ODtirnization Usina Genetic Aleorithms 75
Table 6.1 Parameters of Some In-Line Devices
1 I DEVICE
Air valve
DESIGN LIFE OIE-)
Combination 10 2000
press-
Relief valve
Check vdve
COST ANNU AL 1 ANNUAL
10 4000
25 4000
One way
Surge tank
Air chamber
MAINTENANCE 1 OPERATING
20 Shown in
6.3 -4
20 Show in
6.3.3.2
capital cost
capital cost
O. 1 *
capital cost
0.1 *
capital cost
O.lm
O* 15'
capital cost
No
No
No
In this thesis, the costs of devices are approximated. Based on a specified reference
cost, the cost of diffemnt projects is scaled appropriately. ln fact, the basic costs proposed
by Laine (1996) are still reasonable. TransAM provides a description of the boundary
condition which indicates the device's general characteristics and the types of devices
that can be used.
6.3.3.1 COST OF NODAL DEVICES
There are three kinds of air valves used by TransAM:
Air and vacuum valves - float operated, siamming vacuum breakers;
Fluid Transient and Pibeline Optirnization Usina Genetic Abonthm 76
Vacuum air valves - float operateci, cushionkg (non-slamming) vacuum
breakers;
O Dashpot control - these slow closing air valves release fluid following the
collapse of an air cavity at the valve location.
On the other hand, there are a number of devices which allow fluid to pass h m the
network into sorne receiving body or structure (see Karney and Mclnnis, I992), given by:
Fixed demand;
Distributed demands or ieakage;
Orifice type leaks;
Valve(s) discharging to atmosphere;
Surge tanks (variable geometry permitted);
Constant head reservoirs; and
Air chambers or h ydropneumatic tanks (variable geometry permitted).
Based on Table 6.1, capital costs of combination air valve, relief valve and check valve
are assurned constant. The cost of other devices is introduced in subsequent sections.
6.3.3.2 COST OF IN-LINE DEVICES
It is also possible to provide a preliminary estimate of costs for in-line devices. Many
common in-line devices can be handled in a comprehensive format. in this section, we
Fluid Transient and P id ine Wimization Usinn Genetic Alnorithms 77
focus on the in-line valves. The cost of surge tank or reservoir is indicated in section
6.3.4, and air chamber is addressed in 6.3.3.2.
There are a huge number of valves used in water distribution and industrial
applications. They can be custom manufactureci and designed to suit alrnost any need
Although there are endless variety of valve types and h c t i o n , most of these complex
behavioa are built up by combinïng a number of basic valve fiinctions into one unit.
McInnis et ai. (1997) have proposed the foilowiog vdve classification which is based on
valve characteristics:
a On-Off Control: Valves, which are event actuated and have a predefhed
opening or closing motion.
Modulating Control: Valves wbich adjust their setting on a more or less
continuous basis in response to sensed pressure differences.
For the valve manufaçturer, the cost of a given type of valve is basicaily considered to
be related to the area of the valve opening, the discharge coefncient and the pressure
rating. However, for a given application, the valve size parameter largely determines the
pnce of valves. So, the cost of valves is considered a fimction o f the effective discharge
coefficient for flow through a valve or orifice. TransAM requires two valve discharge
coefficients since some valves may control flow in two directions differentiy. However,
in this thesis, we primarily consider the effective discharge coefficient for flow in normal
(positive) sense, ES.
Fluid Transient and Pibeline O~timization us in^ Genaic Alvorithms 78
Based on the table provided by Laine (KM), we set the effective discharge
coefficient of a chosen 'reference' valve as ES*. Then the cost of related but different
sized valves is scaled as follows:
where:
Mv = capitai cost of valves (S).
Cvi = cost coefficient of valves, in this thesis, we have three values as follows:
For combination air valve: Cv, = $2,000
For pressure relief valve: C, = $4,000
For check valve: Cvc = !§4,000
ESvi = effective discharge coefficient of valves, mZ% or ft.%
ES* = effective discharge coefficient of reference valve. ESvi and ES' are
dimensional quantities but the only requîrement is for those to be expressed
in consistent units.
a = exponentid constant, in this thesis usually assurned to be 1 .O.
6.3.3.3 COST OF AIR CHAMBER
For an air chamber, or hydropneumatic tank, TrausAM makes several assumptions
conceming their behavior:
Frictional and inedal effects in the tank are negligible;
Fluid Transient and Piwline Omimization Usinn Genetic Aleorithms 79
ïhere is no signifiant absorption of gas by the fluid during the transient; and
There is no significant mass of gas added to the system by the cornpressor
during the transient event-
TRANSAM requires only minimai data input in that it is used to determine the initiai
state of the system as weU as any unspecified geometric relationships. More specifically,
three types of data are used: geometnc, vertical position and physical.
According to the introduction of Harvey (1980), three general costs of air chamber
are :
Engineering Design
Materials of Construction
0 Methods of Fabrication.
The matenal costs, which account for 50 to 60 percent of the total cost of a pressure
vessel, often represent a major cost Fabrication costs typicdly account for 35 percent of
total vessel cost. Here the cost of the materiai of the air chamber is multiplied by a
constant (typicdly around 2) to obtain the capital cost of the air chamber.
The material costs of an air chamber depend on two elements: the wall thickness and
the volume of chamber. According to Megyesy (1992), the wall thickness depends on the
maximum allowable working pressure of charnber. So, this factor is a fuoction of water
head H inside the vessel. With the same reference, the volume depends on the discharge,
Q, flowing into the charnber. ln TransAM, the total air chamber volume is computed
based on the given tank geometry.
Fluid Transient and Piwline Omimization Usinp Genetic Alnorithrns 80
B a d on this information, it is reasonable to assume that the volume, V, and water
head, H, are simpiy related to the COS of materiai- Then, the cost of air chamber c m be
determined as follows:
where:
M, = capital cost of air chamber ($)-
Cc = C O S ~ coefficient depending on the air chamber size (Sm4 or $0.00863/ft4).
V, = total air chamber volume (rn3 or d).
H, = maximum water head inside air chamber (m or A).
6.3.4 RESERVOIR COST
Karney and Mcuinis (1990) proposeci that some sort of physical receiving body is
present at the dowmtrem terminus of the pipeline and the cost of the resewoir is an
increasing function of its storage capacity. in this work, the reservoir need not be
downstrearn. Precisely what this irnplies for the reservoir cost terni depends upon the
actual physical situation. The point is that: for many applications reservoir cost does not
enter into the optimization even though the presence of this device may still play a role in
constraining the problem.
Fluid Transient and Pipeline O~timization us in^ Genetic Alnorithms 81
Muir (1991) developed an approximate equation for the capital cost of elevated
storage tanks, as given:
Mt = 300,000 + 140 Vma
Or, more generally, as:
Mt = Cm + Cut x V,,
where:
Mt = capitai cost of elevated storage tanks ($1.
Ca = cost constant, nominally equal to $300,000.
Cut = unit exchange and coa coefficient equal to 140 $/m3 (or $3.96/&).
V,, = maximum capacity of the tank (m3 or A-').
In practice, the capital cost of elevated tanks varies depending on their capacity,
weight and the construction technology used. As a reasonable simplification, the only
parameter used in Muir's thesis is capacity.
In TransAM, the atmosphere may be considered a specialized storage element. More
generally, reservoirs and reIated devices are named as ''extenial energy dissipators".
Extemal energy dissipators are devices that release fluid to or fiom a storage element
with some accompanying energy loss. Since these kuids of devices can be explicitly
solved by a single quadratic equation, the program permits a continuum of orifice/storage
devices to be modeled with a single subroutine. There are three broad categones of
devices that can be defmed as follows:
Simple orifice (valve) - any opening which behaves like an orifice discharging to
atmosphere. This feature can be used to mode1 ruptures, point-source leaks,
Fluid Transient and Piwline Oi,timizatîon Usinn Genetic Aleonthms 82
conventional valves discharging to the atmosphere or head dependent nodal
demands.
Linear reservoir - a device in which the fkee surface elevation can change rapidly
and which may have significant frictional resistance and inerti-a. Common
examples are surge tanks, standpipes and shah.
Constant head reservou - a storage system in which the free surface does not
change appreciably and for which fiction and inertial effects are negiigible.
Most devices in the extemal dissapator class can be explicitly solved, except for air
chambers and Iinear reservoirs (surge tanks) having unusual geometry.
The two types of extemal dissipators, orifice discharge to the amiosphere and
constant head reservoirs, have something in cornmon, Their storage area is considered to
be unlimited. So, they are not considered as a cost factor in optimization. Thus, this thesis
focuses on the linear reservoir.
A good example of a linear reservoir is a surge tank. Surge tanks are ofien
constniçted with sections of differing diameter. Some modified forms of surge tank are
also used in some water supply systems, the most common king the one-way surge tank.
TransAM can accurately model al1 of these different types of surge tanks. Other system
devices that can be approximated using the tinear reservoir model include some head
boxes, rock shah, standpipes and small intemal reservoirs.
Almost any geometrical configuration can be handled in an accurate manner in
TransAM. The linear reservoir tank data is of three types: geometric, vertical position and
Fluid Transient and Picxline Omîmization Usinp Gcnetic Alnorithms 83
physical. The shape and size of tank is described to TransAM by the total number of
tabulated cross sectional areas describing two distinct ranges or segments of tabulated
tank cross sectionai areas starting h m the bottom of the tank, &. The input data
includes the index of the cutting plane which marks the beginning of segment 1, i, and the
index of the cutting plane which marks the beginning of segment 2, j. The meaning of
variables for the tank is shown in Figure 6.1.
Using the input data above, it is easy to obtain the maximum volume of surge tank.
Then, the capital cost of the rese~voir is obtained. The quafion of volume is as following
(also see Figure 6.1):
where :
621 = ZS 1 = the height of air chamber in meters or feet corresponding to Segment
1 (see Figue 6.1).
6Z2k = ZS2 = the height of air chamber in meters or feet corresponding to Segment
2 (see Figure 6.1).
i = NSA = the index of cutting plane which marks the beginning of Segment 2.
j = NEA = the index of cutting plane which marks the end of Segment 2.
na = NAREA = the total number of tabulated cross sectional areas describing both
segment 1 and segment 2 (see Figure 6.1).
AL = ACA(NAREA) = the actual tabulated tank cross sectional areas (in m2 or p)
starting fiom the bottom of the tank.
Fluid Transient and Piuel ine ODtim ization us in^ Generic Algorithms 84
Tabuiated Cross Sectional Areas
Tank
Detail of the three seenment, two step size tank geometry input r - - - - - - - - - - 1
Pipe 1
Orifice
Dacum Z = O
ACX(YAREAj = .qk 9S.A = i N E A = j ZBOT = Zb, ZTOP = Z.,, Z M Z = z\m XLFUSE = t, DEUSE = D, FRISE = 1, zsr = pz1, zs2 = 622,
FRES = f, XLRES = L, ARES = -4,
Figure 6.1 Generalized Extemal Dissipator and Input Variable
Fluid Transien t and P i d i n e ODtirnization Usinn Genetic Altzorithms 85
6.3.5 ELECTRICITY COST
Roberson and Crowe (1980) stated
power required is:
the standard equation to calculate the electncity
where:
HP = power requirement, kW.
Q, = average discharge, m3/s or tt?/s.
H, = average pump head, m or fi.
y = specific weight of water, kN/m3 or lb/ft'.
q = average pump efficiency.
k, = unit conversion factor, 1/550 in imperid uni&
or 1/75 in SI units
Then, we c m transfer the power value to the cost of electricity, as show below
(Laine, 1996) :
where:
%& = electricity cost, $/y.
HP = elecîrical power requirements, kW.
Fluid Transient and Pibeline mtimization us in^ Genetic Alnorithms 86
T = nurnber of hours per year for pump operation, It depends on pump usage
and the maximum value is 8760 hours.
E = price of energy, $/kW.
The price of electricity to &ive pumps accounts for about half of their operating budgets
(Ctingenpeel, 1983). So, the price of energy figures prominentty in the selection of an
optimal system design.
There are two meth& in which costs are assigned to energy usage. One is time-of-
use rate structure. The other is the peak-dmand rate structure. Muir (1 99 1 ) investigated
Toronto Hydro's rate schedule for Commercial-tndustrid users. His result is that the net
discount amounts to 58% to 63% in winter and sumrner respectively.
This cost was assumed to be paid at the end of each of every operating year
throughout the life of the project. So, it should be transfered to the cost in the beginning
of the project. in our research, we analyze reiatively simple pipeline systems. So, the
time-of-use rate structure is adapted.
TransAM provides data for the rated discharge of pump (QR), the rated dynamic head
for each pump (HR) and the rated efficiency of each pump (ER). This information allows
a computation of the power requirement and the eiectricity.
6.3.6 O & M COST
There are three kinds of components for water supply systems that require
maintenance and operation (O & M). These include pumps, reservoirs (e.g., air
Fluid Transient and Piwline Omimization Usinn Genetic Alaorithms 87
chambers), as well as pipelines (e-g., cleaning and relining). The O & M wsts of al1 three
components should be considered. Those costs are assumed to be paid at the end of every
operating year throughout the life of the project The final accounting transfers the cost to
the beginning of the project For simplicity in this study, the maintenance and operating
costs were assumed to be a percentage of the capital costs.
6.4 PERFORMANCE COST FACTORS
The most important area to be explored in an evaiuation of a water supply system's
performance is inevitably its hydradic behavior. The processes of conceiving, designhg,
building and d g a water distribution system are fïrst and foremost driven by the need
to satisQ a given set of demand points with sufficient flow of water at usable pressure
levels. However, this is not the end of the story. Virtuaily, dl pipeline iostallations are
required to make flow adjustments, sometimes quite rapidly, either for operational,
control or emergency reasons. In addition, there are steady state requiremeats. The design
of steady flow in pipeline system has two prïmary objectives. The hydraulic objective is
to secure the desired pressure and fiow rate at specific locations in the system. The
second objective is economic, that is to meet the hydradic requirements with the
minimum expense.
FIuid Transient and Pi~el ine Wmïzation Usinn Genetic Alnoridvns - 88
6.4.1 HYDRAULIC PERFORMANCE
From the hydrauiic point of view, there are îhree types of performance measure to
provide an evduation of a system's performance. The three groups concern respectively
are pressure, velocity and energy considerations (Coelho, 1997). in T ~ ~ ~ s A M , fluid
transients are often caused by power failure. The power failure can generate a sequence
of events in the line which includes rapid acceleration of the fluid in the header and pipes
and, consequently, very large pressure fluctuations. (Mcinnis, Karney and Axworthy,
1997)
in this thesis, the costs influenceci by the hydrauiic performance and the relationship
between the design parameters will be considered by using the TransAM program
coupled to a genetic algorithm.
6.4.2 OPERATING COST FUNCTION
For the solutions nom TransAM, it is impossible to directly a priori avoid infeasible
solutions that violate pressure constraints. Rather, the GA appears to constrain
optimization following two different paradigms: 1) modification of the genetic operators;
and 2) penalizing systems which fail to satisfy the coastraints. This thesis prirnarily uses
the second approach.
. . Like many other non-linear optmzztion approaches, genetic algorithms assign a
penalty cost for each loading case if a network does not satisfjr pressure constraints. In
the current work, the pressure violation at the computational section is selected. The
Fluid Transient and P i d i n e etimization Usinn Gcnetic AIgotithms 89
maximum pressure deficit is typically multipiied by a penalty factor (e.g., K= $70,ûûû/m
of head) (Simpson et al. 1994).
The penalty multiplier is a measure of the worth per meter attributed to pressure
heads below or above the allowable pressure head. The penalty cost should be such that
near-optimal infeasible solutions are fit so that the optimum solution witl be approached
fiom both above and below (Richardson et al. 1989).
However, pcevious work tends to give an absolute penalty to each violation. This
approach makes M e sense when the hydrauiic performance is considered. Rather a
Iengih-based approach rnakes better sense since nodes tend to be arbitrary whereas length
is physical. Compared to the traditional approaches, this method can consider hydraulic
violation in each pipe accurately. So, the penalty would be more accurate than previous
approaches. According to the definition of hydraulic performance, an equation is
proposed as foilows:
bs or bt Mh = Cht or hs x XWpi -Hm) x Lpti a a pi if Hpi Z H- (steady state)
or if Hpi 2 Hm, (transient condition)
bs or bt Mh = CN or ~IS X ZWpi -Hmin) x Lpti or psi if Hpi I Hm, (steady state)
or if Hpi S Hmht (transient condition)
where:
M h = penalty of hydraulic violation ($).
Cb = cost coefficient of performance for steady state condition ($/m2 or $/pl.
Cht = COS^ coefficient of performance for transient condition ($/m2 or $le).
Fluid Transient and Piwline Obtimizaiion Usinn Genetic Alnorithms 94)
Hpi = water head in the pipeline (m or fi).
H,, = allowable maximum pressure in pipeline for steady state (m or fi)
Hrnins = allowable minimum pressure in pipeline for steady state (m or fi)
Hm,, = allowable maximum transient pressure in pipeline (m or A)
Hmi, = allowable minimum transient pressure in pipeline (m or A)
b, = exponential constant for steady state condition, assumed 1 .O
b, = exponentid constant for transient condition, assumed 1.0
= the length of pipeline which does not satisfy the pressure requirements
under transient conditions (rn or A).
= the length of the pipeline which does not satisfy the pressure requirements
under steady state conditions (m or fi).
Based on the aoalysis of the components for the simple pipeline system this chapter
has defined six cost factors. This chapter also discwes the most important variables and
proposed parameters that may be used as estirnators of their cost.
However, before showing the Ml objective hct ion, these costs should be more
clearly quantified in tirne. Costs at different times should not be directiy compared or
combined. They are not in common units. Costs in different time periods may be made
equivalent by multiplying fiiture amouats by a factor becoming progressively smaller into
the more distant future. This factor is the discount rate.
Fluid Transient and Piw line Oanrnization Usine Genetic Altzorithms 91
6.5.1 OPERATING LIFE
Every component in a water distribution system bas an expected operating life. The
assumed operating life for various devices are Listed in table 6.1.
The design lives proposai for the different pipe materiais adopted for use in this study
are based on Laine (1996):
Steel 35 years
PVC 50 years
These values can be adjusted as circurnstances require.
The design life of a pump depends on the specific type of pump. In this thesis, it is
assumed to be 20 years.
6.5.2 INFLATION M T E
Since the design life of a project varies fiom 10 to 50 years, it is important to consider
the inflation rate. For simplicity, this thesis assumes that the inflation rate of both O & M
cost and electricity cost is the same. Values selected range fiom 1 to 3%.
6.5.3 DISCOUNT RATE
"The capital-recovery factor indicates the number of dollars one can withdraw in
equal amounts at the end of each n years, if $1 is initidly deposited at i percent interest"
(James and Lee, 1996). This kind of discounthg faftor is called the series present-wonh
factor, and is calculated as follows:
FI uid Transient and P i d i n e Obtimizuion Usinn Genetic Alnorithrns 92
where:
P W = present worth.
A, = annd value.
nt = operating life.
id = discount rate.
However, when the inflation rate is also considered, the present worth factor is
defined as (White et ai., 1989):
where:
P W = present worth.
A, = annual value.
nt = operating life.
id = discount rate.
r = inflation rate.
Ftuid Transient and Piwline Obtimization us in^ Gcnetk Akorithms 93
Then, by multiplying the first year's electricity and O & M costs by this present worth
factor and adding the result to the capital costs of the other parts of water supply system,
the total costs of the water distribution system are summed into a single present worth
representing total cost.
6.5.4 OBJECTIVE FUNCTION
Given that the individual terms have been introduced, the composite objective
function c m now be presented. The objective fùnction for cost minimization is a
summation of the five fùndamental cost terms.
1. extra high pressure condition
Minimize C = pipe cost + pump system cost + device cost + reservoir cost
+ electricity cost + O & M cost + performance cost
=Mp+Mp+(ZMv+Mx)+Mt+PWxM,+PWxM,+Mh
=C,X wp x L + C . X C ~ X Q , " ~ X ~ 2 . ~ + xCvi x (ESvi /ES*). + Cc x V, x He + (CR + Cu( x Vma)
+PWxExTxQ,x&xyxkp/q+PWxM, , , , ,
+ Chtork x X(Hpi - H , ~ ) ~ " ~ x J&io<orpsï
if Hpi r H,, (steady state)
or if Hpi r (transient condition)
Fluid Transient and P i d i n e Optimization Usine Genetic Alnorithms - 94
2. extra low pressure condition
Minimize C = pipe cost + pump system cost + device cost + reservoir cost
+ electricity cost + O & M cost + @ormance cost
= M p + M p + ( Z M v + M ~ ) + M t + P W x & + P W x & + M h
=C,X
+ xCvi x (ESG /ES*)a + Cc x Vy x Hg + (CH + CUI x V-)
+ P W x E x T x Q , x ~ x y x k , , / q + P W x M ,
inah + Cht or x UHpi -Hmni) x Lqm a psi
if Hpi 5 Hm, (steady state)
or if Hpi 5 Hmht (transient condition)
where:
Mp = the capital cost of pipe (S)
M, = the capital cost of pump system (a)
Mv = the capital cost of in-line valves ($)
M, = the capital cost of air chamber (S)
Mt = the capital cost of reservoir (S)
= the cost of electncity ($)
am = the costs of maintenance and operating (S)
Mh = the penalty o f hydradic violation (â)
P W = the present worth factor
Fluid Transient and Piueiine O~timization Usinn Genetic Alnotithms 95
In the equation above, cost coefficients are provided in a data cost me. Some costs are
evaluated through the TransAM data file, while other costs (e-g., performance cost) are
based on TransAM's output files. A summary of this structure is pmvided in Appendk
A.
6.6 SUMMARY
This chapter sets the stage for optimizing pipeline systems including transient
phenornenon. in particular, the optimization requins the fomiulation of an objective
fimction, which is the main topic of the current chapter.
The components of water distribution include not only "standard" components, e-g.,
pipes, but also other hydrauiic components such as pumps, in-line devices and reservoirs.
The advantage of the objective function presented here is that it accounts for not only
cost criteria, but also energy consumption, O & M cost and hydraulic performance cost,
Based on this analysis, the design of a water distribution systern can be optimized
using genetic algorithms, as illustrated in next chapter.
Fluid Transient and Piwline M m i z a t i o n us in^ Genetic Alnorithms - 96
CHAPTER 7
DESCRIPTION OF CASE STUDY
This chapter presents details of a case study, the New York Water Supply Tunnels
project. To optimke this system using GA, decision variables are determined dong with
their econornic considerations in section 7.2 and 7.3 respectively. A powerful GA model
(Tang, 1999) used in this case study is introduced briefly in section 7.4. This chapter sets
the stage for chapter 8 which discusses resdts of the optimization h m conventional
(steady state) and transient perspectives.
7.1 SYSTEM DESCRIPTION
The case study network shown in Figure 7.1, in which pipes and nodes have been
numbered, is taken fiom the New York City primary water supply tunnel system, to
illustrate the iransient condition that can be handled by the present model. This system
has been extensively studied in the past, particularly for steady state conditions, and thus
provides a nice test case to consider traasients (see Chapter 8).
The basic nodal and pipe information consisting of respective elevations, pipe
lengths, diameters is specified in Table 7.1 and 7.2. The system comprises a water supply
tunnel of diameter (ranging h m 60 inches to 204 inches) and a design discharge h m
the Hillview Reservoir. The primary tunnel system consists of City Tunnels number 1
Fluid Transient and P i d i n e Obtimization Usinn Genetic Alnorithms 97
and nurnber 2. City Tunnel number 1 extends h m Hillview Reservoir to node 16 in
Brooklyn by way of Manhattan. City Tunnel number 2 extends between Hillview
Reservoir and Richmond downtake by way of Queens. The profile comprises twenty
nodes, twenty-one pipes, one source, and twenty demand nodes. The water level in the
Hillview Reservoir is considered to be constant at 300 R The HillMew Reservoir is
located at node 1. The system is a gravity flow system that draws water (201 7.5 ft% or
57,129.5 Us) from the reservoir to downstream network. A single demand patteni was
considered for the impmved tunnel system, and a corresponding minimum allowable total
head was specified at each node, as given in Table 7.1- The lengths and diameters of the
existing pipes are given in Table 7.2. A Hazen-Williams roughness coefficient C = 100 is
assumed for al1 existing and new pipes. The available tunnel sizes and associated costs
considered for the New York City tunnels additions are presented in Table 7.5.
Table 7.ï Node Data for New York City Water Suppiy Pmject NODE
1 MINIMUM TOTAL HEAD (ftet)
300.0 CONSUMPTION ( p i s )
Reservoir
Fluid Transient and Pibelint ODtimizafïon us in^ Genetic Alnoritfims 98
Figure 7.1 New York City water supply tunnels
Fluid Transient and Piwline Optimization Usinn Genetic Alnorithms 99
The details of pipes are shown in Table 7.2, including pipe diameter, pipe length, start
node and end node, etc. These data are used to create an input data file for TransAM
program. Details of this input data file are given in Appendix C.
Table 7.2 Pipe Profde Data for New York City Water Supply Project
No. 1 START 1 END 1 START 1 END 1 PIPE 1 EXIST 1 IINITIAL
Of 1 NODE 1 NODE 1 CHAWAGE 1 CHAINAGE 1 LENCTH 1 D U 1 FLOW
I 1 1 1 1 I 1
[OTE: R = Hillview Reservoir
FIuid Transient and Pibeline O~tirnization Usinn Genetic Algorithms 100
The positions of components were fked at the chosen locations. Profile modifications
through additional excavation are assumed to be infeasible due to the current situation of
the New York City. In this case study, a rapid closing of valve at the Hillview Reservoir
was selected to define the transient performance of the system.
7.2 DESIGN VARIABLES
Various design alternatives which relate to transient conditions need to be considered
to ensure that a global optimal design is achieved. One of the most important criticai
transient conditions in many pipelines is valve closure h m fully open to a close position
in a short time, e.g., one minute. For long pipelines carrying fluid under pressure, the
critical condition goveming the required strength of the pipe is fkquently transient
pressures following a valve closure. in this case study involving an existing project (New
York City Water Supply Tunnels), a fidl valve closure is "invented" to create a suitable
of transient design condition.
in the original work on the New York problem, Schaake and Lai (1969) used a linear
programming appmach to fhd the optimum pipe diameters for assumed values of steady
state head at each node. The decision variable for each pipe was its diameter. A hydraulic
analysis (Bhave, 1985) for the projected demands applied to the existing tunnel system
shows that the head at nodes 16, 17, 18, 19, and 20 fa11 significantly below the required
minimum total head- Nodes 1 to 15 have acceptable hydraulic grade line elevation. These
low pressures could easily lead to column separation under transient conditions. This
condition must be addmsed sinfe the transient pressure resuiting h m the coilapse of
Fluid Transient and P id ine Optimization Usinn Genetic Alvorithms 101
any vapor poçkets at the high point, e.g., node 17, could be quite devastating. in the
supply system, no devices are assumed at nodes 16, 17, 18, 19, and 20. A number of
stmtegies could be available to address the potential cavity collapses or pipe break at
these five nodes. Some cecommendeci options are show as follows:
0 Increase the rated strength of pipes by replacing the existing pipes with a
higher class pipe;
0 Increase the valve closure duration; or
Increase the pipe diameter by replacing the existing pipe with a larger
duplicate pipe.
However, in order to more closely match previous studies, increasing pipe diameter is
used to prevent column separation in this case. Ah, valve closure duration is discussed
in this case study.
The system variables considered in the genetic a lgof i th can be summarized as
follows:
Pipe diameters:
Nominal diameters that range h m 48 in (4 A) to 240 in (20 A) were considered in
the opthnization. For the given design flow rate (2017.5 ph, including 873.7 ft'/s
in number 1 tunnel and 1 143.8 ft% in number 2 tunnel), the line velocities range
fiom 0.33 Ws to 8.28 Ws. This range was reasonable since it encompasses al1
velocities which would be considered normal for a transmission Iine.
Pipe matenal:
The pipe materials considered for the optimization are unlined steel pipes.
Fluid Transient and Piw line Omirnization Usinn Genetic Akorithms 102
Unlined steel pipe have bound application in water distribution systerns. Wave
speeds for this type of pipe were typicaliy in the neighbourtiood of 3600 füs
(1 100 m/s). In order to match previous research (see section 8.1), the pipe
material does not change in the pipeline system.
Valve closure duration:
The valve closure duration is a significant decision variable to influence the
pressure turbulence in transient conditions. The transient analysis considers valve
closure durations of 3O,6O, 90, 150,300 and 600 sec,
Although this case study has considered some comrnon components in water
distribution systems, some limitations on the solution space still exist. These include:
Profile changes were not considered because of site specific constxaints. In
this case, the network layout was a predetermïned configuration.
The nominal diameter set considered was discrete for the pipeline, thus
reflecting the values of pipe diameters existing in practice. By contrast, if the
solution obtained was a continuous one, M e r treatment of variables was
necessary for the solution to be of a practical value.
Pipe material was considered to be constant throughout the pipeline to match
previous studies.
Aiso, in order to match previous studies, some in-line devices were not used
in this water distribution system, including pumps, air valves, check valve,
and pressure-reducing valve (PRV), etc.
Fluid Transient and Pimline atimization Usin~Genctic Alnorithms 103
The demand in this system did not change with the saison. In this case study,
the author uses single demand pattern, presumed to represent the cntical
design condition identifiai in previous studies.
The design options under consideration can be summarized as follows and taken fiom
the profile of the New York City Water Supply Tunnels project For the each pipe
section, pipe diameter was selected as a discrete diameter k m a set of 10 options. The
range of available diameters is taken -und the existing pipe diameter. Details of the
range can be found in Appendix D, the input data for GA program, which is named as
NE WYORKTDF.
Table 7.3 Design Options for Case Study
Option Type
Pipe muterial
Pipe diameter
The simple genetic algorithm formulation developed in this thesis was applied to the
New York City tunnels network problem. A &bit binary coded substring permits
representation of LO discrete alternative choices for a design variable. Twentyone
existing pipes in the New York City network might be duplicated. The result is a vast
solution space of 1 d' different pipe network designs.
The cost huictions of various components, including standard and non-standard
components, are addressed in chapter 6. They are used to calculate the total cost of
system, including capital cost and operating cost.
Description of Option
Options
Options at node I
Total Number
Unlined steel
4 A , 5 & 6 A , 7 A , 8 & 9 A , l O A , l l f t , 1 2 A ,
of Options
1
17
13 ft, 14 ft, 15 fl, 16 A, 17 ft, 18 A, 19 A, 20 fi
Reservoir with a control valve 1
Fluid Transient and Piwline Obtimization Usinn Genctic Aborithms 104
The GA parameters chosen for the simple GA runs were adopted on the bais of
expenence of Simpson et al. (1994). Also, other GA mearchers @eJong, 1975;
Grefenstette, 1986; Goldberg, 1989) have suggested good performance of the GA may be
obtained using high crossover probabilities @, = 0.5 to 1 .O) and low mutation probability
@, = 0.00 1 to 0.05). In this thesis, a value of p,,, = 0.0 1 (probability of mutation) is
selected. Since the string length is 84 bits for the New York probiem, on the average, 42
bits will be mutated h m 50 strings crossed over to fonn a new population. A hÏgh
probability of crossover @, = 1.0) is employed for the GA m. The GA runs were
allowed 50,000 evaluations of different designs. This numbet of designs is only a
extremely srna11 fiaction of the total solution space. In this case, parameters of the genetic
algorithm are the ones shown in Table 7.4. However, in the GA program (Tang, 1999),
these parameters could be changeci with the preference of the user. According to Dandy
et al. (1 996), the GA results are relatively insensitive to these parameters. So, in this case
study, the author used the parameters as summarized in Table 7.4.
Table 7.4 Parameters of Genetic Algorithm
ITEM
Processing Ceneration
NUMBER
200
Simulating Number
Number of evaluations
Crossover pro ba bility
250
50,000
1 .O
Muîation probabiiity
Pressure Violation Penalty Multiplier (SM/foot)
0.0 1
50
Fluid Transient and Pipeline QDtimization Usinn Genctïc Alnorithms 105
73 ECONOMK CONSIDERATION
For each design, costs of various components are involved in the optimization
process. These costs are used to determine the system cost. in this thesis, a series of
equations compute the costs of each component with cost coefficients. In order to match
previous research on the New York City project, this thesis uses the suggested pipe cost
in Table 7.5 (Morgan and Goulter, 1985). Some costs are extendeci h m the or ig id
values, since the original maximum diameter of Morgan and Goulter (1985) is 17 feet.
However, in transient conditions, due to extra pressure in pipeline, it is possibly desirable
to increase the pipe diameters to more than 17 feet The costs bellow are input to the data
file of GA program (see Appendix D, PIPEDATADBD).
The costs of the other pipeline components are the same as described in Chapter 6. in
this case study, the profile comprises 21 pipes and one reservoir. The cost of the
reservoir, Hillview reservoir, is not considered for the purposes of this investigation. This
upstrearn reservoir was treated as a constant and, therefore, it would not influence the
cost comparisons. Operating and maintenance costs of this system are calculated
automatically and incorporated into the total cost of this project.
Although the system did not use some of the available transient protection
components, the procedure of the case study still shows the power of genetic algorithms
used in pipeline optimization. At the very least, it is a good starting point h m which to
begin the exploration of the interaction of the fluid transient behaviour and the cost
function using genetic algorithrns. So, this study represents a significant step for the New
Fluid Transient and Piwline ODtimization Usinn Genetic Alnorithms 1 06
York City Water Supply Tunnel pmject, espefiaiiy compared to the previous mdies
which have considered steady state costs alone.
Table 7.5 Pipe Cost of Case Study
Nominal Diameter Base Cost,
Dollars per foot
Note: Imperia1 units are used here to facilitate direct cornparison with previous studies.
* This cost is an extension of previous costs
Fluid Transient and Pibeline Obtimization us in^ - Genetic Alnonthms 1 07
7.4 COMPUTïNG
The computer platforni used to apply genetic algorithms to the case study is
sumniarized in Table 7-6.
Tabie 7.6 Computer PlaHorm for Case Study
CPU
The implementation of the genetic algorithm technique to the case study requires the
use of two distinct pmgrams. One program was the master program (Tang, 1999), which
encodes the Genetic Algorithms approach. The other program was a transient simulation
program - TransAM.
Hard drive
7.4.1 MASTER PROGRAM
Tr~e
The master program which was written in C* language carries out tasks associated
with the genetic algorithms with the exception of transient simulations. The master
program evaluates possible designs or component combinations using a set of feasible
Pentium II
CIO&
Memory
R4M
system components. The feasible or viable designs were then stored in a file. This is
followed by a search of the file or solution space and an identification of the optimal
design. Details related to operation of the master program are summarised in Figure 7.2.
300 MHz
4.0 GB
32 MB
Fluid Transient and Pi-peline &tirnimion Usinn Genetic Alnorithms 1 08
The design evaluation module of the program perfiorms the following operations
Generation of a number of initial design configurations;
Determination of the steady state conditions for a given configuration;
Generation of the input files used to drive the simulation moâel;
Operatiodinitiation of the simulation program using TtansAM;
hterpretation of the simulation output;
Modification to the system configuration (Le., pipe strengths and tanks
caiculations where appropriate);
Cost and fitness calcdations;
Operation of GA program; and
Generation of the output file that includes the costs and nodal pressures.
When considering transients in the optimization process, the execution process
creates some dificulties. Because the dynamic performance and the system
characteristics or designs are interdependent. The dynamic performance of the system
was determined by the system characteristics. However, the correct selection of the
system characteristics (especially to the pipe strength and diameter) cannot be detennined
without knowledge of the transient pressures they must withstand.
To overcome this difficulty, an iterative procedure was utilized by the master
program. It first detennines the bydraulic parameters in steady state conditions and the
pipe diameters were selected based on the steady state pressures. The system was
subjected to a rapid valve closure at source and demand locations using the transient
simulation program. The master program then interprets the output file and modifies pipe
FIuid Transient and Pibeline O~timization Usinn Genetic Algorithms 109
diameters. The pipe diameters were adjusted in accordance with the maximum pressures
produced by the valve closure. Then, the program determines the upgraded design for
steady state conditions- A new &ta file that incorporates the upgraded system
characteristics and steaày state conciitions is created and subrnitted for simulation. The
output file h m the simulation was analyzed. The pipe diameter was not modifieci;
instead pipeline pressures are screened against the design envelope (i.e., maximum and
minimum permim'ble line pressures).
If a design makes it through the screening exercise, and if no TransAM errors were
encountered, then the system was considered viable. The cost functions relevant to the
site under consideration as describeci in chapter 6 are applied to these viable systems.
The costs and pressure summaries for the viable designs were stored in a file- The
systems in this file define the population of feasibte designs for the given site. This
population of viable designs represents the solution space for the optimization process.
The master prognun completes the optimization process by searching the solution
space/file of viable designs and identiQing the least cost design.
In addition, to the identification of the least cost or optimd design, the mastet
program was aiso capable of summarising the performance of the various design
strategies employed in the context of the site under consideration.
Details regarding the operation of this module are presented in Figure 7.2. A h , the
input data for the master program is given in Appendix D, including the graphic resdts
(see Figure D. 1.1 , D. 1.2, D. 1 -3, D. 1.4) and solutions.
Fluid Transient and Pimline Ostimization Usinn Genetic Alnorithms 110
GA MODULE v
Generate initiai population K7
Decode each string to the comsponding decision variables
Write design and penomiance data to file K7
Compute each of the network costs in the generation v
Compute penalty cost for each network
Compute the total cost of network T 7
Evaluate the fitness of system T7
Reproduction
Has the fixed number of evaluations, No <- hction of chromosome, been reached ?
K7 Yes v
Have termination criteria k e n met? C) NO 0 Back t o v I
Fluid Transient and Pimline Obtimization Usinn Genetic Akorithms 111
7.4.2 TRANSlENT SIMULATION PROGRAM
The transient simulations required by the process were obtaiwd using the TransAM
program. In Section 2.2, the author has discussed this program.
The system describeci in section 7.1 was represented in the mode1 by 20 nodes and 21
pipes as illustnited in Table 7.1 and 7.2. The input data file is given in Appendix C. A
summaq of the use of the TransAM progtam is shown in the Figure 7.3:
TnnsAM MODULE I/
Simulate steady state peiformance T 7
Create input file for transient simulation v
Transient simulation of initial design v
Evaluate performance of initial design v
ModiQ initial design in pipeline HGL -7'
Simulate steady state performance of rnodified design -7'
Create input file for transient simulation of modified design v
Transient simulation of modined design v
Evduate performance of modified design
Finure 7.3 Flowchart Re~resentation of TmnsAM
Fluid Transient and Pibeline Obtimization Usinn Genetic Alnorithms 112
As mentioned in Section 7.1, cavity formation iaduced by valve closure was possible
at nodes 16, 17, 18, 19, or 20. To simulate vapoumus cavitation at internal pipe sections,
a parameter, VAPCAV, in TransAM program is used. If VAPCAV = 1, vapour cavities
will be permitted to form at internal pipe section locations whenever the pipe pressure is
less than or equal to the vapour pressure. Without consideration of vapourous cavitation
in pipeline, the negative pressure predicted may be both extreme and impractical.
7.4.3 RUN PROCEDWRE
The simple genetic algorithm formulation is applied to the New York City Water
Supply Tunnels problem. A Cbit binary coded substring permits repcesentation of 10
discrete alternative choices for a design variable. Since there are 21 existing pipes in the
New York City tunnels that may be changed or dupiicated, the coded strings representing
a trial pipe network design are constnrcted of 84 binary bits (21 by 4-bit coded
substrings). As has been mentioned, the result is a vast solution space of 102' different
pipe network desigm. The GA runs were allowed 50,000 evaluations of different designs.
The nurnber of designs is thus an extremely small k t i o n of the total solution space. The
50,000 evaluations were executed on a pentiurn II computer with a run time of
approximately 70 hours.
The cost coefficient pressure violation is a constant of a hydraulic grade line violation
per foot of pressure head deficit A particular level of the cost coefficient sets the severity
of penalty costs irnposed. The selected value of the cost coefficient must produce penalty
costs such that near-optimal infeasible solutions cost slightly more than the optimal
Fluid Transient and Pibeline Optirnization Osinn Genetic Alnorithms 113
solution. The optimal solution is not usually hown, and an appropriate value of the cost
coefficient of pressure violation differs h m one problem to the other. As a result, a lot of
trial and error adjustments of the cost coefficient of pressure violation are necessary. The
reference value of the cost coefficient is based on the research of Dandy et ai, (1996). The
number of infëasible network solutions present in the search and the feasibility of the
lowest-cost network solutions determined by the search should provide an indication of
the suitabiüity of the chosen value of the cost codficient of preçsure violation.
Details of a case study, the New York City Water Supply Tunnels problem, were
described in this chapter. The implementation of genetic aigorithms was possible through
the use of a personal computer with sufficient speed. A number of decision variables used
in optirnization program are addressed. in this chapter, a master program that utilizes the
transient simulation program TransAM was developed to determine the optimal design
for the case study descrikd in section 7.1. The execution of the comprehensive
optimization procedures on a 300 MHz pentium il computer was successful and the
outcome of the procedures is discussed in the next chapter.
Fluid Transient and Pibeline Oatimization Usine Genctïc Aleorithms 114
CHAPTER 8
OUTCOMES AND DISCUSSION
This chapter presents the results and discusses the performance of îhe GA approach
for optirnizing the case study describai in Chapter 7. The previous search works h m
other researchers are discussed and analyzed as well. The previous case studies which
neglected transient considerations are addressed first.
8.1 PREVIOUS CASE STUDlES
A number of studies in pipe network optimization have examined the expansion of
the New York Water Supply Tunnels (Schaake and Lai, 2969; Quindry et al., 198 1;
Gessler, 1982; Morgan and Godter, 1985; Bhave, 1985; Kessler, 1988; Fujiwara and
Khang, 1990; Murphy et ai., 1993; Dandy et al., 1996). Originally, the New York City
Water Supply tunnels were considered by Schaake and Lai (1969) as a case study to
demonstrate the effectiveness of their techniques. Mer ht, a number of studies in pipe
network optimization have applied it to their respective approaches. The best results
found in previous optimization studies are surnmarized in Table 8.1 (Fujiwara md
Khang, 1990; Dandy et ai., 1996).
in these papers, a continuous diameter design is an optimized set of pipe diameters
that may take on any continuous reai value, while a discrete diameter design is a set of
Fluid Transient and Pidine Obtimitation Usinn Genetic Alvorithms 11s
pipe diameters that are selected h m a specified set of pipe sizes. On the other hanci, a
split pipe design may be derived h m a continuous diameter into partial lengths of the
two adjacent discrete diameters (one small and one larger) to create a pipe with
equivalent hydraulic properties.
Table 8.1 Comparative Designs for the New York Tunnels Pmblem 1 1 DUmetcrs of Dupiicate Tunnels, inches 1
Pipe
1
2
3
4
5
6
7
8
9
10
1 I
12
13
14
Dia.
Design
Schaakc &Lai (1%9)
52.02
49.90
63 -4 1
55.59
5725
59.19
59.06
54.95
0.0
0.0
116.21
12525
126.87
133.07
C
Savic Et al.
(1997)
O
O
O
O
O
O
1 0 8
O
O
O
O
O
O
O
Morgan Md
Goulta c issn
O
C
E3be (1985)
O
O
O
O
O
O
O
O
O
O
O
O
O
O
Q u i n e ual .
(1981)
O
O
O
O
O
O
O
O
O
O
119.02
134.39
132.49
132.87
Cmlcr (1982)
O
O
O
O
O
O
1 0 0
100
O
O
O
O
O
O
D
Dandy Et al. ((1996)
O
Krrrkr (1988)
O
O
O
O
O
O
O
O
O
O
O
O
O
O
C
Fuji- Pnd K)Png sm)
O
O
O
O
O
O
1 44
O
O
O
O
O
O
O
[ Mumhy Et al. (1993a)
O
O
O
O
O
O
73 -62
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
D
O
O
O
O
O
O
O
O
O
O
O
O
O
S C D D D
Fluid Transient and Piwhe OMimization Usinn Generic Alvorithms 116
As the mention above, Schaake and Lai (1969) used a linear programming approach
to fïnd optimal pipe diameters for assumed values of the total head at each node. The
decision variable for each pipe was its diameter r a i d to the power 2.63, thus leading to a
set of linear constraints. Non-hear terms in the objective fünction were appmximated
using piecewise linearization. No check was made to detennine whether assumed nodal
heads led to an optimum solution overaii- As shown in Table 8.1, the final solution
obtauied involves duplicating almost al1 pipes in the system at a cost of $78.09 million
(al1 costs in this paper are givm in 1969 dollars). As the minimum cost solution to a pipe
network problem with one demmd pattern and no constraints on minimum pipe
diameters tends toward a brancheci system, it is expected a better solution is possible by
duplicating fewer tunnels.
Quindry et al. (1981) developed an extension of the linear programming approach
developed by Schaake and Lai (1969). The optimal solution was still obtained by an
assurned set of nodal heads. To identie the relative changes required in nodal heads,
dual variables were used to get the maximum rate of improvement in the objective
fùnction. The heads were then adjusted and the linear program was rem. The iterative
procedure was made until no M e r improvement was obtained. The solution obtained
involves no duplication of city Tunnel number 1. The total cost of the design was $63.58
million.
The optimization mode1 of Gessler (1982) used a partial enurneration technique and
discrete pipe sizes to search a subset of the total solution space. Two separate regions of
the total solution space was searcheci with consideration of the reinfiorcement of either
City Tunnel nurnber 1 or City Tunnel number 2. The lowest-cost discrete diarneter
Fluid Transient and Pibeline mtimization Usina Genetic Alnorithms 117
solution obtained in each case was used as a starting solution for a gradient search
technique that used continuous pipe sizes. The lowest-cost design cons ide~g the
reinforcement of City Tunnel number 1 involved the duplication of seven tunnels. The
total cost of the pmject is !Ml .8 million.
Bhave (1985) applied a simple iterative procedure based on the identification of an
efficient branched configuration. The nodal heads for the branched configuration were
treated as the design variables, and were initiaüy taken so that each existing link needs
strengthening by a new pipe parallel to the existing one, then given the maximum
reduction in system cost. The method is illustrateci through an application to the City
Tunnel number 2 as the branched configuration. The resuits ùivolved the duplication of
only six tunnels at a total cost of $40.18 million,
Morgan and Goulter (1985) developed a heuristic iinear programming-based
procedure for the least cost layout and design of New York water supply tunnels. The
methodology is capable of analyzing a wide range of demand pattern and pipe failure
combinations. A split pipe approach was use4 in which the decision variables were the
lengths of pipe of a specified diameter that replace the curent size. Hydrauiic consistency
is ensured throughout the procedure through the use of the Hardy-Cross network solver
technique. The procedure c m also be extended for use in the expansion or reinforcement
of existing network systems. While the techniques used to reduce the size of the
constra.int set to enable the procedure to handle a wide range of Ioading conditions do not
guarantee global optimality, a pragmatic "reasonable" optimum is achieved. The solution
involves duplicating six tunnels at a cost of $39.2 million.
FIuid Transient and Pipeline htimization Usina Generic Alnorithms 118
A decomposition technique was developed by Kessler (1988) to demonstrate the New
York water supply tunnels problem. First, the heads at the nodes are fixed, and a
minimum concave cost of flow algorithm is used to fhd the pipe flows. These are then
fixed and the head variables are found using a linear progmmmbg. The solution is
continued until convergence is achieved. This split pipe solution shows a local optimum.
The total cost of design is $39 million.
A two-phase decomposition method is proposed by Fujiwara and Khang (1990) for
the optimal design of New York water supply tunnels as well as for the parailel
expansion of existïng ones. The fkt phase of the method uses a gradient approach with
the flow distribution and pumping heads as decision variables and is an extension of the
linear programming gradient method proposed by Alperovits and Shamir (1977) for
nonlinear modeling. A correction was then applied to the assumed flow in each I w p
using the Lagrange multipliers associated with the previous solution. The technique is
iterative and produces a local optimal solution. In the second phase the link head losses of
this local optimal solution are fixed, and the resulting concave program is solved for the
link flows and pumping heads; these then serve to restart the first phase. A nonlinear
optimization mode1 was run that found the optimum flow in each pipe for these nodal
heads. This gave an improved local optimal solution. The whole procedure continues
until no fiirther improvement can be achieved. The authors proposeci a continuous
diameter pipe solution with a cost of $36.1 million.
Dandy et al., (1996) considered a case study in New York tunnels too. An improved
genetic algorithm formulation was developed using variable power scaling of the fitness
function. In addition to the more commonly used bitwise mutation operator, an adjacency
Fluid Transient and Piwfine ODtirn-on us in^ Genetic Alnorithm 119
or creeping mutation operator is introduced. Finaily, gray codes rather than binary codes
are used to represent the set of decision variables which make up the pipe network
design. Results h m the GA are compareci to previous complete entuneration, linear,
nonlinear and dynamic programming. They evduated the efficiency and effectiveness of
the methods under steady state conditions. The least-cost of this approach is $38.8
million by ushg discrete diameters.
Savic et al. (1997) developed a cornputer model, GANf.=T, which aiso involves the
application of genetic dgorithms to the problem of least-cost design of water distribution
works. Genetic algonthms are introduced in their original form followed by different
improvements that were found to be necessary for their effective implementation in the
optimization of water distribution networks. An example taken fiom the literature
illustrates the approach used for the formulation of the problem- To illustrate the
capability of GANET to efficiently ident* good designs, three previously published
problems were solved. Two network examples, including New York water supply
tunnels, illustrate the potential of GANET as a tool for water distribution network
planning and management. The total cost obtained for the New York problem was $37.13
million.
The common objective of the studies was to determine the most economidly
effective design for additions to the existing system of tunnels that constituted the
primary water distribution system of the city of New York. The same input data, e.g.,
existing pipe data, discrete set of available diameters, and associated unit pipe costs, were
used in this study.
Fluid Transient and Pimline *timitation Usinn Genetic Aborithms 1 20
Due to the age and i n d demands, existuig gravity flow tunnels have been found
to be inadequate to meet the pressure requirements for the projected cowumption level.
ïhe proposed method of expansion was the same as in previous studies, Le., to reinforce
the system by consûucting tunnels parallel to the existing tunnels. The behavior
presented in the foliowing section analyzes the transient performance in New York water
supply tunnels, using genetic algorithms.
8.2 PERFORMANCE OF GA INCLUDING TRANSïENTS
The performance of the genetic algorithm approach to the New York City case study
is addressed in this section. Each GA run used approximately 5.1 seconds of central
processing unit (CPU) time on a Pentium II cornputer. A considerable proportion of this
time is for the hydraulic analysis of each of designs.
The selected value of the cost coefficient for pressure violation is, at least for the
current state of knowledge of pipe behavior, a aial and error procedure. During the
simulation, norninally infeasible GA designs demonstrate substantial cost savings for
some small violations of pressure head constraints. Infeasibility may be acceptable in
some circcumstances, particularly if a small hydradic head deficiency is accompanied by
large cost savings. The value should be chosen such that neawptimal infeasible solutions
almost always cost slightly more than the optimal solutions. The nurnbea of infeasible
network solutions in these GA runs and the feasibility of the lowest-cost network
solutions provide an indication of the suitability of the chosen value of the cost
coefficient of pressure violation. A value of cost coefficient, $50.0 rnillion/fmt,
Fluid Transient and Pibeline mtimization Usinn Genetic Alnorithrns 121
generated many low-cost marginaily infeasible network designs. The result is shown in
Table 7.4 as well.
The TransAM program does not contain a dedicated steady state solver. M e r ,
assurned initial conditions are input as data, o h obtained h m a steady state solver-
However, since most steady state solution techniques produce resdts which contain an
error (out of balance) in either heads or discharges or both, spurious transients may be
introduced. This is pariiculsrly true of the New York City Waîer Supply Tunnels Pmject,
since this problem contains both large and small diameter pipes. TraosAM can be run to
convergence and thus used as a sophisticated steady state solver to tefine or obtain initial
conditions.
During steady state runs, ali devices are in a 'static' condition. To create this situation
in a transient simulation, one must specifjr device operation in such a way as to mimic
these more or less unchanging conditions (McInais et al., 1998). Setting a T~atisAM
parameter INITSS equal to one causes the program to output a record of nodal heads and
consumptions and pipe &ta which may be 'recycleci' as the steady state initiai data. At
the same tirne, the simulation duration (TLAST) was specified. If TLAST is long
enough, e.g., 3 minutes, in this case, the procedure will permit al1 significant transient
behaviour to die out so that steady state conditions are achieved. The simulation results
are shown in Table 8.2, and Table 8.5. A complete nodal &ta specification is required by
TratisAM to construct both pipe flows and boundary condition input data Details of the
results can be found in Appendix C, the input data of TransAM program, including the
graphic results for each nodal. The hydraulic analysis for the projected demands shows
that nodes 16, 17, 18, 19, and 20 fa11 significantly below the required minimum total
Fluid Transient and P i d i n e O~timiPition Usinn Genetic Alnorithrns 122
head. Nodes 1 to 15 have acceptab1e hydraulic grade line elevations. The design datum in
this case study for most ndes is assurned as 100 feet, equd to the minimum required
head minus 155 feet,
Table 8.2 HGL of C u t Study in Steady State Condition
1 Nodal Number 1 Minimum Rcquired HGL in ~t&dy State I 1 Head I 1
2
Difference
O
+36.527
uma (fi) I Condition (fi)
300.0
255.0
300.0
29 1.527
FIuid Transient and Pibeline ODtimization Usine Genetic Alnonthms 123
For transient runs, two issues need to be addressed. One is the vapouruus cavitation
probiem, and the other is the valve closure dwation. As mentioned before, TransAM can
simulate the vapourous cavitation boundary condition. This is signifïcant because if the
negative pressure at some nodes is large, vapourous cavitation is inevitable. N o d l y , no
vapourous cavitation is permitted directly at nodes. (However, to overcome these large
negative pressures, air valves could be used. However, it is beyond the research scope of
this study.) A primary cornparison for determinkg sensitivity of naasient response io
water vapor cavitation is shown in Table 8.3 (see Figure C. 1.1 and C. 1.2 ah ) .
Table 8.3 Comparison of W a l Min. Head with and w/o Cavitation
1 Nodal Number 1 Without Cavitation / With 'In Pipe' Cavitation
The valve closing duration used for this cornparison is fixed at 60 sec. Table 8.3
shows that nodes with negative pressure are improved when vapourous cavitation is
allowed, especially for node 16, 17, 18, 19, and 20. So, vapoufous cavitation shouid be
considered in this analysis.
The second issue relating to the transient analysis is the valve closure duration. The
different duration will aimost certainly create different cesults of network. A cornparison
of influence of closure duration is given in Table 8.4 (also see Figure C. 1.2, C.2.1, C.2.2,
C.2.3, C.2.4, and C.2.5). The cornparison shows that the system pressure is improved
with the time increasing. if the duration of closure is less than 90 seconds, the system is
threaten by the negative pressure; however, for closures longer than 90 seconds, the
duration has little influence on the system.
The resdts are an indication of the selection of valve closure duration. To simulate
the transient conditions in New York City Water Supply Tunnels project, the valve
closure duration is selected as a relatively short tirne, e-g., 60 seconds. Otherwise, for a
long closure time (e-g., 5 minutes), even though the transients will occur, the system is
still d e without great adjustment to steady state conditions. This conclusion is proven by
the outcome of GA nins. in this case study, two optimai results are obtained, one optimal
result is developed in 60 seconds valve closure duration, the other valve closure duration
is 300 seconds. Details of the valve closure duration are shown in Table 8.5, Table 8.6
and Table 8.7. Table 8.4 provides a good cornparison of these simuiation runs with
different valve closure duration. The nodal minimum heads reveal that the greater the
valve closure duration, the less the infîuence of transient conditions. This result is
reasonable and expected.
FI uid Transien t and Pi~eline Obtiminition Using Genetic Alnorithm 125
Table 8.4 Compatûon of Nodd Mia. Head for Diffcrent Valve Ciosure Duration
As rnentioned before, in this case study, the valve closwe duration is selected as 60
seconds and 300 seconds. The best solutions are given in Table 8.5, Table 8.6 and Table
8.7 respectively. Since GAs are stochastic-search techniques, the solution found was not
always the same and therefore, several runs were necessary to ensure that the solution
Fluid Transient and Pibeline Optirnization Usinn Genctic Algorithms 126
identified were of good quaiity. The graphic redts of hydraulic performance in transient
conditions can be seen in Appendix D (see Figure D. 1.1, D. 1.2, D. 1.3 and D. 1.4).
Table 8.5 Optimal Sol~tion of Case Study
Pipe
No.
1
2
From
Node
To 1 Existing 1 Initial 1 Optimal 1 New Dia. 1 New Dia.
2
(iaches)
180
(eh) 873.7
(h) 873.66
((60 closure) -
(Sm. closure) -
Fluid Transient and Piwline Obtimization Usinn Genetic Alnorithm 127
8.3 LEAST COST DESIGNS
The least-cost GA designs for 60 second and 3 0 second closures are s h o w in Table
8.6 and Table 8.7. For the 60 second closure, the system duplicates pipe 15 at the
upstream end of City Tunnel number 2. The result also indifates pipe 16, 17, 18, 19 and
21 require duplication. The total cost of least-cost design is $67.60 million. Compared to
praious research (see section 8.1), the design accouatuig for transient considerations is
more expensive. However, the network system is d e r and slightly better behaved than
the final solution of other previous designs (see Table 8.1) with steady state
considerations alone. For the 300 second closw, the system requires little adjustment
compared to previous studies. In this case, the system needs replacement of pipes
numbered 16, 17, 18, 19, and 21. The total cost for the 300 second closure design is
$36.67 million, a smdl difference compared to the previous studies.
Table 8.6 ResulQ of GA Runs (60 sec. closure)
I 1 Diameter (fctt) ( Diameter (fwt) 1 (fcet) 1 (SM) 1 Pipe Number
I 1 1
Total Cost: $67.60 million L J
Note: Imperia1 units are used to facilitate cornparison with previous studies.
Existing Du plicated Length Cost
Fluid Transient and Pi~el ine O~timization Usinn Gcnetic Alnorithm - 128
Tabk 8.7 R u a l b of GA Runs (300 sec. closure)
Total Cost: !§ 36.37 million I
Pipe Number
16
17
18
19
20
21
Note: Imperia1 units are used to facilitate cornparison with previous studies.
Table 8.8 and Table 8.9 show the corresponding total hydraulic heads at several
critical nodes, e.g., 16, 17, 18, 19, 20, and 21, before the system optimization and &er
network optimization. It can be found that the system becomes safer h m the view of
nodal heads. The negative pressure has been improved, due to the duplication of
diameters in some pipes. In this case, the optimal solution meets the hydraulic
requirements under transient conditions. The graphic results for 60 second closure are
shown in Figure D. 1.1, D. 1.2, D.1.3 and D.1.4. For the 300 second closure, the system
becomes safer as well. Details of the hydraulic d y s i s are presented in Table 8.9.
Cost
(SM)
7.0488
1 1.388
6.4080
3.1824
O
8.3424
Length
(f-t)
26,400.0
3 1,200.0
24,000.0
14,400.0
38,400.0
26,400.0
ExWîïng
Diameter (fcct)
6
6
Duplicatcd
Diameter (fkct)
7
9
5
5
5
6
7
6
O
8
Fluid Transient and Piwline Optirnïzatïon Usinn Genetic Alaorithrns 129
Table 8.8 Hydnulic Analysis for CA Designs (60 sec. closure)
1 Node 1 Before Optimization 1 A f k Optimization 1 1 Number
1 Min. ~ e a d ' O 1 25.3 1 O 2.0 1 #1 HGL
1 Min. Head 1 -27.426 1 -3 .4 1 3 -82 1 1 1.8
Steady State
@et)
295.930
Steady State Transient (feet)
#17 HGL Min. Head #18 HGL Min, Head
Note: Negative value indicates the viotated pressure;
* In steady state, minimum head = HGL - minimum quired head;
In transient, minimum head = HGL - design daîum.
Transient (feet)
170.3
Min. Head #20 HGL Min. Head
Table 8.9 Hydrauiic Analysis for GA Desigas (300 sec. closure)
@et)
295.934 I 147.0 1
1 Node 1 Before Optimization I After Optimizsition I
270.876 1 -63.6
-101 -725 23 1.884 -23.1 16
272,990 1 156.4 -1 -924 193.040 -38.04
0.190 276.364 2 1 -364
-1 63.6 101.3
1.3
Steady State 1 Number / (-1
38.6 192.8 92.8
2.3 23 1.9 131.9
- -33.6 22 1.3 12 1.3
#1 HGL Min. ~ e a d #16 HGL Min. Head
25.664 271.158 16.158
Transient (feet)
#17 HGL Min. Head #18 HGL Min. Head #19 HGL Min. Head #20 HGL Min. Head
295.930 O
232.574 -27.426
Steady State
( feet)
- -
270.876 - 1.924
193 .O40 -38.04
1 53.275 -101.725 23 1.884 -23.1 16
Transient (feet)
170.3 25.3 96.6 -3.4
295,937 O
265.467 5.467
252.4 134.6 193 .O
-63.6 -163.6 101.3
283.2 138.2 232.6 127.6
7
273.1 10 0.3 1
264.734 1.3
-66.4 -33.6 221.3 121.3
9.734 256.482
1 .482 26 1.224 6.224
93 .O 185.6 85.6
23 1.9 131.9
Flu id Transient and P i d i n e Optimization Usinn Genetic Al~orithms 130
This chapter first reviews previous studies of New York City Water Supply Tunnels
Project. These previous studies are always focus on the steady smte research by some
optimization approaches, such as 1inea.r programming, non-linear programming,
enurneration approach and genetic algorithms. in this thesis, a transient consideration is
introduced by an upstream valve closure. To implement thîs rnethud, a GA program
coupled to the transient analysis program, T r a n s e is developed. The performance of
simple genetic algorithm forxnulations applied to the New York City tunnels problem was
investigated. The optimization results are given and discussed. In addition, these resuits
have been compared to solutions obtained previously in the literature using other
techniques. Aithough this solution (for 60 second valve closure) is more expensive, it
yields a better performance than that of previous studies. Also, as the valve closure time
increases (e.g., to 300 seconds), the influence of transient conditions is decreased. This
gives a sense to the relationship between fluid transients, valve closures and optimal
designs. The following c hapter presents conclusions of this study .
Fluid Transient and Pi~e l ine Outimization us in^ Genctic Akorithms 131
CHAPTER 9
CONCLUSIONS
in this thesis, the si@cance of fluid ttansients on the optimal design of pipe
systems is discussed, FIuid ttansients play a significant mle for most water distribution
systems, even though optimization approaches have traditiondy not considered them.
However, the inclusion of transient analysis in pipeline optimization is reasonable and
feasible through a simuiation approach and with improvements in computer technology.
The presented work attempts to obtain a more complete solution to the problem of
optimal design of water distribution networks. The proposal mode1 is capable of handlhg
almost al1 standard and nonstandard components of pipe networks including pipes,
pumps, reservoirs, check valves, air valves, pressure-reducing valves and air chambers.
The optimization problem is addressed here using a genetic algorithm approach.
Genetic algorithms are extremely powemil techniques which are capable of fmding the
least cost solution in relatively few hydraulic simuiations. In addition, a genetic algorithm
can generate near optimal solutions for the designer. At the same t h e , the GA approach
is simple to implement and represents an opportunity to achieve large savings in the cost
of water supply system. This thesis has examined the mechanics, power, and application
Fluid Transient and Piwline Obtimiration Usinn Gcnctic Al~orithms 132
of the GA approach for the optimal solution of a pipeline engineering optimization
problem.
A simple GA coasisting of reproduction, crossover, and mutation is shown to be
capable of finding near optimal solutions. The optimization scheme incorporates both
steady state and transient concerns and is shown to be feasible through a case study of a
pipeline system that consists of a reservoir and 21 pipes. The specific pipeline is the well-
known New York City Water Supply Tunnels project. The design flow considered is
201 7.5 A)/s (= 57.13 m3/s). The route of the looped network is fixeci. Profile changes are
not considered feasible for the case study.
Severai design measures are considered, but primary emphasis is on the change of
pipe diameter. Al1 reasonable combinations are considered in the design appmach. The
complexity of the optimal problems for water distribution is extremely high. This thesis
tries to describe a near global objective fiiaction. It takes into account not only capital
cost of system components, but also the operating costs (with consideration for the cost
of money, depreciation, inflation, energy, manpower, and maintenance costs). The
combinatorial optimization problem of least-cost design water distribution systems is
formulated and it is show that GAs are suited to =Ive this kind of problem.
This study of the pipeline optimization by GA differs from previous investigations in
that the GA assigns a penalty cost for all pipelines which does not satisfy the minimum or
maximum pressure constraints, not ody to the pressure violation at the worst node. The
pressure deficit is multiplied by a penalty factor (e.g., $50.0 million/foot). The penalty
cost is a measure of the worth per foot attributed to pressure heads below the dowable
minimum pressure head or above the allowed maximum pressure head. The penalty cost
should be such thaî near-optimal infeasible solutions are highly fit so that the optimum
solution will be approached h m both above and below.
Although multiple loading conditions were not covered in this study, this
consideration may be achieved without major changes in the program. Because the same
decision variables c m be considered for both singie and multi loading cases. Thus, the
chromosome string length does not have to be changed. The change would only cause an
increase in the nm rime since additional evaluatious of the system's hybulic behavior
under different loading conditions wodd be needd Additions of purnps, in-line devices
and reservoirs, etc., as decision variables can aiso be incorporated into this GA program
(Tang, 1 999), but they are beyoad the scope of this thesis.
The program in this thesis has the ability to integrate management and operationai
aspects of a water supply system analysis and exemplifies the next generation capabilities
of genetic algorithms. For example, consider the problem that defhes an optimal capital
improvement program to meet yearly increasing demands over a long term planning
horizon, within specified annual capital and operathg budget constraints. The GA
optimization program can solve this problem directiy using adjustments of input constant
parameters and thus can find the solution automatically.
Although the program used in this thesis is only a research tool, it is not complicated
to use and does not require a large amount of mathematid sophistication for
understanding of its mechanisms. The interface program makes it easy to input the data
step by step.
The results are used to make a comparative study and provide insight into the
expected performance of solutions identifiai in past studies. The process required three
Fluid Transient and Piwline Or,tirnization Usinn Genetic Al~orithms 134
days to explore the solution space and identiQ the optimal solution using a 300 MHz
pentium II cornputer. The optimal design for the case study comprises of six duplicated
pipes with an expected cost of $67.60 million. This cost is more expensive than the
steady state design which is at cïsk h m rapid valve closure. The cornparison of the
solutions shows that this work pduced a good and d e design, even though the cost is
more expensive. Moreover, the research community involved in optimization of water
distribution networks has starteci to become aware of the shortcomings of the methods,
which are able to find only local minima (Hansen et al., 199 1 ; Eiger et al., 1994).
Although GAs carmot -tee that the global optimum is fouad, they have been
successfûlly applied to the design of water distribution networks. in addition, the research
method is conceptually simple and has a global sampling capability.
Fluid Transien t and Pi~eline ODtim W o n Usinn Genetic Alnorithms 135
CHAPTER 10
FUTURE WORK
In this thesis, a global objective fùnction which considered d l standard and non-
standard components is formulated to get a more complete optimization solution.
. . However, for pipeline optunization, the cost fùnction of each component in networks
needs to be more fûlly developed. In addition, the exponent coefficient in some cost
functions needs more research to create a more reasonable value.
In this thesis, the objective fimction has included most components of pipeline, the
operational set points for them, cost of service issues, long-tem capitai cost issues as a
function of tirne of day energy costs. However, some aspects, such as seasonal usage
Ievel, fire flow storage sizing and system storage sizing and placement, should be
considered to obtain a comprehensive objective function.
In addition, the GA approach could be incorporatecl into other research areas, such as
water resources planning, drought analysis, water quality parameters, emergency
planning, and system reliability analysis. These issues may be combined with the
program developed in this thesis to create a more p o w d optimization system.
Fluid Transient and Pipeline - Optimization us in^ Genetic Alnorithms 136
The vaiue of genetic algorithms is in their ability to reduce the workload, such as
computing t h e and cornputer memory, associated with the comprehensive optimization
of a network design to feasible level.
Fluid Transient and Piwline - O@mization Usinn Genaic Al~orithms 137
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Fluid Transient and Pipeline Oi>timization Usine Genetic Alnorithms 151
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Fluid Transient and Piwline *timizaîion Usinn Genetic Alnorithms 152
APPENDM A
INPUT DATA FOR USER
A.l DESCRIPTION
Based on the analysis in chapter 6, we write the cost function of pipeline system, as
following:
1. extra high pressure condition
Minimize C = pipe cost + pump system cost + device cost + reservou cost
+ electrïcity cost + O & M cost + performance cost
=Mp+Mp+(ZMv+ME)+Mt+PWxM,+PWxM,+Mh
=Cm x Wp x L+CixCup X Q ~ ~ - ~ X
+ xCvi x (ESvi /ES*)= + Cc x V, x H s + (Ca + CM x Vmu)
+PWxExTxQ,xH,xyxk&+PWx&
bsortn +Chtorhs~~(H~i-Hmax) boto or psi
if HPi > H- (steady state)
or if H, r Hmt (transient condition)
2. extra low pressure condition
Minimize C = pipe cost + pump system cost + device cost + reservoir cost
Fluid Transient and Pixwline Obtimiziuion Usinn Genetic Alnorithms 153
where:
Mp = capital cost of pipe ($)
M, = capital cost of pump system ($)
Mv = capital cost of in-he valves ($)
M, = capital cost of air chamber ($)
Mt = capital cost of reservoir (a)
M, = cost of electrïcity ($)
Mm = costs of maintenance and operating ($)
Mh = penalty of hydrauiic violation ($1
P W = present worth factor
This appendix is divided into several sections, each of which describes the input that
requirements for a special data subset needed by the program user. In each of sections,
Fluid Transient and Piwline Optimization Usinn Genetic Aleonthms 1 54
the individual set of data is explained, and input formats for pmgram are outlined The
data groups have been divided into several parts:
TRANSAM data file
0 Cornpleted or simulated TRANSAM output file
Input data file
1 - Cost data source file
2- Parameters & constants Aatir f71e
Before we show the final input data, the details of these date are described in the
following sections.
A.2 PIPE COST DATA
The cost of pipe is equal to following:
Mp=Cmx W p x L
and, the mass of wall material of pipe, Wp (in kg/m or lb/tt), is as follow:
Then, we have the follow input data:
Cm - A Constant (REAL). An input cost coefficient depending on the pipe material. In
this work, we assume it nominally at $2,00O/kg (or S908Ab).
FIuid Transient and Pibeline Obtimization Usinn Genetic Alnorithms 155
L - The Total Length of Pipeüne (REAL). In TRANSAM program, the exact length of
each pipe is calculated h m the profile of the pipe. It can be calculated h m TRANSAM
program. This is a reai variable and should be given in feet or meters.
D - Pipe Diameter of Pipe (REAL). The intemal diameter of the pipe in meters or feet
Actual (not nominal) pipe diameten should be used whenever possible.
y - Unit Weight of Fîiiid (REAL). This is a real variable in W/m3 or lb&. For the
water, it is 9.8 1 kN/rn3.
H - Fluid Pressure Head of Pipe (REAL). It is the design pressure of pipe and is
provided by manufacturer. The unit is meters or feet.
CF*, - Circumferential Stress (REAL). It is ailowable level of circumferential stress of
the pipe. This is an input real variable in MPa or psi.
p, - Material Density (REAL). The pipe materid density in kg/m3 or lb/&
A 3 PUMP COST DATA
The pump cost equation is as following:
0.7 M,=C.xC,xQ, xHw 0.4
So, the input data is as following:
C. - A Constant (REAL). It is a input t h e coefficient changing with the year. It is
assumed as 1.1 4 in 1 999.
Cu, - An Unit Exchange Coefficient (REAL). It is a constant in $ x s0-7/m2' or $ x sO-'
flb2". In this work, we assume it norninally at $690,000 s'-'/mu (or $35,390 so" /lb23.
Ftuid Transient and Pipeline Optirnization Usinn Genetic Algorithm 156
Qp, - Rateâ Discharge (REAL). The rated discharge, given in cubic meters per second
or cubic feet per second, for each pump in sequence.
H, - Rated Head (REAL). The rated dynamic head for each pump. Head is expressed
in either feet or meters.
A.4 DEVICE COST DATA
We have considered five kinds of devices. The costs of them have been show in 1st
report. The cost is follow:
where:
cva - Cost Coefficient of Air Vaive Cost (REAL). An input cost coeficient depending
on the air valve. In this work, we assume it nominally at $2,000.
C,, - Cost Coefficient of Pressure Relief Valve Cost (REAL). An input cost
coefficient depending on the pressure relief valve. In this work, we assume it norninally
at $4,000.
Cvc - Cost Coencient of Check Valve Cost (REAL). An input cost coefficient
depending on the check valve. In this work, we assume it nominally at $4,000.
ESVi - Valve Discharge Constant (REAL). The input variable ES, effective coefficient
of discharge, corresponds to Qo / H ~ ' ~ for flow in the normal or positive sense.
ES,, = discharge constant for air valve.
ESvp = discharge constant for pressure relief valve.
Fluid Transient and Pibeline Obtimimtion Usinn Genetic Alnorithms 157
ESvc = discharge constant for check valve.
ES* - Known Valve Discharge Constant (REAL). This value corresponds to the valve
shown in Laine (1996) table. ES, and ES' are dimensional quantities but the only
requirement is for those to be expressed in consistent units.
a - A Constant (REAL). It is an exponential adjustment coefficient for the valve
discharge coefficient. in this work, we assume it as 1 .O.
One way surge tanks are discussed in next section.
For an air chamber, the cost equation is given:
M x = C C x V , x H x
The volume equation is that:
where:
Cc - A Constant (REAL). It is an input cost coefficient depending on the air chamber
size. In this paper, we assume it nominally at $2,000/rn~ (or $1 7.26/ft4).
6Zik = ZS1 (REAL). The height of air chamber in meters or feet corresponding to
Segment 1.
622r = ZS2 (REAL). The height of air chamber in metea or feet corresponding to
Segment 2.
i = NSA (REAL). The index of the cutting plane which marks the beginning of Segment
1.
Fluid Transient and Pi~e l ine Obtimization us in^ Genetic Aleoritfvns 158
j = NEA (REAL). The index of the cutting plane which marks the end of Segment 1.
n = NAREA (INTEGER). The total number of tabulated cross sectional areas describing
both Segment 1 and Segment 2.
Ar = ACA (REAL). The actual tabulated m s s sectional areas (in m2 or fl?) starting fiom
the bottom of the air chamber.
Ha, - The Pressure In Air Chamber (REAL). It can calculate h m TRANSAM
program in meters or feet
A.5 RESERVOIIUTANK COST DATA
The cost or tank is given:
M t = C n + C u t ~ V n u r
where, the volume of tank is as follow:
V , , , = b Z l k x A k + 2 6 Z Z k x A k + 6 Z I k x A k k = l k = 1
Cu, - A Unit Exchange Coefficient (REAL). It is an input constant in $lm3 or $/p. in
this work, we assume it nominaily at $140/m3 or $3.96/ft).
CH - A Constant (REAL). An input cost coefficient. In this paper, we assume it
nominally at $300,000.
For the tank volume, the input data is the same as air chamber.
Fluid Transient and Piwline ODtirn-on Usinn Genetic Alnorithms 159
A.6 ELECTRICITY COST DATA
The cost is given:
hrI ,=HPxExT
in which,
So, the input data is that:
Q, - Average Discharge (REAL). The average discharge, given in cubic meters per
second or cubic feet per second, for each pump in sequence.
He - Average Head (REAL). The average dynamic head for each purnp. Head is
expressed in either feet or meters.
y - Unit Weight of Fluid (REAL). This is a real variable in kN/m3 or lb/P. For the
water, it is 9.81 kN/m3.
q(=ER) - Average Pump Effaciency (REAL). The average efficiency of each pump
given as a decimal vaiue, i.e., an average efficiency of 87% will be input as 0.87.
HP - Power Consumption (REAL). It is total electncal requirement of purnp, kW.
E - Price of Energy (REAL). The price couId be changed with tirne, %/kWhr.
T - Pump Operathg Time (MTEGER). It is the nurnber of hours per year for pump
operation, it depends on the users and the maximum vaiue is 8760 hours (365 days).
k, = unit conversion factor, 1 /55O in imperid units
or 1/75 in S I units
Fluid Transient and Piwline Omimization Usinn Genetic A lnorithms 1 60
A.? O & M COST DATA
The maintenance and operating costs, Cm, is a percentage, Pi, of the capital costs. As
a result,
Coni=Ppx Mp+Pp. x M p a + D i x Myi+Prx Mr+PtxMt
So, each capital cost has its percentage. We should input them as follow:
P, - A Constant (REAL). The percentage of pipe capital cost gives as a decimal value.
In this work, we assume it as O. 1.
P, - A Constant (REAL). The percentage of pump capital cost gives as a decimal
value. in this work, we assume it as 0.2.
Pt - A Constant (REAL). The percentage of capital cost of reservoidtank gives as a
decimai value- In this work, we assume it as 0.15.
P. - A Constant (REAL). The percentage of capital cost of combination air valve gives
as a decimal value. in this work, we assume it as O. 1.
Pr - A Constant (REAL). The percentage of capital coa of pressure relief valve gives
as a decimal value. in this work, we assume it as 0.1.
P, - A Constant (REAL). The percentage of capital cost of check valve gives as a
decimal value. In this work, we assume it as 0.1,
P., - A Conatant (REAL). The percentage of capital COS of air chamber gives as a
decimal value. In this work, we assume it as 0.15.
FI uid Transient and Pi~eline Obtimization us in^ Genetic Alnorithms 161
A.% PERFORMANCE COST DATA
Once we have detected non-feasible solution, we need to penalize the solution for its
lack of performance. A proportional extent of hydradic constraint violation is W c d t to
defme and the calculation stops. The next equation is proposeci by this paper:
b~ CM a M h = Cht a hr X Z(Hpi -&MX) Lpo a or psi if Hfi 2 H- (steady tat te)
or if Hpi 2 Hm,, (transient condition)
Mh = Cht or hs bsorbt
x ( H i m i x L, or psi if Hpi C HmVLs (steady state)
or if Hpi S HmkI (transient condition)
where:
Mh -- penalty of hydradic violation (S).
C h s - A Constant (REAL). An input cost coefficient of performance for steady state
condition. in this work, it was assumed at $5,000/m2 or $465/p.
Ch, - A Constant (REAL). An input cost coefficient of performance for transient
condition. . In this work, it was assumed at $6,000/m2 or $498/*.
Hpi - Fluid Pressure Head of Each Pipeline (REAL). The maximum or minimum
water head in the corresponding pipeline under transient conditions, which is calculated
fiom TransAM program (m or A).
Hm,, - Maximum Pressure In Each Pipeline (REAL). It is the albwable maximum
pressure in pipeline for steady state (m or A).
Fluid Transient and P i d i n e Obtimization Usine Genetic Alnonthms 1 62
Hminr - Maximum Pressure In Each Pipeline (REAL). It is the allowable minimum
pressure in pipeline for steady state (m or fi)
- Minimum Pressure Ia Each Pipeline (REAL). It is the allowabIe maximum
transient pressure in pipeline (m or ft)
Hminet - Minimum Pressure In Each Pipeline (REAL). It is the allowable minimum
transient pressure in pipeline (m or A)
b, - A Constant (REAL). It is an input expoaential constant for steady nate condition,
assumed 1 .O
bt - A Constaat (REAL). h is an input exponential constant for transient condition,
assumed 1 .O
Lpti - Lengtb of Each Pipeline (REAL). This is the length of the pipeline which does
not satis@ the pressure requirements under transient conditions (m or ft).
Lp,i - Length of Each Pipeüae (REAL). This is the length of the pipeline which does
not satisQ the pressure requirements under steady state conditions (m or fi).
A 9 DISCOUNT RATE
Ln order to get the present worth, we have the follow equation:
Fluid Transient and Pid ine Omimization Usine Genetic Alnorithrns 163
where:
P = the present worth
A = the annual value
n = the operating Iife
i = the discount rate
r = the inflation rate
Then, we need to input the discount rate as follow:
1 - Discount Rate (REAL). It is a positive variable. Ln this paper, we assume it as O. 1.
Every component in water supply systern has its operating life, as following:
N, - Steel Pipe Operatiag Life (INTERGER). In this work, we assume it as 35 years.
Npp - PVC Pipe Operathg Life (INTERGER). in this work, we assume it as 50 years.
N, - Combination Air Vaive Operating Lire (INTERGER). In this work we assume
it as 10 years.
Np" - Pressure Reüet Valve Operating Life (INTERGER). In this work, we assume it
as I O years.
N, - Check Vaive Operating Lifk (INTERGER). In this work, we assume it as 25
years.
Npt - ReservoirlTank Operathg LMe (INTERGER). h this work, we assume it as 20
years.
Fluid Transient and Pi~ei ine O~timization Usinn Genetic Alnondims 1 64
Np, - Air Chamber Operatuig Life (INTERGER). In this work, we assume it as 20
years.
A. 1 1 INFLATION RATE:
We assume that the inflation rate of both O & M and electricity cost is the same.
R - Inflrtioci Rate (REAL). It is a positive variable. ln this work, we assume it as 0.06.
A. 12.1 TRANSAM DATA FILE
To pipe: D
To pump: Qps HP
To in-line valves: ESva ES, ES,
To reservoir/tank: ZS 1 ZS2 NSA NEA NARE ACA
To air chamber: ZS 1 ZS2 NSA NEA NARE ACA
To electricity cost: Q, & ER
A. 12.2 DATA FILE COMPLETED FROM TIWNSAM
To pipe: L
TO performance: Lw L p i Hpi HI-t H- Hmht Hmins
Fluid Transient and Piwline ODtimization Usinp Genetic Alaorithms 165
To air chamber: H,
A. 12.3 INPUT DATA FILE
A. 12.3.1 COST DATA FILE
To pipe: c m
TO pump: Cw
TO valves: Ca Cv Cv,
To air chamber: CC
To reservoir: C, c m
To performance: Chi chs
A. 12.3 -2 PARAMETERS AND CONSTANTS FILE
To pipe:
To pump:
To in-line valves:
To electricity Cost:
To O & M cost:
To peI.formance:
To operating life:
To inflation rate:
H Y Cali PP
Ca
ES* a
Y E T k,
PP p, Pt Pa Pr pc p,
bt bs
N, N, NP NP, NF *, NP,
R
Fluid Transient and Pipeline Obtintization Usinn Genetic Algorithms 1 66
To discount rate: 1
A.13 EXAMPLE OF INPUT DATA FILE
A. 13.1 COST DATA FiLE
To pipe:
To pump:
To valves:
To air chamber:
To reservoir:
To performance:
A. 1 3.2 PARAMETERS AND CONSTANTS FILE
To pipe:
To pump:
To in-line valves:
To electricity Cost:
To O & M cost:
To performance:
To operating life:
To inflation rate:
Fluid Transient and Pipeline Obtimization Usinn Genctic Afnonthms 167
To discount rate: O, 1
Fluid Transient and Piwline ODtimization Usinn Genetic Akonthms 168
APPENDM B
IMPORTANT EVENTS IN THE GENETIC ALGORITHM
COIMIMUNITY
Over the past severai decades, many papers and books have developed or applied
genetic algorithms. in chapter 4, the author reviews a number of these. Further details are
addressed in this appendix. The primary reference for this material is the book, Generic
AIgorifhms and Engineering Design, published by Gen and Cheng in 1997 who overview
these contributions. In addition, a number of references p s t - 1 997 are included.
B.1 BOOKS ON GENETIC ALGOIUTHMS
Probably, the earliest work on genetic algorithms is the focus of the work by Fraser, a
biologist who wanted to simulate evolution with special emphasis on the interaction of
epistasis with selection (14-17). The terni epistasis is used to denote the impact of one
gene-the epistatic one-on the expression of another gene. in the field of genetic
algorithms, the term is used to denote the effect on chromosome fitness of a combination
of alleles, which is aot merely a linear function of the effects of the individual alleles
(1 8).
Fluid Transient and Piwline ODtïmization us in^ Genetic Al~orithms 169
It was not until 1975, when the f h t book Adopution in N~tural and Artzjkial
Sysrem of Holland and the dissertation An Anulysis of the Behavior of a Class of Generic
Adoptive Systerns of De Jong (20) were published (21)' that genetic algorithms theory
attracted the attention of other scientists. ln effect, Hoiland had created the field of
genetic algorithms. The unique features of genetic algorithms has been shaped by the
careful and insightful work of Hoiland and his students (9). in Holiand's works, the
motivation was to design and implewnt robust adaptive systems, capable of d d i n g with
an uncertain and changing environment. His work emphasised the need for systems
which adapt themselves with time to the environment in which they operate. This led to
an initial farnily of reproductive plans, which fomed the basis of what we cal1 simple
genetic algorithms today (22).
Since then, genetic algorithms have gained fame in three important fields: research
into basic genetic algorithm, optimization using genetic algorithm, and machine learning
with classifier systems (9). This research thnist is well descnbed in Goldberg's book of
Genetic Algorithms in Seorch. Optirnizution and Machine Lemning.
Over the past 10 years, applications of genetic algorithms to reai-world problems
have increased greatly. Mmy researchea have been adapting the algorithm to naturai
representations of the search space for a given optimization problem and have developed
new genetic operators that are well suited to the special data structures. Consequently, in
the field of municipal eng inee~g , such extensions and modifications to the genetic
algorithms have led to new ways of solving pipeline optimization problems in a more
efficacious way. This problem-oriented approach demonstrates an enonnous difference
with respect to basic genetic algorithms to the extent the boudaries that of the other
FIuid Transient and Piwline atimization Usinn Genetic Aleorithms 1 70
evolutionary aigorithrns become blurred (1). A good description of the progress made in
the research is discussed in Michalewicz's book entitled Genetic Algorithm + Data
Structures = Evolution Prog~anrs~
In years past, several books on genetic algorithms have been published; a list of these
is provided in Table B. 1. Also, other related compilations and proceedings can be found
in references (24-27).
Table 8.1 Books on Genetic Algorithms
1 1 Year 1 -
Authors Book Title I 1975
1987
1 1 1 Machine Learning 1
Holland(6)
1989
Adaptation in N a m and Artificial Systems
Davis(7) Genetic Algorithms and Simulated Annealing
Goldberg (3)
t 1991
Genetic Algorithrns in Search, Optimization and
Davidor (28)
Davis (9)
Genetic Algorithms and Robotics I
1992 / Koza (29)
1
1 1 Michalewicz (8) 1
1 Genetic Algonthms + Data Stmcture = Evolution
Handbook of Genetic algorithms
Gene tic Programming
Buckles and Petry (68)
I I 1 Programs (2nd edition 1994,3rd edition 1996) 1
Genetic Algorithms
1 1994 1 Bauer (30) 1 Genetic Algorithms and investment Strategies 1 I 1 Grefenstette (3 1 ) 1 Genetic Algorithms for Machine Leamhg I
Bhanu and Lee (32) Genetic L e h g for Adaptive Image
Segmentation
I 1 Koza (33) 1 Genetic Programrning II I
1995
Stender and Hillebrand
(69)
Chambers (34)
' Genetic Aigorithms in Optimhtion, Simulation
and Modelling
Practical Handbook of Genetic Aigorithrns, vols. 1
and 2
Fluid Transient and Piwline ODtimization Usinp Genetic Alnorithms 171
Biethahn and Nissen (36)
--- -
Fogel(37)
Chambers (70)
Wmter et al. (71)
Mitchell (38)
Lawton (39)
Winter et al. (40)
Herrera and Verdegay
(41
Pal and Wang (72)
Devillers (73)
Michalewicz (74)
Back et aI. (42)
Gen and Tsujhura (43)
Sanchez (75)
Man et al. (76)
Quagliarella et al. (77)
Mazumder and Elizabeth
(78)
Evolution and Optimum Seeking I Evolutionary Algorithms in Management
Application
Evolutionary Computation I 1
Practical Handbook of Genetic Algorithms 4
Genetic Algorithrns in Engineering and Computer
Science I 1
An Introduction to Genetic Algocithms
Evoiutionary Algorithms in Theory and Practice
A Practical Guild to Genetic Algorithms in C* 1 Genetic Algorithms in Engineering and Computer I Science I Genetic Algorithms and Soft Computing
Generic Algorithms for Pattern Recognition
Pmgrams (3rd)
Handbook of Evolutionary Computation
Evolutionary Computations intelligent . S ystems
Genetic Algorithms and Fuzzy Logic Systerns:
Sofi Computing Perspectives
Genetic Algorithms for Control and Signal
Genetic Algorithms and Evolution Strategy in
Engineering and Computer Science: Recent 1 Advances and Industrial Application
Genetic Algorithms for VLSI Design, Layout &
Test Automation I
Fluid Transient and Piwline Oi,timimtion Usinn Genetic Alnotithms 172
Over several decades, a number of researchers have applied the genetic algorithm
technique to certain aspects of the design of pipeline systems. A l in of these is provided
in Table B.2 as follows,
Table BI Papers on Cenetic Algorithms
Year
1987
1993
1994
1995
Goldberg and Kuo (84)
Dandy et al. (85)
Simpson et al. (86)
Walter and
Cembrowicz (87)
Walters and Lohbeck
(88)
Murphy et al. (89)
Simpson et al. (90)
Simpson and Goldberg
(91)
Beckwith and Wong
(92)
Davidson and Godter
(93)
Halhal et al. (94)
Mackle et al, (95)
Savic and Walters (96)
Paper Title
Genetic algorithms in pipeline optimization
Review of pipe ietwork optimization techniques
Pipe network optimization using genetic aigorithms
Optimal design of water distribution networks
Optimal layout of tree networks using genetic
algori thms
Optimum design and operation of pumped water
distribution systems
Genetic algorithms compared to other techniques for
pipe optimization
Pipeline optimization via genetic algorithrns: fiom
theory to practice
Genetic aigorithm approach for electric pump
scheduling in water supply systems
Evolution program for design of rectilinear
branched networks
Structured messy genetic aigorithm for the optimal
improvement of water distribution systems
Application of genetic algorithrns to p m p scheduling
for water suppiy
Place of evolution prograrns in pipe network
Fluid Transient and Piwline Omimization Usina Genetic Al~orithms 1 73
Dandy et al. (97) An Unproved genetic algorithm for pipe network
Frey et ai. (98)
1 distribution networks with an evolution program for
optimhtion
Genetic algorithm pipe network optimization: the next
Savic and Walters (99)
generation in distribution system anaiysis
Integration of a mode1 for hydraulic analysis of water
1 genetic algorithm
Takeuchi and Kosugi
(1
Frey and Gransbury
(101)
Haihal et ai. (102)
pressure regulation
Neural network implementation to leak
localization problems of pipe networks
Saving money t h u g h the use of optunization
anal ysis
Water network rehabilitation with structured messy
Reis et al. (1 04) 1 Optimal location of control valves in pipe networks by
Milutin and Bogardi
(103)
Evolution of release allocation patterns within a
multiple-reservoir water supply system
Savic and Walters (105)
: 1 06) 1 economic solution by ushg genetic algorithms I
genetic al gorithm
Genetic algorithms for Ieast-cost design of l
Castillo and Gonzalez
water distribution networks
Distribution network optimization: finding the most
1 using genetic aigorithms I Walters et al. (107)
B.2 CONFERENCES AND WORKSHOPS
Calibration of water distribution network models
Since 1985, several conferences and workshops have been held to provide an
international forum for exchanging new ideas, progress, or experience on genetic
Fluid Transient and Piwline ODtimwon Usinn Genetic Alnorjthms 1 74
algorithms and to promote better understanding and collaborations between the theorists
and practitioners in this field, The major meetings are listed in Table B.2.
Table B3 Conferences on Genetic Algorithms
- --
Coafircace Name
International Conference on Genetic Algonthms
International Conference on Parallel Problem Solving From N a m
IEEE international Conference on Evolutionary Computations
International Conference on Artificial Neurai Nets & Genetic
Algorithms
Annual Conference on Evolutiooary Programmîng
Workshop on Foudation of Genetic Aigonthms
International Workshop on Combinations of Genetic Algorithms and
Neural Networks
AISB Workshop on Evolutionary Cornputhg
Genetic Programming Conference
The Asia-Pacific Conference on Sirnuiated Evolution and Learning
In 1985, a series of biannuai International Conferences on Genetic AIgorithms
(ICGA) were instituted to bring together those researchers who are interested in the
theory and application of genetic algorithms (see Table B.3).
Fluid Transient and P i d i n e Or,timization us in^ Genetic Akorithms 175
Table B.4 International Conference on Cenetic Algorithms
1 Y'?a,= 1 Proceeding Editors 1 Meeting Place 1 1985
1 1991 1 BelewandBooker(12) 1 San Diego, USA 1
I
Grefenstette (44) 1 Pittsburgh, USA
1987
1989
1
1993
1 1997 1 Back (79) 1 Ann Arbor, USA 1
Grefenstette (1 3)
SchafSer (4)
1995
The biannual intemational Conferences on Parallel Problem Solving jFom Nature
(PPSN) is the European equivalent to the ICGA (see Table B.4). The first meeting was
held in Gemany, 1990. The unimg theme of the PPSN conference is natural
cornputaiion, (Le., the design, theoretifal and empincal understanding, and cornparison of
algorithrns gleaned fiom nature together with theu application to rd-world problems in
science and technology).
Cambridge, USA
George Mason University, USA
Forrest (23) Urbana-Champaign, USA
Eshehan (45) Pittsburgh, USA
Table B.5 International Conference on Paraliel Problem Solving from Nature
Meeting Place
Dortmund, Germany
Brussels, Belgiwn
Jenisalem, Israel
Berlin, Gennany
Amsterdam, Netherlands
Year
1990
1992
1994
1996
1998
Proceeding Editors
Schwefel and Manner (46)
Manner and Manderick (1 1)
Davidor, Schwefel and Manner (47)
Ebeling and Voigt (48)
Eiben, BacL, Sxhoenauer and Schwefel(80)
Fluid Transient and Piwl ine Optimization Usine Genetic Algorithms 176
The workshops on Foundation of Genetic Algonthms (FOGA) have k e n Held
biannually, starting in 1990 (see Table B.5). FOGA aitematees with the ICGA. The [CGA
conferences have been held in the odd-numbered years, while the FOGA conferences
have been taking place in the even-numbered years. Both events are sponsored and
organized under the auspices of the International Society for Genetic Algorithms. This
series of meetings provides a forum for the discussion and presentation of theoretical
publications on genetic algorithms.
Table B.6 worksbop on Foundation of Genetic Algoritbms
Year
1990
1992
in 1992, the fim annual conference on evolutionary programrning was held in San
Diego. The series annual meetings were sponsored by the Evolutionary Programming
Society (see Table B.6). Participants were exposed to the field of evolutionary
cornputation in generai, evolutionary programrning, evolution strategies, genetic
algorithms, genetic programming, and cultural algorithrns in particular.
Proceeding Editors
Rawlins (49)
1994
Meeting Place
Blwmington, USA
Whitley (50) Vail, USA
Whitley and Vose (19) Estes Park, USA
Fluid Transient and Pibeline Oi,timization Usinn Genetic AInon'ttims 177
Table B.7 Aanual Conference on Evolutiou y Programming
Year Proceeàing Editors
1 1992 Fogel and Atmar (5 1)
1993 Fogel and Atmar (52)
1994 Sebald and Fogel(5)
1 1995
Meeting Place
McDonneH, Reynolds, and Fogel(53)
1996
1997
1998
San Diego, USA
La Jolla, USA
San Diego, USA
-
Angefine and Back (54)
Angeline et al. (8 1)
Porto, Saravanan, Weagen and Eiben (82)
San Diego, USA
San Diego, USA
Indimapolis, USA
San Diego, USA
In 1993, another series of bimuai meetings were held in Austria, cailed the
International Conference on ArtiGciai Neural Nets and Genetic Algorithms (ANN&GA)
(see Table B.7). The series meetings were devoted to the topics of A . and GA as well
as to the interactions between them.
Table B.% International Conference on Artificial Neural Nets and Genetic
Algorithms
1 1997 l George, Nigel and Rudolf (83) l No-ch. England I
Year
1993
1995
-
Proceeding Editors
Albrecht, Reeves, and Steele (55)
Pearson, Reeves, and Albrecht (56)
- -
Meeting Place
Innsbruck, Austria
Ales, France
Fluid Transient and Piwline Optimization Usinn Genetic Al~orithms 178
Another important annual conference is the IEEE International Conference on
Evolutionary Computation (KEC) (see Table B.8). The first ICEC meeting was held in
Orlando in 1994. The ICEC conferences are sponsored by the IEEE Neural Network
Council and encompass ail the various flavours of this technology including evolution
strategies, evolutionary programmuig, genetic algorithms, and genetic programming.
Table B.9 IEEE Internrrtioarl Conference on Evolutionary Compatatioas
Year
1W4
The AISB workshop on evolutionary cornputhg (10) was held at the University of
Leeds, United Kingdom, in 1994. The workshop was sponsored by the Society for the
Study of Artificial intelligence and Simulation of BehaMour and brought together most of
the people doing research on evolutionary computing in the United Kingdom. Another
European conference on artificial evolution was held in Brest in 1995 (59).
Two workshops, AI'93 and M'94 Workshops on Evolulionmy Computation, were
held in Melbourne and Amiidale, Australia, respectively. Some selected papers from the
workshops were included in an edited volume Progress in Evolutiomry Cornpufation by
X. Yao (6O,6 1). Another international workshop on genetic algorithms and engineering
design was held in Ashikaga, Japan, May 1996. All papers of this workshop were
1995 .- 1996
-
Pmceediag Editors
Fogel(57)
Meeting Place
Orlando, USA -
DeSilva (58)
Fogel(2)
Perth, Australia
Nagoya, Sapan
Fluid Transient and Pibeline O~tirnization us in^ Geaetic Alnorithms 1 79
included in the Proceedings of Mini-Symposium on Genefic Algorithm ami Engineering
Design, edited by M. Gen and K. Ida (62).
The first Asia-Pacific conference on Simuklred Evolution and Learning (SEALT96)
was heId at Kaist, Korea, November 1996, in conjunction with Micro-Robot World Cup
Soccer Tournament (MIROSOT'96) (63). The Fimt Generic Programming (GP)
conference was held at S tdo rd University, July 1996, in Co-operation with the
Association for Computing Machiaery, SIGART, the American Association for Artificial
Intelligence, and the EEE Neural Networks Council (64). The First Internurional
Conference on Evolvable Sysrem was held at Tsukuba, Japan, October 1 996 (65).
B.3 JOURNALS AND SPECIAL ISSUES ON GENETIC ALGORITHMS
The Journal of Evolutionary Cornpufation (De iong, editor-in-chief, MIT Press,
started in 1993) provides a fonun specifically targetuig theoretid publication on genetic
algori thms.
A new International Journal i E E Transactions on Evolutionary Cornpufation was
started in May 1997. The journal particularly emphasizes the practical application of
evolutionary computation and related techniques to solve real problems (The editor-in-
chief is David B. Fogel). Another new one Evolutionory Optirnizution had also been
started in 1997 (Editor-in-Chief is A. Osyczka).
Fluid Transient and Piwline Obtimization Usinp Genetic Alnorithms 180
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Fluid Transient and Pibelinc Obtimization Usine Genetic Alporithms 192
INPUT DATA FOR TRANSAM PROGRAM
*This file dernonstrates the New York City primary water supply tunnel system The
*tunnel systern is a gravity flow system that draws water (201 7.5 feeWs or 57,129.5 Us)
*fiom the Hillview Reservoir at node 1. A single demand pattern was considered for the
'improved tunnel system, and a correspondhg minimum allowable total head was
'specified at each node. The imperial system of units was used to enable *easy
*cornparison with previous studies.
1 GENERAL SYSTEM DATA 1 1 NP NRSP NNODE IPRINT IUNITS DURATION KPCHAR IOUT INITSS
21 1 20 10 2 1000 1 1 O 1 ALIN FRlCTN AITER TOLVAR AFAC VAPCAV VAPHED
1 'DARCY 0.0 0.0 0.15 1 25 1 NXPLOT NTPLOT PLOT3D EGYPLT
41 129 'TPLOT' 'DEFAULT 1 IEPRNT ECALC NEGY NTFC ...... TFC(1) ..-... PHILMT TAULMT
I O O O O 0.02 0.0 1
1 NODE DATA 1 OUT OF 1 NODEID NODEHGL
1 295.930 2 29 1.527 3 285.5 18 4 283.795 5 282.306 6 281.183 7 279.474 8 276.932 9 275.13 1
CONSUMPTION -20 1 7.5 92.40000000 92.40000000 88.20000000 88.20000000 88.20000000 88.20000000 88.20000000
1 70.00000000
BALANCE . m o o
-.000061 -.O00122 .000000 .000000 .00003 1 .000000 .O00015 .O00 137
Fluid Transient and Piwline Ogirnization us in^ Genetic Algorithms 1 93
1 PIPE DATA 1 IGLOBAL LEAK LEAK DAMPING START STOP 1 TYPE RATE FRICTION
NONE' .O00000 .O00 1 PIPE U/S D/S FLOW LENGTH 1 NO NODE NODE (cfs) (fi)
I--- PIPE PROFILE DATA - I
DAMP DAMP 1000.00 1000.00
DIA WAVE VEL. FRIC. LEAK 1 INPUT FAC. .O15 .O1 5 .O15 .O15 .O15 .O1 5 .O15 .O1 5 .O 15 -015 ,015 .O 15 .O 15 .O15 ,015 .O15 .O15 .O15 -015 .O15 .O15
RATE IWAVESP -00 3000.0 .O0 3000.0 .O0 3000.0 .O0 3000.0 .O0 3000.0 .O0 3000.0 -00 3000.0 -00 3000.0 -00 3000.0 -00 3000.0 .O0 3000.0 -00 3000.0 -00 3000.0 .ûû 3000.0 .O0 3000.0 .O0 3000.0 .O0 3000.0 -00 3000.0 .O0 3000.0 .O0 3000.0 .O0 3000.0
1 PIPE 1 1 PID PROFILE POINTS
1 2
Fluid Transient and Pipeline O~timization Usina Genetic Alnorithrns 1 94
1 Station - Elevation Pairs O 145 11600 100
( PIPE 2 1 PID PROFKE POiNTS
2 2 1 Station - Elevation Pairs
11600 100.0 3 1400 100.0
1 PIPE 3 1 PID PROFILE POINTS
3 2 1 Station - Elevation Pairs
3 1400 100.0 38700 100.0
1 PIPE 4 1 PID PROFILE POINTS
4 2 1 Station - Elevation Pairs
38700 100.0 47000 100.0
1 PIPE 5 1 PID PROFILE POINTS
5 2 1 Station - Elevation Pairs
47000 100.0 55600 100.0
( PIPE 6 1 PID PROFILE POINTS
6 2 1 Station - Elevation Pairs
55600 100.0 74700 100.0
1 PIPE 7 1 PID PROFILE POINTS
7 2 1 Station - Elevation Pairs
74700 100.0 84300 100.0
Fluid Transient and Piwline Obtimization Usinn Gdc Al~orithms 195
1 PIPE 8 PID PROFILE POINTS
8 2 ( Station - Elevation Pairs
84300 100.0 96800 100.0
1 PIPE 9 1 PID PROFlLE POINTS
9 2 1 Station - Elevation Pairs
98600 100.0 108200 100-0
IPIPE 10 1 PID PROFILEPOINTS
10 2 ( Station - Elevation Pairs
87400 100.0 98600 100.0
1 PIPE 1 I 1 PID PROFILE POINTS
11 2 1 Station - EIevation Pairs
72900 100.0 87400 100.0
1 PIPE 12 [ PID PROFILE POiNTS
12 2 1 Station - Elevation Pairs
60700 100.0 72900 100.0
1 PIPE 13 1 PID PROFILE POINTS
13 2 1 Station - Elevation Pairs
36600 100.0 60700 100.0
1 PIPE 14 1 PID PROFILE POiMS 14 2
1 Station - Elevation Pairs
Fluid Transient and Piueline Obn'mization Usinn Genetic Algorithms 196
f PIPE 15 1 PID PROFILE POINTS
15 2 1 Station - Elevation Pairs
O 145.0 15500 100-0
1 PIPE 16 1 PID PROFILE POINTS
16 2 1 Station - Elevation Pairs
108200 100.0 134600 117.8
( PIPE 17 1 PID PROFILE POINTS
17 2 1 Station - Elevation Pairs
O 100.0 31200 100.0
1 PIPE 18 1 PID PROFLEPOINTS
18 2 ] Station - Elevation Pairs
31200 100.0 55200 100-0
( PIPE 19 1 PID PROFILE POINTS
19 2 1 Station -- Elevation Pairs
O 100.0 14400 100.0
1 PIPE 20 1 PID PROFILE POINTS
20 2 1 Station - Elevation Pairs
14400 100.0 52800 105.0
Fluid Transient and Piueline ODtimization Using Genetic Alnonthms 197
1 PIPE 21 PID PROFILE POINTS 21 2
1 Station - Elevation Pairs O 100.0
26400 105.0
1 BOCMDARY CONDITION (DEVICE) DATA 1 1 NBDC (Nurnber of Devices)
7
1 Device 1 IS A RESERVOIR 1 BCTVPE NDN BCOUT
'CH RES' 1 'OUTPUT 1 NLBC (node list)
1 1 ZDEV XLRES PERCH AMPCH
145 155 O O 1 XLRISE DRISE FRISE
O O O 1 ESout ESin TAU0 TAUF TV1 TV2
1000 1000 1 O 60 O 1 SETO SET1 SET2 NST NENT MM
O O O 1 3 4 1 Tabulated Tau Points
1.0 0.7 0.4 O
1 Device 2 IS QWT 1 BCTYPE NDN BCOUT
'QWT' 4 'OUTPUT 1 NLBC (node list)
2 3 15 14 1 QWTO QWTF QV1 QV2
92.4 O 60 O 1 SETO SET1 SET2 NSQ NENQ MMQ
O O O 1 3 O
1 Device 3 IS QWT 1 BCTYPE NDN BCOUT
'QWT' 5 'OUTPUT 1 NLBC (node list)
4 5 6 7 8 IQWTO QWTF QV1 QV2
88.2 O 60 O
FIuid Transient and Piwline ODtimization Usinn Genetic Al~orithms 198
1 SETO SETl SET2 NSQ NENQ MMQ O O O 1 3 O
1 Device 4 IS QWT 1 BCTYPE NDN BCOUT 'Qm 4 'OUTPUT
1 NLBC (node list) 13 12 18 19
IQWTO QWTF QV1 QV2 117.1 O 60 O
1 SETO SETl SET2 NSQ NENQ MMQ
Device 5 IS QWT BCTYPE NDN BCOUT
'QWT' 4 'OUTPUT' NLBC (node list)
11 9 20 16 QWTO QWTF QV1 QV2
1 70 O 60 O ] SETO SETl SET2 NSQ NENQ MMQ
O O O 1 3 O
1 Device 6 IS QWT 1 BCrVPE NDN BCOUT
'QWT' 1 'OUTPUT' 1 NLBC (node list)
10 [QWTO QWTF QV1 QV2
1 O 60 O 1 SETO SETl SET2 NSQ NENQ MMQ
O O O 1 3 O
1 Device 7 IS QWT 1 BCTYPE NDN BCOUT
'QWT' 1 l o ~ u r 1 NLBC (node list)
17 ( Q W O QWTF QV1 QV2
57.5 O 60 O ISETO SET1 SET2 NSQ NENQ MMQ
O O O 1 3 O
Fluid Transient and Pibelhe Obtirnùsaiùsaion Usinn Gcnetic Al~orithms 199
(,UTPUT PATH 1 NOUTP
I PIPE PATH LIST
8 15 14 13 12 11 10 9 16
I ENERGY OUTPUT PATH@)-1 1 NEP(I) PIPE PATH LIST
1 NODAL TRACES 1 1 NOUTN OUTPUT FOR NODES
5 16 17 18 19 20
1 PUMP STATION VALVES 1 1 NPTAU PSNAME[l .... NPTAvJ
O
1 End of Data File
Fluid Transient and Pibctine Ohmization Usinn Genetic Alnorithms 200 I
Fluid Transient and Piwl ine -timization Usinp Genetic Alnonthrns 201 -
Fluid Transient and Piwline Outimization us in^ Genetic Aleorithms 202
Fluid Transient and Pineline Obtirnization Usinn Genetic Alnorithm 203
Fluid Transient and Piwline ODtimization us in^ Genctic Algorithms 204 - --
Fluid Transient and Pi-mlhe O~timization Usinn Genetic Al~orithms 205 - --
Fluid Transient and Pimeiine O~timization us in^ - Genaic Alszorithms - 206
Fluid Transient and Pibeline ODtimization Usinn Genetk Alnorithms 207
Figure C A 2 Extreme Head Summary Plot (t=60s, cavity, node 1-20-
- - - - Max. HGL - - -SS HGL - - - - - Min. HGL - Pipeline
O 50000 100000 1 50000
C hainage (feet from node 1,15,14,13,12,11,20,16)
FIuid Transient and Piwline Cbtimization Usinn Genetic Aleorithms 209
ti 1 Cf) Cf)
Fluid Transient and Piwline Obtimitation Usinn Genetic Alnorithm 210
APPENDM D
INPUT DATA FOR GA PROGRAM
D-1 DATA FLE OF PIPEDATADBD
Pipe 1. D.
Wave Speed (W 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000
Base Cost ($/fi) 93.5 134.0 176.0 221.0 267.0 316. O 365.0 417.0 469.0 522.0 577.0 632. O 689.0 746.0 804.0 862.0 921.0 980.0
Pipe Diameter
(fi) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Allowed Nodal Maximum Head In Transient (A)
900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900
Ailowed Nodd Minimum Head In Transient (ft)
O O O O O O O O O O O O O O O O O O
D.2 DATA FILE OF NEWYORKTDF
No. of Pipe Size 1. D. Pipe Sizes 10 9 10 11 12 13 14 15 16 17 18 10 9 10 11 12 13 14 15 16 17 18 10 9 10 11 12 13 14 15 16 17 18 10 9 10 11 12 13 14 15 16 17 18 10 9 10 11 12 13 14 15 16 17 18 10 9 10 11 12 13 14 15 16 17 18
FIuid Transient and Piwline %timization Usinp Genetic A ltzorithrns 21 1
Allowed Nodal Maximum Head In Steady State
(ft) 700 700 700 700 700 700 700 700 700 700 700 700 7 0 0 700 700 7 0 0 700 700 7 0 0 700
Allowed Nodal Minimum H e a d In Steady S t a t e
(ft) 155 155 155 155 155 155 155 155 155 155 155 155 155 15s 155 160 172.8 155 155 155
End (no components) O
Fluid Transient and Pi~eline mtimization Usinn Genetic Alnorithms 212
D.3 DATA FILE OF NEWYORK-CAD
Number of Population Length of Probability Steady State Generations Size Each Gene of Mutation Duration
6 6 7 I 1000 sample
Fluid Transient and Piwline Obtimization us in^ Genetic A
Fluid Transient and Piueline ODtimization Using Genetic Alnorithrns 214
Fluid Transient and Piwline Oi,tirnization Usinn Genetic Alnorithms 215
Figure 0.1.4 Extreme Head Summary Plot (optima, Node 1-8-16)
--------- ---
- - - - Max. HGL ---SS HGL - - = = - Min HGL - Pipeline
--- - -
