Seediscussions,stats,andauthorprofilesforthispublicationat:http://www.researchgate.net/publication/256097672

OptimumDesignandOperationofPumpedWaterDistributionSystems

CONFERENCEPAPER·FEBRUARY1994

CITATIONS

9

DOWNLOADS

3,603

VIEWS

234

3AUTHORS,INCLUDING:

GraemeClydeDandy

UniversityofAdelaide

166PUBLICATIONS3,737CITATIONS

SEEPROFILE

AngusR.Simpson

UniversityofAdelaide

553PUBLICATIONS3,437CITATIONS

SEEPROFILE

Availablefrom:AngusR.Simpson

Retrievedon:01August2015

Optimum Design and Operation of Pumped Water Distribution Systems

by

Laurie J Murphy, Graeme C Dandy and Angus R Simpson

Department of Civil and Environmental Engineering. University of Adelaide

Adelaide South Australia 5005

Phone: 61-8-303-5451 Fax: 61-8-303-4359

Email: asimpson@crackle.adelaide.edu.au

1994 Conference on Hydraulics in Civil Engineering The Institution of Engineers, Australia

Brisbane, Australia

February 1994

Citation: Murphy, L.J., Dandy, G.C., and Simpson, A.R. (1994) "Optimum design and operation of pumped water distribution systems." Proc., Conf. on Hydraulics in Civil Engineering, Institution of Engineers, Australia, Brisbane, Australia, February.

1

Optimum Design and Operation of Pumped Water Distribution Systems

LAURENCE J MURPHY, GRAEME C DANDY and ANGUS R SIMPSON Department of Civil and Environmental Engineering, University of Adelaide

SUMMARY All communities need an adequate water supply. A water distribution pipe network, water storage tanks and pumping station facilities are the usual features of a water supply system. The selection of the layout, capacity and operation of these components of the distribution system significantly affects the hydraulic and economic efficiency of the design. The genetic algorithm (GA) technique is applied to the search for the optimal water distribution system design. The GA technique simulates mechanisms of natural population genetics in an artificial evolutionary strategy. The genetic algorithm optimisation model coupled with a steady state hydraulic simulation model generates and evaluates trial pipe network designs in search of optimal designs just as nature may save, combine and manipulate genetic information in the process of evolution. The genetic algorithm search is applied to a case study which demonstrates its flexibility and the opportunity for significant cost savings offered by this method.

1 INTRODUCTION

A supply of clean water is a basic need of all communities. The water needs of the community may vary with fluctuations in population and industry activity. A growing community must consider the provision of an upgraded water distribution system to meet increased water needs under different demand patterns~ The costs of expansions to a water distribution system may include substantial capital costs for components such as pipes, pump stations and storage tanks and operating costs such as energy costs for pumping. An optimisation procedure may be used to minimise these costs while satisfying the water demands on the system.

The optimisation of a new or expanded gravity pipe network design involves the selection of the combination of 'design variables' which satisfies some specified system performance criteria such that total design cost is a minimum. A number of models have been developed to identify the optimal set of pipe sizes for gravity pipe networks including: linear programming (Morgan and Gouher 1985); non-linear programming (Dandy et al 1993); enumeration algorithms (Gessler 1982); and genetic algorithms (Murphy et al 1993, Simpson et al 1994). The genetic algorithm search coupled with a hydraulic simulation procedure is well suited to the search for the minimum cost pipe combination for a gravity pipe network (Dandy et al 1993). The design may be for a new pipe network or additions to an existing pipe network. It is required to satisfy minimum pressure heads at the demand nodes in the system for various water demand patterns.

The optimum design of pumped pipe networks is quite a deal more complicated than for gravity systems. The set of design variables may include the material and diameter of new pipes; the equivalent diameter of cleaned and lined or duplicated existing pipes; the location, size and operation schedule for new or upgraded pump stations; and the location, size, shape and elevation of new storage tanks. The pipe network design is required to meet performance criteria such as minimum pressure heads at demand nodes for peak and emergency water demand patterns. In addition, adequate pressure heads and acceptable tank water levels should be maintained throughout the day and pump station flows should be within the operational limits of the pumping facility. A limited number of researchers have tackled the optimisation of pumped pipe networks. Some approaches to the pumped pipe network design problem are provided by researchers who participated in the 'Battle of the Network Models' optimisation search (Walski et

2

aI1987). The design of expansions to the Any town network from the 'Battle of the Network Models' conference sessions is the case study problem investigated in this paper. Walski et al recommended that the Any town network serve as a benchmark problem for other optimisation models. The genetic algorithm technique has been shown to be effective in a mixture of applications (Goldberg 1989). In this paper. the genetic algorithm search is applied to the complex solution space for a pumped pipe network optimisation problem.

2 GENETIC ALGORITHMS

A genetic algorithm (GA) is a structured search method based on artificial evolution (Holland 1975). GAs are a computer simulation of the evolution of living things. The process of natural adaptation of living things to the surrounding conditions continuously provides near­optimal solutions. Just as a chromosome of genetic information may describe the characteristics of an individual. some piece of code is used to describe a trial solution to the pipe network design problem. The piece of code occurs in some chosen format (typically a string of digits) which can best describe the complete set of solutions to be explored by the GA. A coded string may be mapped to a trial pipe network design by some decoding procedure. The string of artificial genetic code is decoded to the associated set of design variables which may include:

• proposed new pipes sizes • proposed modifications of existing pipes • proposed elevated tank sites • proposed expansions to existing pump stations • pump station operation for peak and emergency demands • pump station operation for average daily demands

The decoded trial network design undergoes a stringent evaluation procedure so that the coded string may be accompanied by a corresponding measure of its worth called its fitness. In nature. fitness may reflect an organism's compatibility with its surrounding conditions and ultimately determine its survival. The fitness of coded strings controls the survival of the artificial chromosome. The GA successively evaluates and regenerates popUlations of coded strings which represent some distribution of trial pipe network designs in the solution space. The starting population of coded strings is usually generated randomly.

The GA search uses operators which imitate mechanisms of population genetics and natural rules of survival to create a new population of coded strings from an old population. The traditional GA may consist of three simple operators called reproduction, crossover and mutation. The reproduction operator is a survival-of-the-fittest selection process. The survival of a living thing in nature depends on its strength and good fortune. In a similar fashion. the selection of a coded string from the competing population depends on its fitness relative to fellow strings and chance factors. The simplified genetic mechanisms of crossover and mutation combine and manipulate the coded strings selected from the old population before they proceed to the new popUlation. The crossover operator breaks two selected parent strings and exchanges corresponding segments of code to produce two offspring strings. The mutation operator randomly chooses and alters bits of code. Further details of the GA operators are given in Murphy and Simpson (1992).

3 EVALUATION SCHEME

The proposed pipe network design is evaluated with respect to its economic and hydraulic suitability so that the GA coded string may be assigned an appropriate value of fitness. The number of new parallel pumping units to be installed in the existing source pump station is specified by the coded string. The GA coding is flexible and may be modified to consider new pumps of different sizes which may be available arranged in any serial or parallel combination. The coded string specifies proposed pump operation for the peak demand patterns and an average

3

day pump operation schedule for the average daily water use pattern. The pump operation schedule is specified such that the average day pump flow just exceeds the average day demand and pumps operate close to the rated pump conditions (point of best pump efficiency).

A hydraulic simulation model is integrated with the GA optimisation model to assess the hydraulic capability of proposed layout, sizing and operation of the pipe network. The computer evaluation times should be kept to a minimum since the GA may evaluate something in the order of 20,ODO to 50,ODO designs. A steady state hydraulic analysis (for instantaneous flow and pressure distributions) is time consuming and only a limited number of hydraulic analyses may be performed to evaluate each trial design. The number of steady state hydraulic analyses which are needed to perform an accurate extended period hydraulic simulation (for fluctuating flow and pressure distributions and tank water level variations for some period of time) of the average daily demand pattern is unacceptable, particularly for a pumped network which includes a number of small elevated tanks. Therefore, a selected number of steady state hydraulic analyses are performed for the peak demand patterns and at about four representative times during the average day. Elevated storage tanks primarily help to smooth peak daily water demands and also store water for emergency demands. Performing about four steady state simulations on the pipe network subject to average daily demands checks that the storages provided by the tanks are being used effectively to moderate the peak daily demands. Checks are also made that the pump stations have the capacity and head to recharge all tanks during periods of low daily demands. The series of steady state simulations monitor power consumption and are used to predict power usage for the average day and hence the present worth of pump operation energy costs over the lifetime of the design. Lower off-peak electricity tariffs (if available) may be exploited by the adjustment of the pump operation schedule.

The network may have existing elevated water storages, however these alone may be inadequate for the forecast increased water demands. New elevated tanks may be located at some nodes in the pipe network. A mass balancing procedure measures the amount of water 'stored' in the network at any time of the day by the difference between the accumulated volume of water pumped into the network according to the pump operation schedule and the accumulated volume of water consumed at the demand nodes on an average day. Should the existing tanks have inadequate storage capacity, then additional tanks are required at locations in the pipe network specified in the GA coded string. The fractions of the additional storage needed at each tank site may be given in the GA code. Operating tank water levels are known for the existing tanks and are derived for the new tanks.

The elevated water tanks are assumed to be demand nodes during the sequence of average daily demand patterns with the pump station being the only source. The water demands at these new demand nodes are positive during periods where the pump flows exceed the network demand flows and the tanks are filling and negative when the pump inflows are less than network consumption and the tanks are contributing to the demands (usually periods of high demand). The set of ideal positive and negative water demands for the tank sites is determined by dividing the net system inflow or outflow amongst the tanks in a similar ratio to the distribution of the total system storage amongst the tanks. The ideal positive and negative water demands make the most effective use of all the elevated storages during the average daily cycle. The pressure heads at the storage nodes calculated by the steady state hydraulic analysis indicates a pattern of achievable water levels for the tanks. The achievable water levels for the existing tanks must fall within the operating water levels specified for each tank. The set of achievable water levels can be compared with a set of likely water levels predicted by a mass balancing procedure given tank volume and height. For lthis study, the achievable water levels for tanks draining should be less than the predicted water levels while the achievable water levels for tanks ftlling should be greater than the predicted water levels for new and existing tanks. Some further restrictions on tank water levels are likely to be placed on each of the potential tank sites for a real pipe network.

4

The costs such as pipe costs, pump capital costs, energy costs and tank costs are summed together to equal the total estimated design cost. Pipe costs are calculated for the lengths of new pipe, pipes laid parallel to existing pipes as duplications and existing pipes cleaned and lined. Pipe costs may be a function of the length of pipe to be installed or rehabilitated and may be influenced by accessibility and the condition of existing pipes. Pump costs are usually a function of the pumping capacity to be supplied. Tank costs may be a function of the elevation and the volume of storage. Land acquisition costs may need to be included for storage tank and pump station sites.

Residential Area

[74]

'-

Residential Area

[36] 40

N

Source Pump Station

Clearwell, Water Treatment Plant

Figure 1 The Any town Network (Walski et al 1987)

Energy costs may be estimated by the average day pump operation schedule. The fitness of the coded string is some function of the pipe network design costs and penalty costs for a given design. Poor designs which do not meet the specified system performance criteria for the network are allocated penalty costs. The peak and emergency demand flows must be supplied to demand nodes with some minimum allowable pressures. An infeasible pipe network design is one which does not maintain pressure heads at the demand nodes within allowable limits or which cannot provide some specified tank

5

water level trajectory and the infeasible design incurs a penalty cost which is a function of the distance from feasibility. Other constraints may be applied such as allowable limits for pipe velocities and the GA has the flexibility to incorporate the violation of any additional constraints as penalty costs. A feasible pipe network design will have zero penalty costs.

4 THE ANYTOWN NETWORK

The 'Battle of the Network Models' study (Walski et al 1987) introduced the Any town pipe network which required upgrading to meet increasing community water demands. The Any town pipe network was the water distribution system for a hypothetical small town with constraints and design complications typical of a real water distribution network. The proposed new design could introduce new pipes, pumps and tanks or add to or modify existing pump stations and pipes. The 'Battle of the Network Models' problem was intended to help bring closer the optimisation models of researchers and the design procedures of the experienced practising engineer.

Table 1 Pump characteristics for each pump at the source pump station of the Any town network

Discharge Pump head Efficiency (%) (gpm) (ft) (wire-to-water)

0 300 0 2000 292 50

4000* 270 65 6000 230 55 8000 181 40

* Rated discharge

The town in Figure 1 can be separated into an old central city area (southeast of pipe [28]), some industry around node 160, the surrounding residential areas and a proposed industrial park to be located north of town. The water is supplied from a river and is drawn from a clearwell at a water treatment plant at node 10 and pumped into the system. The source pump station has three identical pumps connected in parallel. The pump characteristics for each of the pumps are provided in Table 1. The water level at the clearwell is maintained at 10 ft. The US customary units have been used in this study. The existing pipes and proposed new pipes in the Any town network are numbered from [2] through to [82]. The older and more difficult pipes to access in the central city area are the thick solid lines in Figure 1. The new pipes in the proposed industrial park and the proposed new pipe [54] are represented by the dashed lines. The thin solid lines are the existing pipes in the surrounding residential area. The physical properties which characterise the pipes such as length, diameter and roughness are tabulated in Table 2. The Hazen-Williams roughness coefficients are projected C values for the year 2005.

The source nodes and demand nodes are numbered from 10 through to 170 in the Any town network in Figure 1. The elevations of the demand nodes reproduced in Table 3 are determined from network topography. The town has two existing water tanks at nodes 6S and 165 both with 250,000 gallons of elevated storage at opposing sides of town. The elevation of the bottom of both tanks is 215 ft and the tanks are full at 255 ft. The tanks should be operated between water levels of 225 ft and 250 ft. The minimum water level of 225 ft is not the very bottom of the tank since some storage is retained as an emergency water supply. The shape of the tanks is assumed to be cylindrical. Pipes [78] and [80] are riser pipes to the elevated tanks.

The average daily demand flows for 1985 and predicted average daily demand flows at the nodes determined by forecasted consumer water needs for the year 2005 are given in Table 3. The system is subject to the following peak and emergency demand patterns and the water must be supplied with adequate pressure head:

(1) instantaneous peak flow

6

(2) fIre flow of 2,500 gpm at node 90 (3) fIre flows of 1,500 gpm at nodes 55,75 and 115 (4) fIre flows of 1,000 gpm at nodes 120 and 160

Table 2 The pipes of the Any town network

ExisUng Hazen-Pipe Length Diameter Williams

(ft) (in) roughness C

[2] 12000 16 (city) 70 [4] 12000 12 (residential) 120 [6J 12000 12 (city) 70 [8] 9000 12 (residential) 70

[10] 6000 l2 (city) 70 [12] 6000 10 (city) 70 [14J 6000 12 (city) 70 [16] 6000 10 (CIty) 70 [18] 6000 12 (CIty) 70 [20] 6000 10 (city) 70 [22] 6000 10 (city) 70 [24] 6000 10 (city) 70 [26] 6000 12 (city) 70 [28] 6000 10 (city) 70 [30] 6000 10 (residential) 120 [32] 6000 10 (residential) 120 [34] 9000 10 (residential) 120 [36] 6000 10 (residential) 120 [38] 6000 10 (residentI&1) 120 [40] 6000 10 (residential) 120 [42] 6000 8 (residential) 120 [44] 6000 8 (resIdential) 120 [46] 6000 8 (resIdential) 120 [48] 6000 8 (city) 70 [50] 6000 10 (residential) 120 [52] 6000 8 (residential) 120 [54] 9000 New 130 [56] 6000 8 (residential) 120 [58] 6000 10 (residential) 120 [60] 6000 8 (residential) 120 [62] 6000 8 (residential) 120 [64] 12000 8 (residential) 120 [66] 12000 8 (residential) 120 [68] 6000 New 130 [70] 6000 New 130 [72] 6000 New 130 [74] 6000 New 130 [76] 6000 New 130 [78] 100 12 (riser) 120 [80] 100 12 (riser) 120 [82] 100 30 (pump main) 130

7

The instantaneous peak flows are 1.8 times the average day flows (Table 3) and the minimum allowable pressure head at all nodes is 40 psi. The fIre flows should be met while supplying peak: day flows at other nodes (1.3 times average day flows) and pressures of at least 20 psi should be provided at the nodes. The peak and emergency demands need to be satisfIed while the water distribution system is restricted with tanks at their low operating level and with a pump out of operation. The duration of fIre flows is 2 hours.

An approximate variation in water use for an average day is given in Table 4. There are no check valves or pressure reducing valves in the system at present. The cost per unit length for pipe material and laying of new pipes and duplicating existing pipes and costs per unit length for cleaning and lining existing pipes is given in Table 5. Pipe costs are higher in the old central city area since excavation is more difficult than in the surrounding areas. A pipe which has been cleaned and lined has an Hazen-Williams coefficient of C=125 and the new pipes have a C=130.

Table 3 The nodes of the Any town network

Average Expected Node daily water average daily Elevation

use in 1985 water use in (ft) (gpm) 2005 (gpm)

10 Clearwell Clearwell 10 20 500 500 20 30 200 200 50 40 200 200 50 50 200 600 50 55 - 600 80 60 500 500 50 65 Tank Tank 215 70 500 500 50 75 - 600 80 HO 500 500 SO 90 1000 1000 SO 100 SOU 500 SO 110 500 500 SO 115 - 600 80 120 200 400 120 130 200 400 120 140 200 400 80 JS()_ 200 400 120 160 800 1000 120 165 Tank Tank 215 170 200 400 120

Pump capital costs are based on rated discharge (QR) and head (HR) of the new pump unit. The cost C, for new pump stations is estimated by

(1)

The capital cost for the upgrade of the existing pump station is estimated by

C = 350 ~O.7 HRo.4 (2)

8

Pump station operating costs are based on a unit energy cost of $0. 12/kWh throughout the day. An interest rate of 12% and an amortisation period of 20 years are considered. Tank costs are a function of volume as shown in Table 6.

Table 4 Water use pattern throughout the day for the Any town network

Demand Time of Average day period day demand factor

1 12 midnight-3am 0.7 2 3am-6am 0.6 3 6am-9am 1.2 4 9am-12 noon 1.3 5 12am-3pm 1.2 6 3pm-6pm 1.1 7 6pm-9pm 1.0 8 9pm-12 midnight 0.9

Table 5 Pipe costs for the expansions to the Any town network

Pipe costs ($/ft) Pipe Duplicating exisnng Clean and line

diameter New pipes existing pipes (in) pipe L'ity Residenttal L'ity Residential 6 12.8 26.2 14.2 17.0 12.0 8 17.8 27.8 19.8 17.0 12.0 10 22.5 34.1 25.1 17.0 12.0 12 29.2 41.4 32.4 17.0 13.0 14 36.2 50.2 40.2 18.2 14.2 16 43.6 58.5 48.5 19.8 15.5 18 51.5 66.2 57.2 21.6 17.1 20 60.1 76.8 66.8 23.5 20.2 24 77.0 109.2 85.5 - -30 105.5 142.5 116.1 - -

Table 6 Tank costs for the expansions to the Any town network

Tank volume Cost (gal) ($)

50,000 115,000 100,000 145,000 250,000 325,000 500,000 425,000

1,000,000 600,000

9

5 GENETIC ALGORITHM DESIGN

The genetic algorithm optimisation technique was applied to the design of additions to the Any town pipe network (Walski et al1987). The GA search identified a number of alternative designs. A design engineer using a GA search as a preliminary design tool could evaluate alternative designs generated by the GA based on other non-quantifiable objectives specific to the system such as possible future expansions and demands. A low cost design determined by the GA technique for the Any town network expansions for $11.335 million is presented in Figure 2 and the design costs are summarised in Table 7. The design costs are approximated by the coded string evaluation scheme during the GA search.

Table 7 Summary of design costs

Cost Apprmomated Measured description ($million) ($million)

Pipes 4.506 4.506 Pump capital 0.0 0.0

Tanks 0.606 0.857 Energy 6.075 5.972 Total 11.187 11.335

For the Any town case study, it is assumed that the source pump station which already exists with three identical parallel pumping units may be upgraded by any number of additional parallel pumps with identical characteristics. The GA chooses not to upgrade the existing source pump station. The GA coding scheme may be modified to consider additional pumping units of different sizes which may be available.

Walski et al (1987) believed 500,000 gallons of elevated storage is low for the size of the town with a predicted total daily consumption of 14,112,000 gallons for the year 2005. The GA design situates a new 750,000 gallon elevated tank adjacent to node 140 and another new 300,000 gallon elevated tank adjacent to node 70. It was assumed for the hypothetical Any town network, that a new tank may be located adjacent to any demand node in the pipe network, however the number of these potential elevated water tank sites may be limited for a real pipe network. The operating and emergency components of the volumes of the tanks and recommended tank operating water levels are given in Table 8.

Table 8 New and existing tank dimensions

Elevated Tank capacity (gal) Operating water storage levels (ft)

tank Volume Effective Emergency Low High

storage storage 65 250,000 156,250 62,500 225.0 250.0 165 250,000 156,250 62,500 225.0 250.0 175 750,000 350,000 400,000 220.0 240.0 185 300,000 150,000 150,000 238.0 248.0

The design must satisfy the peak and emergency demands with only 2 pumps operating and tanks at the low operating water levels. The performance of the GA design under the demand patterns is summarised in Table 9. The emergency storage volumes for the new tanks were approximated by considering fire demands and corresponding tank outflows for a duration of 2 hours. Tank 175 has 400,000 gallons of emergency storage to meet the fire flows in the proposed new industrial park. Tank 185 has additional emergency storage to meet the fire flow at node 90 since the existing emergency storage at tank 65 cannot supply the emergency demands for 2 hours. The pressure heads at the

10

demand nodes are sufficient since they are all greater than 40 psi for the peak instantaneous flow pattern and greater than 20 psi for the fIre flow patterns.

Table 9 Peak and emergency demand patterns

Demand Pattern

(1) peak: mst. flow (2) fIre at node 9U

(3) fire 55, 75, 115 (4) fIre 120, 160

175 New 20"

~($0.006m)

/ ::: .. ::: ... -::. ~ ........... -....... ., :-:-:-:-:.:-:-:-:-:.:-: / -_ ...... .......... .. ---_ .... .. _--- ..

New Tank 750,000 gal ($0.5125m)

170

Criucal pressure (psi)

Minimum pressure

40.11 4l.36 25.88 42.71

Criucal Pump node station 150 10,219 15U 9,913 55 9,953

170 9,949

Dup.16" ($0.291m)

Tank 65

1,090 842 487 353

Source flows (gpm) Tank 165 1,723 451 377 341

Dup.12" ($O.l94m) - --

Tank 175 3,101 1,759 3,272 1,540

40

Figure 2 Proposed expansions for the Any town network

11

Tank 185 1,507 975 811 736

Dup.14" ~ ($0.241m)

~

The GA design operates 3 parallel pumps between 6am and midday and 2 parallel pumps for the rest of the day for the average daily demands. An extended period simulation was performed to simulate daily pump operation and hence accurately measure energy costs for the average day in 20 years time. The present worth of energy costs for the design life is estimated to be $5.971 million. Tank water level trajectories for the elevated tanks for the average day are plotted in Figure 3.

260

.-. 250 ;:: '-'

... ~ ; 230

.: .. ... .. .. ... . "",. '.

•• # ••• ..... ' .. .lIC ,.' "., c •.• ." •• CIS ",' .,

--.--Tank 65

-0--Tank 165

--+-- Tank 175

----<>- Tank 185 E-o 220 + __ < ....... • <. __ +

210 I '----------' 6pm 12 midnight 6am 12 noon 6pm

Time or day

Figure 3 Tank water level trajectory

6 CONCLUSIONS

This paper describes the use of the genetic algorithm technique for identifying the optimum design and operation of pumped water distribution systems. The technique was applied to the Any town network considered in the 'Battle of the Network Models' study (Walski et al 1987). The genetic algorithm identified a number of alternative near-optimal designs for the Any town network expansions. The GA design presented in this paper for $11.335 million compares favourably with the designs presented in the 'Battle of the Network Models' study which varied in cost from $12.3 million to $13.8 million (Walski et al 1987). However, it is difficult to compare the designs due to differing interpretations of the problem and the reliability requirements. Walski et al observed that tank sizing and location and pump operation significantly affect pipe sizing. The GA optimisation technique in this paper designs the new pipe network, selects a pump operation schedule and locates and sizes new tanks simultaneously.

7 REFERENCES

Dandy, G.C., Simpson, A.R., and Murphy, L.J. (1993). "A Review of Pipe Network Optimisation Techniques." Proc., WATERCOMP '93, Melbourne, Australia, March-April, 373-383

Gessler, J. (1982). "Optimisation of Pipe Networks." Proc., International Symposium on Urban Hydrology, Hydraulics and Sediment Control, University of Kentucky, Lexington, KY., 165-171

Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison­Wesley Publishing Company, Inc., 412pp

12

Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.

Morgan, D.R., and Goulter, I.C. (1985). "Optimal Urban Water Distribution Design." Water Resources Research, 21(5), 642-652

Murphy, L.J., and Simpson, A.R. (1992). "Pipe Optimisation using Genetic Algorithms" Research Report No. R93, Dept. Civil Engineering, University of Adelaide, June, 95pp

Murphy, L.J., Simpson, A.R., and Dandy, G.C. (1993). "Design of a Pipe Network using Genetic Algorithms." Water, August, 40-42

Simpson, A.R., Dandy, G.C., and Murphy, L.J. (1994). "Genetic Algorithms Compared to Other Techniques for Pipe Optimisation." J. Water Resources Planning and Management Division, ASCE (to be published July 1994)

Walski, T.M., Brill, E.D., Gessler, J., Goulter, I.C., Jeppson, R.M., Lansey, K., Han-Lin Lee, Liebman, J.C., Mays, L., Morgan, D.R., and Ormsbee, L. (1987). "Battle of the Network Models: Epilogue." J. Water Resources Planning and Management, ASCE, 113(2), 191-203

Disk M40 (Angus Simpson): File BrisbaneGAFeb94 10 Nov 93 2:40pm

13