Evolutionary bi-objective optimisation in the elevator car routing ...

European Journal of Operational Research 169 (2006) 960–977

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Evolutionary bi-objective optimisation in the elevatorcar routing problem

Tapio Tyni *, Jari Ylinen

KONE Corporation, R&D, P.O. Box 677, Hyvinkaa 05801, Finland

Accepted 13 August 2004Available online 30 November 2004

Abstract

The paper introduces a genetic algorithms based elevator group control system utilising new approaches to multi-objective optimisation in a dynamically changing process control environment. The problem of controlling a groupof elevators as well as the basic principles of the existing single-objective genetic elevator group control method aredescribed. The foundations of the developed multi-objective approach, Evolutionary Standardised-Objective WeightedAggregation Method, with a PI-controller operating as an interactive Decision Maker, are introduced. Their operationas a part of bi-objective genetic elevator group control is presented together with the performance results obtained fromsimulations concerning a high-rise office building. The results show that with this approach it is possible to regulate theservice level of an elevator system, in terms of average passenger waiting time, so as to bring it to a desired level and toproduce that service with minimum energy consumption. This has not been seen before in the elevator industry.� 2004 Elsevier B.V. All rights reserved.

Keywords: Combinatorial optimisation; Control; Energy; Genetic algorithms; Transportation; Multi-objective optimisation; Elevator

1. Introduction

An elevator system is a vertical transportationsystem responsible to transport passengers, living,working or visiting in the building, comfortableand efficiently to their destinations. A properly

0377-2217/$ - see front matter � 2004 Elsevier B.V. All rights reservdoi:10.1016/j.ejor.2004.08.027

* Corresponding author.E-mail addresses: [email protected] (T. Tyni), jari.

[email protected] (J. Ylinen).URL: http://www.kone.com

sized and well behaving elevator system improvesthe usability of the building, thus not only affectingthe comfort and service level directly experiencedby the passengers, but also adding value to thebuilding owner in terms of satisfied customersand tenants.

An elevator group or bank of elevators consistsof a system where several elevators reside physi-cally close together and respond to a common setof landing or hall call buttons located in the vicin-ity of the elevators at each floor. A passenger

ed.

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T. Tyni, J. Ylinen / European Journal of Operational Research 169 (2006) 960–977 961

orders a lift by pressing either an up or down callbutton, depending on the location of his/her desti-nation floor with respect to the passenger�s arrivalfloor. When an elevator car arrives, the passengerenters the cage and gives his/her destination floorusing car call buttons located in the cage. Theorder in which the elevator cars respond to thelanding calls given by passengers—i.e. the routesof the cars—play a vital role in the performanceof the vertical transportation system. In the eleva-tor community, this problem is referred to as‘‘landing call allocation problem’’ or ‘‘elevator dis-patching problem’’ (Fig. 1).

The landing call allocation problem may beconsidered as a version of the travelling salesmanproblem (TSP)—a combinatorial optimisationtask without a known method to be solved in poly-nomial time. In the TSP the salesman has a task tomake a round trip around the cities, by visitingeach city only once so that the distance he travelsis the shortest possible. In the elevator car routing

Fig. 1. Super-tall buildings rely on sophisticated, fast and quietvertical transportation systems (computer rendering—X-raypicture of a super-tall building).

context the TSP problem can be converted to mul-tiple travelling salesmen problem (MTSP), wheresalesmen (elevator cars) visit the cities (car callsand landing calls) so that each city (call) is visitedonly once and the cost function

PCðSi;Ci [ LiÞ is

minimised. The partial cost C is gathered along theroute when a set of car and landing calls Ci [ Li isvisited by the elevator i, starting the roundtripfrom the elevator�s initial state Si. The size of theproblem space is Ns = En, where E is the numberof elevators and n is the number of active landingcalls. The problem is too large to be solved system-atically, except only in the smallest elevatorgroups, so other methods have to be applied.

Examples of the methods that have been ap-plied are intelligent agents [5,15], fuzzy logic[10,21], neural networks [8,14,17] and evolutionaryand genetic algorithms [7,16]. The work done inthe field can be basically divided into threebranches: (i) the presented method is used to assistthe existing dispatching algorithm; (ii) the methodis used to tune the parameters of the existing dis-patching algorithm and (iii) the presented methodmakes the actual control decisions and actions inreal time. In [20] we presented a landing call allo-cation method based on Genetic Algorithms(GA) falling into category (iii) in the classificationabove. As far as the authors are aware of, the pre-sented method is the first landing call allocationalgorithm that performs true route optimisation,finding the optimal routes for each elevator in realtime. The traditional methods, often stronglybound to expert knowledge and a priori heuristicsof the elevator application domain, are able toprovide only partial solutions. Their output is usu-ally one allocated landing call per elevator, rea-soned as the ‘‘best’’ by the method in question.Here we would like to distinguish between theterms ‘‘landing call allocation’’ and ‘‘elevator carrouting’’, so that the former is reserved for themethods providing partial solutions and the latterfor methods performing true route optimisationaccording to some objective function. The methodpresented in the paper is the core of theTMS9900GATM elevator group control system,part of the KONE AltaTM, the third generationhigh rise elevator system from KONE intendedfor skyscrapers [12].

962 T. Tyni, J. Ylinen / European Journal of Operational Research 169 (2006) 960–977

The optimisation in [20] was based on a single-objective function. In this paper, we extend thealgorithm to a multi-objective optimisation (MO)capability and utilise two conflicting objectives—landing call waiting time and energy consumptionof elevators along their routes. Due to the asym-metric properties of the elevator hoisting function,it is possible, by selecting the elevator car routescarefully, to conserve energy and still serve passen-gers in adequate time.

Special attention is paid to the issues of multi-objective optimisation in a real time control appli-cation. The time frame available to obtain thecontrol decisions is limited—routing decisions haveto be made twice in a second. The constrained timeframe imposes requirements regarding the compu-tational efficiency of the optimisation algorithm.Most of the work in the evolutionary multi-objec-tive (EMO) field deals with design type of applica-tions where the time to obtain the solution isimportant but usually not a crucial requirement.The research has concentrated on developingmethods that could obtain as many evenly distrib-uted solutions as possible from the Pareto-optimalset of the problem, even from concave regions ofthe Pareto front. These algorithms are computa-tionally expensive and the requirements concern-ing the control system hardware would be toodemanding for commercial purposes.

Due to the processing time restrictions we pre-sent an approach based on the straightforwardand computationally efficient Weighted Aggrega-tion (WA) method. WA optimisation reduces theoriginal MO problem to a single-objective optimi-sation problem, which have run times in O(GN),where G is the number of generations and N isthe population size, whereas the run times of thenon-dominated sorting methods, like NSGA-II,are in O(MGN2), where M is the number of objec-tive functions [9]. The WA method presented inthis paper is able to perform the bi-objective opti-misation task with contradicting objectives in realtime within the given 500-ms time frame. Thedrawback of the WA method is that it has prob-lems in two areas: (i) the definition of the weightvalues depends on the optimisation problem and(ii) it cannot obtain solutions lying in the non-con-vex regions in the Pareto-optimal front [6].

To address problem (i), we present a generalmethod which normalises the objective functionsat the beginning of each evolutionary search, let-ting the Decision Maker (DM) simply express hispreferences with weight values in the range[0� � �1] at any time. To deal with problem (ii), acontrol loop is established to ensure that the timeaveraged solutions meet the requirements givenby the system operator. In the control loop a PI-controller acts as a DM adjusting the weights ofthe WA optimiser according to the deviationsfrom the target passenger waiting time defined bythe system operator. In the elevator world, the sys-tem operator is usually the building manager.

The ultimate goal behind the approach we pre-sent is to regulate the service level of the elevatorsystem in terms of passenger waiting times or calltime. During the design phase of the building,the elevators are sized to give appropriate serviceduring intensive traffic peaks [2,11,19]. Duringother traffic periods, when traditionally only thepassenger waiting time is optimised, the systemprovides inadequate good service at the expenseof energy consumption and system wear. The bear-ing idea is to specify the average waiting time thesystem should maintain in all traffic situations—the elevator car routes should satisfy the specifiedaverage passenger waiting time with the least con-sumption of energy.

2. Principle of the genetic elevator car routing

method

The principle of the Genetic Elevator Car rout-ing problem is described to the extent that servesthe purposes of the present paper dealing withmulti-objective optimisation in the elevator carrouting problem. For readers with further interest,a detailed description of the method and its per-formance can be found in [20].

Fig. 2 visualises how the elevator car routingproblem is presented to the Genetic Algorithm.In the example the elevator group consists of twoelevators. Elevator A is standing with doors openat floor 2. It has three car calls to floors 4, 5 and7. Elevator B has no car calls and is standing withdoors closed without a specific direction at floor

A A B BA B B B

B A A B

.

.

.

Pop

ulat

ion

ofro

ute

alte

rnat

ives

1.G A

System state

Coding of acive landing calls to genes

A routealternative

C = CT = CTA+ CTB

121110 9 8 7 6 5 4 3 2 1

A B

Sele

ctio

nC

ross

over

Mut

atio

n

CostEvaluation

Model ofElevator A

Model ofElevator B

Calls for A

Calls for B

Σ

Σ Σ Σ

CTA

CTB

2.

3.

4.

CC

C

.

.

.

Direction gene for elevators without direction

Fig. 2. Illustration of the genetic elevator car routing method.


11. At this particular time the routing problemconsists of four active landing calls that shouldbe served by the elevators: two up calls at floors4 and 8 and two down calls at floors 9 and 6.The elevator�s system state consists of the generalstate of service (in service/out of service), car posi-tion, collecting direction (up, down), motionalstate (standing, moving, decelerating), car load,door state (opening, open, closing, closed) andthe car call vector.

The chromosome is built up by taking the land-ing calls one by one and inserting them into thechromosome as ‘‘call genes’’. The locus of a callgene represents the landing call and the allele ofthe gene represents the elevator car that shouldserve the call. This coding approach offers a natu-ral way to meet the requirement that each callshould be responded to only once by one of theelevators.

If an elevator has a direction, there is no prob-lem—the direction can be fed straight away to themodel of the elevator, as is the case with elevator Ain this instance. When an elevator is standing at afloor without a specific direction (for example afterit has served the last car call), it has an option tostart collecting the landing calls in either up ordown directions. The question is, which directionwould be better? This problem can be resolved in

an elegant way: if an elevator has no specific direc-tion, a ‘‘direction gene’’ is included into the chro-mosome, specifying the direction in which theelevator should start. In fact, the direction genespecifies indirectly the first landing call in the se-quence of calls to be served that a single elevatorshould obey.

The optimisation is performed continuously inreal time twice a second or immediately if the land-ing call situation changes. As the traffic situationsvary greatly in the course of the day, the elevatorcar routing problem is an optimisation problemof dynamic nature. During the same optimisationproblem, the system state changes as the elevatorsproceed along their routes. However, despite thechanges in the system state, the genetic searchshould provide the same route solution it did thefirst time the new problem occurred, i.e. new activelanding calls appeared. This also applies to thetype of new optimisation problems where an eleva-tor has served a call and the call disappears—therest of the routes should remain as they were inthe original problem. Genetic search has randomproperties, and in the case of multi-modal pro-blems, which is what this problem appears to be,there is no guarantee that the search ends up withthe same solution each time the optimisation is re-run. Here we have improved the stability of the

mropes

m load

mcar

mcw

h

Motor

Counter-weight

Car

Ropes

Fig. 3. Elevator hoisting function components.


solutions by initialising one of the chromosomes ofthe initial population with the route solution fromthe previous optimisation cycle. That particularchromosome is superior compared to the other,randomly generated chromosomes of the initialpopulation, biasing the search towards the previ-ous solution. The stability issues are also studiedin detail in [20].

The route alternatives for the cars representedby the chromosome are fed to a cost evaluationprocedure, which decodes the chromosome and as-signs the landing calls and the possible directiongene to the appropriate elevator models. Each ele-vator model then forms its route in the building onbasis of the system state, the landing calls assignedto it and the behavioural rules an elevator has toobey. The essential rule is the collective serviceprinciple—the elevator can reverse its directiononly when it has no car calls in its direction ofmovement.

The cost of the route alternative is returned tothe optimiser. The traditional objective functionshave been the sum of call times or estimates ofthe passenger waiting times. Once the route hasbeen formed in the elevator model it could alsobe used to evaluate some other objectives—like en-ergy consumption of the route alternative, amongothers.

3. Energy consumption of the elevator hoisting

function

The components of the hoisting mechanism ofan elevator are so designed that the system is inbalance when the car is half-loaded and at thesame height h as the counterweight

mcw þ 12mropesðhÞ ¼ mcar þ 1

2mLmax þ 1

2mropesðhÞ; ð1Þ

where mLmax is the maximum rated load; refer toFig. 3. When the car and counterweight are lo-cated at different heights in the shaft, the ropes be-come unbalanced. In mid and high-rise elevatorswith shaft lengths up to several hundreds of me-ters, the imbalance due to ropes has to be compen-sated with another set of ropes connecting the carand counterweight through the pit. In that case,Eq. (1) reduces to

mcw ¼ mcar þ 12mLmax: ð2Þ

In low-rise elevators, the rope masses are muchsmaller compared to the other masses in the hoist-ing system and Eq. (2) can be applied with suffi-cient accuracy as well.

When an elevator car runs from a floor atheight h1 to some other floor at height h2 thepotential energy in the system changes:

DE ¼ mgðh2 � h1Þ ¼ mgDh: ð3ÞIn Eq. (3), the mass m is the static mass balance ofthe system:

m ¼ mcar þ mL � mcw ¼ mL � 12mL max: ð4Þ

Consider an empty car moving downwards. Thecounterweight is heavier than the car and thehoisting motor has to apply energy to the systemin order to increase the system�s potential energy.In the opposite case, when an empty car moves up-wards, the heavier counterweight pulls the car andthe motor has to brake, i.e. it functions as a gener-ator. Depending on the motor drive electronics,the released potential energy is either wasted intoa braking resistor or, as in the more advanced sys-tems, it can be returned to the power supply net-work. When the car is fully loaded, the directionsare reversed—moving the car upward consumes

120

0 5 10 15 20 25 30 35 40 45 50

90

60

30

0time / s

acceleration

speed

position

energy

energy / Wh

P = 30kW

P = -18kW

Fig. 4. Car acceleration, speed, position and energy consumption for an upward trip and then a return trip down to the starting floorwith a full load of 21 persons.


energy and moving it downward restores thepotential energy. In fact, passengers transportedinto the building conserve energy, which in turnis released when passengers leave the building.All the potential energy bound to the passengerscannot be restored because of the mechanicaland electrical losses in the transportation system.

Fig. 4 shows an example representing an eleva-tor travelling upwards (2–15 seconds) and thendownwards (30–43 seconds) with a fully loadedcar. The nominal speed of the hoisting system is

200-250150-200100-15050-1000-50-50-0-100--50-150--100

0 2 4 6 8

10 12 14 16 18 20

1

7

13-150

-100

-50

0

50

100

150

200

250

Ener

gy c

onsu

mpt

ion

[Wh]

Car load [passengers] Flig

ht d

istan

ce

[floo

rs]

Up

Fig. 5. Energy consumption of an elevator during upward (left) andCar load 100% equals 21 passengers.

3.5m/s, acceleration 1.2m/s2 and maximum load1500kg or 21 persons. This 13-floor hoisting sys-tem is used in the examples throughout this paper.

If the distance is long enough so that the con-stant speed phase can be attained, a trip betweenfloors includes three phases: acceleration, constantspeed and deceleration. In Fig. 4, moving the fullyloaded system upwards with a constant speed of3.5m/s requires 30kW of power from the hoistingmotor during the period from 5 to 9 seconds.Whereas, under the same conditions, during the

0 3 6 9

12 15 18 21

1

7

13-150

-100

-50

0

50

100

150

200

250

Ener

gy c

onsu

mpt

ion

[Wh]

Car load [passengers]

Flig

ht d

istan

ce

[floo

rs]

Down

downward (right) movement as a function of running distance.

8 7 6 5 4 3 2 1

A B C87654321

A B C

Fig. 6. Two route alternatives for elevators when optimisingpassenger waiting times (left) and energy consumption (right).


downward constant-speed portion of the trip, themotor power is �18kW, i.e. it functions as a gen-erator supplying energy to the power line or to abraking resistor, depending on the technologyused in the motor drive system. In the end, thenet energy consumed during this round trip is55Wh.

Fig. 5 shows the energy surfaces of the examplesystem as a function of car load (in persons) andrunning distance in floors.

Considering the energy surfaces in Fig. 5 andthe simple routing problem example in Fig. 6, itis quite clear that there may be noticeable differ-ences in the consumption of the energy dependingon the routes of the elevator cars serving the pas-sengers. When the normal passenger waiting timesare to be optimised, the optimal routing is as inFig. 6 left, and in respect of energy consumptionthe optimum routes are as in Fig. 6 right. Gener-ally, when optimising the energy consumption ofthe elevator car routes, the cars should travel up-wards as empty as possible and downwards as fullas possible.

4. Evolutionary standardised—objective weightedaggregation method (ESOWA)

The literature on evolutionary multi-objectiveoptimisation deals largely with problems of analy-sis and design type, e.g. optimising some mechan-ical structure. The focus can be seen e.g. in [4].These problems are off-line in nature, the compu-tational expense of the algorithm is importantbut not the most crucial aspect.

Instead, in real time control type optimisationproblems, the time frame available to achieve thesolution is limited and crucial. For example, inthe case of our elevator group control application,routing decisions have to be made twice a second.With the popular Pareto-dominated EMOs,the processing times comply with the formulaO(MGN2), where M is the number of objectivefunctions, G is the number of generations and N

is the population size [9]. As the Weighted Aggre-gation (WA) method is essentially a single-objec-tive optimisation method, the processing timesfollow the formula O(GN). Using Pareto-domi-nated sorting algorithms would yield O(MN)longer processing times as compared to the WAalgorithms, which would be unacceptable in thisreal time application.

The WA method is classified either a posteriorior a priori method, depending on how it is applied.In this paper, we consider it as an a priori methodas the Decision Maker (DM) balances the impor-tance of each objective function in terms of weightcoefficients and the method then returns a solutionfrom that region in the Pareto front. In the WAmethod, a problem to be solved is

minimizeXni¼1

wifiðxÞ( )

subject to x 2 D;

ð5Þ

where wi P 0 8i ¼ 1; . . . ; k ^Pk

i¼1wi ¼ 1 and D isthe feasible region of the solutions [6]. The methodreturns the multi-objective problem to a scalaroptimisation one, and all the developed evolution-ary methods in that field are readily available.

To obtain the non-dominated set of decisionvectors x, the optimisation problem is normallyrun with different linear combinations of weightswi. A problem arises when the ranges of eachobjective function differ significantly or are notknown beforehand or the optimisation taskchanges constantly. To balance the effect of eachobjective function on the aggregated cost C, a pri-ori knowledge about the problem is needed to ad-just the weights to proper ranges. In the off-linetype applications this is tolerable, as it is possibleto experimentally learn the ranges of each objec-tive function and adjust weights accordingly. In

Table 1Steps of the evolutionary standardized objective weightedaggregation method

1. Create the initial population of N decision vectorsrandomly, compute the sample mean mi andvariance s2i in Eq. (7)

2. Compute the standardized objective functions /_

i inEq. (8)

3. Compute the aggregated sum in Eq. (9)4. Apply the genetic operators (selection, crossover and

mutation) specific to your (single-objective) evolutionaryoptimiser to create the next generation of population

5. If not converged, go to the step 2


real-time control applications in dynamical envi-ronments, there is no chance for such experimentsas the system is running on its own, making con-trol decisions without human intervention.

A technique to overcome the difficulties men-tioned above is to consider the objective functionfi as a random variable and apply standardisation.If an objective function fi has a distributionDiðli; r

2i Þ, then a standardised objective function

/i ¼fi � li

rið6Þ

has a distribution Di(0,1). The underlying mean land variance r2 of the objective functions are not(normally) known a priori. Instead, they have tobe estimated using their counterparts sample meanm and sample variance s2,

mi ¼1

N

XNj¼1

fi;j;

s2i ¼1

N � 1

XNj¼1

ðfi;j � miÞ2;ð7Þ

where N is the sample size. The standardisation isnow formulated as

/_

i ¼fi � mi

sið8Þ

and the optimisation problem is now

minimizeXni¼1

wi;/_

iðxÞ( )

subject to x 2 D;

ð9Þ

where again wi P 0 8i ¼ 1; . . . ; k ^Pk

i¼1wi ¼ 1.With the evolutionary algorithms, the sam-

pling is a built-in feature of the algorithm. Theinitial, (uniformly) randomly generated first gener-ation of decision vectors x take N random sam-ples from the objective function space for eachfi : Z

n ! R. The sampling and normalisationapproach with the evolutionary algorithms withpopulation size N is straightforward as illustratedin Table 1.

As a random variable, the sample mean m alsohas a mean lm and a standard deviation rm. Func-tion f : Zn ! R is considered as a random varia-ble with mean l and standard deviation r. The

Central Limit Theorem [13] states that if the sam-ple size N is large (say N P 30) and the populationfrom which the samples are drawn is large in com-parison to N, then the sample mean m is approxi-mately normally distributed with mean lm = l andrm = r/

pN. The analysis of variance is more com-

plicated but has similar behaviour. If needed, theconfidence interval of the sample mean and vari-ance can be improved by increasing the populationsize N for the initial generation.

Fig. 7 illustrates the search behaviour with asimple and smooth convex test function in Eq.(10). The objective functions operate in differentranges, in spite of the fact that the search is ableto find solutions from the convex Pareto front atroughly equal distances when the weights movewith linear combinations of w1 = [0,0.1, . . ., 1]and w2 = [w1 � 1]. Note that the entire objectivefunction normalisation is hidden from the user,taking place ‘‘on the fly’’ inside the algorithm dur-ing the search. The basic genetic algorithm was asimple GA with integer genes coded to range�1.5/

p10 6 xi 6 1.5/

p10, population size 100,

uniform crossing over and elitist selection with20 parents.

f1ðx1; x2; . . . ; x10Þ

¼ 0:01 1� exp �X10i¼1

ðxi � 1=ffiffiffiffiffi10

pÞ2

! !3

;

f2ðx1; x2; . . . ; x10Þ

¼ 100 1� exp �X10i¼1

ðxi þ 1=ffiffiffiffiffi10

pÞ2

! !3

:

ð10Þ

4 3 2 1 0 1 24

3

2

1

0

1

2

0 0.005 0.010

50

100

Fig. 7. Standardised fitness space (left) and search results in the original fitness space (right) from Eq. (10). Random fitness from theinitial population (small dots), found improved fitness values from each generation (circles) and found solutions (large dots). Searchperformed with 11 weight combinations w1 = 0, 0.1 , . . . , 1 and w2 = 1 � w1.


5. Passenger traffic in the building

Typically, in residential and office buildings, thedaily passenger traffic repeats itself regularly fromday to day. The traffic can be divided into threemain components: incoming traffic from the en-trance floor(s) to different floors in the building,outgoing traffic flows from the ordinary floors tothe entrance floor(s) and interfloor traffic betweenordinary floors (entrance floor(s) excluded). Fig. 8shows a measured example of a traffic pattern

0

2

4

6

8

10

12

14

16

7:00

7:45

8:30

9:15

10:00

10:45

11:30

12:15

13:00

13:45

14:30

15:15

16:00

16:45

17:30

18:15

19:00

InterfloorOutgoingIncoming

Fig. 8. Typical working-day passenger traffic pattern as meas-ured from an office building. The graph shows the morningincoming peak, lunch hour traffic and evening outgoing peak aspercentages of the building�s population.

from an office building. Mathematically, the trafficis modelled as an unstationary Poisson process [3]

Pfk arrivals in DtgðtÞ ¼ ðkðtÞDtÞk

k!e�kðtÞDt; ð11Þ

where k(t) is the time-varying mean of a trafficcomponent. Eq. (11) gives the probability for theevent that k passengers will arrive during a (short)time period t + Dt, over which the k(t) can be con-sidered as constant.

Traditionally, the operation of the landing callallocation algorithms is tuned to fit the prevailingtraffic type detected by the elevator group controlsystem. The basic traffic types that are normally de-tected are normal traffic, incoming peak, outgoing

peak and two-way peak. The landing call allocationalgorithm then uses pre-set parameter sets for theparticular, detected traffic type, adapting its opera-tion and control strategies to the current traffic sit-uation. Elaborated methods have been developedto get even more detailed traffic types, e.g. in [18],where reasoning with fuzzy sets is utilised to detect36 different traffic types. In addition, traffic inten-sity information from each floor can be gatheredto adjust the operation of the control system.

The problem with this approach is how to de-fine the actual parameter values for each traffictype for the building and the elevator system in


it. One approach is offline simulation. The buildingand the elevator group are configured into the sim-ulator [18,19]. If the building is in the design phase,then the traffic can be estimated from the build-ing�s design parameters. The simulation is carriedout for each detected traffic type and the parame-ters are tuned manually to give the best perform-ance. That is a drawn-out and tedious process [1].

When the optimisation process is automated, italso enables online tuning of the parameters,reducing the sensitivity to changes in the environ-ment and system. However, the drawback is thatthe on-line simulation is a computationally inten-sive task consuming resources from the controlsystem�s Decision-Making tasks. Even if the re-sources were available, the principal question stillremains—what is the basis to choose the controlparameters for the traffic situation at hand? Inprior art, the definition has been more qualitativethan quantitative in nature. As an example, rela-tive values among the parameter set may be de-fined so that during light and medium traffic theemphasis is on energy consumption while duringheavy traffic peaks the focus is on passenger serv-ice. Nevertheless, no method of how these morequalitative settings are tied to actual quantitativenumbers describing the service level of the trans-portation system has been seen so far.

6. The control method

A severe limitation of the WA method is its dis-ability to deal with the non-convex regions of thePareto front [6]. The non-convexity is also presentin the elevator car routing problem. Fig. 9 showsan elevator group of 7 elevators, an optimisationproblem instance and the corresponding fitnessspace. The example implies that the Pareto frontin this application may contain none, one, two,or even more local concave regions not reachableby the WA method.

In order to provide good service, the elevatoringguidelines recommend that an elevator systemshould be able to transport 12–15% of the build-ing�s population within a 5-minute period. Thatis, the passengers can be transported into thebuilding in 42–33 minutes. The traffic applied in

these calculations is the pure incoming traffic peakas the operation of the system is not influenced bythe properties of the car dispatching function, thusallowing mathematical analysis of the elevator sys-tem�s traffic handling performance. As the elevatorsystem is sized to give good service during theintensive morning incoming traffic peaks, it canbe stated that the service during normal and lighttraffic is ‘‘unnecessarily good’’. The system hasexcessive resources for the traffic outside the peakperiods and produces inappropriately short wait-ing times at the expense of, for example, energyconsumption and system wear.

The control principle is to find routes for theelevator cars that will satisfy the given target pas-senger waiting time with minimum consumption ofenergy, i.e.

minimize ff1ðxÞ;f2ðxÞg ð12Þsubject to x2D;

x ¼ fx2 P jðf1ðxÞ� f 1 Þ

2 ¼ming: ð13Þ

In the Decision Maker�s utility function Eq. (13),f 1 is the specified target for the average call time

the system should maintain in the prevailing trafficconditions and x* is the decision vector or alloca-tion decisions from the set of non-dominated solu-tions P* forming the Pareto front. In order toobtain the P* with the WA method, the optimisa-tion should be run with a number of linear combi-nations of weights wi, whereupon Eq. (13) shouldbe applied. To reduce the computational burdenand further, to compensate the difficulties of theWA method with the concave Pareto-regions, wetake an approach where the optimisation is exe-cuted only once per control cycle. To reach thecorrect regions of the Pareto front, the weights wi

are adjusted continuously during the course ofthe operation so that the time average of termðf 1ðxÞ � f

1Þ2 in Eq. (13) is minimised. During

each control cycle, a dedicated controller acts asa Decision Maker comparing the differences be-tween the predicted average call time f1(x*), pro-duced by the elevator system model in anevolutionary optimiser, to the target value f

1.The DM thus guides the optimiser by adjustingthe objective function weights according to thePI-control rule in order to satisfy Eq. (13) over

Fig. 9. A traffic situation (left) and corresponding fitness spaces (right). Random initial values (black crosses), 64,000 random values(grey diamonds), best fitness from each generation (red circles) and final solutions found by ESOWA (black dots). There are two locallyconvex regions on the Pareto front, pointed by arrows. (For interpretation of the references in colour in this figure legend, the reader isreferred to web version of this article.)

Passenger transportation process

Waitingpassengers

w1=1-u

w2=u ESO

WA

ElevatorGroup

Optimalroutes x*

Systemstate

OptimiserP

+1

-1

I+1

0

+e

+0.95

0.10

u

uP

uI

E

Controller as Decision Maker

-

Estimator

Model

Average CT predictionsAv

erag

e C

Tes

timat

es

Call buttons

Realised CT

Passenger flow intothe elevator system

Passenger flow fromthe elevator system

System Operator

f1(x*)

f1*Target CT

f1

Error

Limiter

Limiter

Limiter

Fig. 10. Overall system structure. A PI-controller (Proportional and time-Integral terms) acts as a Decision Maker guiding theOptimiser to provide a specified service level in terms of average call time. The predicted Average Call Time f1(x*) is obtained from theOptimiser�s system model as a ‘‘side product’’ of the optimisation.



course of time. Block diagram of the approach isshown in Fig. 10.

The kth predicted average call time f 1ðx kÞ from

the Pareto front is smoothed in the estimator blockwith

f_

1;k ¼ f_

1;k�1 þ ðf_

1;k�1 � f1ðx kÞÞ � GE ð14Þ

and compared in the error block to the target servicelevel f

1 defined by the system operator, usually theBuilding Manager taking care of the building�sfacilities. The difference ek ¼ f

1 � f_

1;k between thetarget and estimated average call times is input tothe controller block. The control rule is the standardPI. The output uk of the controller is the sumof termuP proportional to the error e(t) and uI the time inte-gral of error e(t), in the continuous time domain

uðtÞ ¼ uPðtÞ þ uIðtÞ ¼ GPeðtÞ þ GI

Z t

t0

eðtÞdt: ð15Þ

It is characteristic of the closed loop controlledsystem that the controller tends to keep the differ-ence between the target and the actual value closeto zero. This action takes place regardless ofwhether the deviation from the desired value hasoccurred due to reasons internal or external tothe controlled process.

A natural choice for the integrator gain GI

comes from the nature of the passenger traffic.As the traffic intensity unit in the elevator worldis ‘‘passengers in five minutes’’, GI may be selectedso that the integrator provides a time constant ofthe same order of 5 minutes. The selection of theproportional gain GP is more problematic. Thetotal gain of the closed loop system is the control-ler gain GP multiplied by the variable system gainGS = df1/dw1. GS depends on the region of the Par-eto front the system is operating in. If the totalgain in the control loop is too large, the series

limk!1

ðf1ðx kÞ � f1ðx

k�1Þ ð16Þ

does not converge and the system is unstable. Toavoid instability, conservative values for the pro-portional gain GP have to be used; the integralterm will have the main responsibility in the con-trol loop. The estimator gain GE is selected so thatit smoothes the predicted values without introduc-ing too much delay.

7. Results

As it is not possible to obtain comprehensivedata in a controlled manner from elevators run-ning in a real building, a building simulator withsimulated passenger traffic and elevators is astandard development tool in elevator industry[19,18]. The example building and elevator systemwe use here is the elevator group of 7 elevators and19 floors illustrated in Fig. 9. The specifications ofthe hoisting system were given at the beginningof the paper. The nominal transportation capacityof the system is 200 passengers in 5 minutes, whichequals 13.1% of the building population and isclassified as good [11]. Three independent simula-tion series were run with pure outgoing traffic.The results shown here are averages of the threeseries. Pure outgoing traffic was selected becausein that traffic type the optimiser has most freedomto arrange the routes, as there is no constrainingcar calls, revealing most clearly the capabilities ofthe control principle. Within one simulation series,the traffic intensity was increased from 2% of thebuilding population to 20%, in 2% steps. Eachintensity step was run for 30 minutes.

Fig. 11 shows as an example the behaviour ofthe DM-control loop during one simulation runwith 8% intensity. The horizontal axis is time upto 1800 seconds. The topmost curve shows thenumber of active landing calls. Presented in thelow section of the graph are call time estimatesfrom the estimator, realised call times, and 5 min-utes moving average of the realised calls. In themiddle is the weight w1 i.e. the DM�s preferencefor call time importance for the optimiser.

A representative example of the behaviour is be-tween 800 and 900 seconds. A burst of 11 activelanding calls appears in the system and the calltime estimator indicates that the average call timewill increase. Because of that, the Decision Makerincreases the importance of call times in the opti-misation. Once that burst has been handled, thecall time predictions from the estimator tend todecline, but DM responds by increasing the prefer-ence of energy consumption. During the opera-tion, the 5 minutes moving average of therealised call times follows very closely the 20-sec-onds goal for the service level. This implies that

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 18000

20

40

60

80

100

1

Number of calls

w1

CT estimateRealised CTRealised CT, 300s moving average

0.2

0.4

0.6

0.8

1.0

2

4

6

8

10

12

Fig. 11. Behaviour of the Decision Maker�s control loop at a traffic intensity of 8%.


the system model in the optimiser the routing ac-tions are based on describes the system with highfidelity.

That the system is under good control can beseen from the realised call time distribution inthe time domain behaviour in Fig. 11 and in thecumulative distribution histogram in Fig. 12.About 95% of the realised call times fall below50 seconds, and no excessively long times appear.The average call time over the whole simulation

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fi15_20s

0.95

mean CTm( )

Realised CT

t [s]

Best fit Weibull(α

α

, β)

= 1.256, β = 20.70

300s Running averate ofrealised CT

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 12. Cumulative probability distribution of realised call times (lef(right). Averaged over three 30-minute simulation runs.

run is 20.7 seconds with a narrow deviation as seenfrom the distribution of the 300 seconds movingaverage histogram in Fig. 12 left.

The behaviour of the call time weight w1 as afunction of traffic intensity is shown in Fig. 12right. The graph is the average over the three 30minutes test runs. The system reaches its capacitylimits with the given service level of 20 secondsat 18% traffic intensity, after that the system onlyoptimises the waiting time.

0 2 4 6 8 10 12 14 16 18 20 22

0.1

0.95

1

Traffic Intensity (%) of population

w1

w1 -

w1 + σσ

t). Average value of weight w1 as a function of traffic intensity


Fig. 13 collects the main results from the threesimulation series with three different control strat-egies. The horizontal axis is traffic intensity as apercentage of the building population. The threedifferent routing strategies are pure call time opti-misation with f

1 ¼ 0 seconds, pure energy optimi-sation with f

1 ¼ 1 seconds, and adequate servicelevel with f

1 ¼ 20 seconds.Considering the call times, the figures produced

by pure energy optimisation would be definitelyuseless in practice. The standard approach, purecall time optimisation, pushes the figures downto 10 seconds during low traffic intensities. Thesetwo methods together set the limits for the possiblesystem operating range. It is remarkable how wellthe third control strategy, in which we are speciallyinterested here, is able to maintain the given goalof 20 seconds.

The middle section of Fig. 13 is of special inter-est. It shows what happens to the energy consump-

0 2 4 6 8 100

10

20

30

40

50

60

70

80Average Call Time [s]

C

Operating ran

G

0 2 4 6 8 10

16

12

8

4

0

4

8

12

16

20

24240

Average Power [kW]

02 2 4 6 8 101

0.5

0

0.5

1

1.5Marginal cost ∆P/∆CT [kW/s]

2

Fig. 13. Performance results of three different control strategies: pureand specified service level 20 seconds (diamond).

tion when the service level requirement is relaxed.The power figures are obtained by dividing thecumulated energy consumption during the testrun by the test run length, i.e. P = Energy/time.The power figures thus represent the averagepower level the elevator group hoisting functionhas used during the test run.

The reduction of energy consumption and the re-quired power level are dramatic in the low andmed-ium traffic intensities. The best case is at an intensityof 6%, where the hoisting power drops 14kW—from 19 to 5kW. The extra seconds provided tothe passengers by the standard call time optimisa-tion are really expensive, as shown in the lowest sec-tion of the graph. The small difference in the 20%intensity is explained by the limit of 0.95 for theweight w1 (see Fig. 10). The system is never allowedto go to the pure call time optimisation mode, noteven at the highest traffic intensities, but the energyaspect is always kept more or less in consideration.

12 14 16 18 202

01

E-optimisation, Goal@ s∞

T-optimisation, Goal@0s

ge

oal@20s

12 14 16 18 202

0

11

12 14 16 18 20 22

0

1

Traffic Intensity (%) of population

energy optimisation (circle), pure call time optimisation (box)


Fig. 14 shows the positive side effects of the ap-proach. There is as dramatic a fall in the runningdistance of the elevators as there is in the hoistingfunction�s power level. Also the number of starts isreduced significantly.

0 2 4 6 8 10

2

4

6

8

10

00 2 4 6 8 10

100

200

300

400

500

600

700

0800

Number of Starts

Goal@20s

Running distance [km]CT-optim

12

14

16

18

20

Fig. 14. Total running distance and number of starts of the

7 8 9 10 11 12 130

10

20

30

40

50

60

.

Average Call Time [s]

Fig. 15. Average call time over a working day in an office building(down), pure energy optimisation (up) and waiting time optimisation

As both the running distance and the number ofstarts have been decreased, it means the optimiseruses the resources in a way that allows more pas-sengers to be collected into the car during oneround trip. This is in line with the properties of

12 14 16 18 202 2

1

12 14 16 18 20 22

1Traffic Intensity (%) of population

E-optimisation, Goal@∞ s

isation, Goal@0s

elevator group. Average of three 30 minutes test runs.

14 15 16 17 18 19

Hour

with traffic as shown in Fig. 8. Pure waiting time optimisationwith goal of 20 seconds (middle).


the outgoing traffic: the cars should be filled as fullas possible in order to release the potential energythat each passenger possesses.

The running distance and number of starts alsohave a system wear and maintenance aspect. Therunning distance affects directly, for example, thewear of the rope assembly. After each start to adestination floor, the elevator stops and the doorswill operate. The doors are the most sensitive com-ponent in the elevator system. Each removed startis also a removed door operation with a positiveimpact on the door maintenance needs.

Results from daily traffic are shown in Fig. 15.Outside the morning, lunch and outgoing peaks,the average call times in the ordinary waiting timeoptimisation are around 10 seconds. In these peri-ods of time it is possible to reduce the consumptionof energy. Running the system with the 20-secondtarget average call time reduces the daily energyconsumption from 288kWh consumed by purewaiting time optimisation down to 231kWh, whichcorresponds to a �20% relative decrease. At thesame time, the running kilometres are reduced by22% and the number of starts by 9%.

8. Discussion

The approach to controlling the elevator groupso that the passenger service level is regulated is anew concept in the elevator industry. In the eleva-tor industry, controlled systems have been used fora long time. The hoisting motor does not run withfull power when the elevator is driven from onefloor to another. Instead, there is a control systemthat accelerates and decelerates the car gently toassure a good ride comfort. The door motor doesnot open and close doors as quickly as possible.Instead, there is a control system which drivesthe door according to a smooth speed curve. Sim-ilarly, the group control system should not operatewith full power all the time. Instead, the groupcontrol system shall provide adequate passengerservice with minimum energy consumption. Withthe presented approach, the elevator group per-formance is under full control and can be definedexplicitly and understandably simply with oneparameter, the average call time or passenger wait-

ing time. As a bonus, the weight w1 varying inrange from 0 to 1, can be presented to the systemoperator as a relative load indicator.

The presented ESOWA enhancement to theWA method—the standardisation of the objectivefunctions based on the statistical properties of theinitial population—is of a general nature and canbe used in any application if the problem nature al-lows the straightforward WA method to be ap-plied at all. With ESOWA, the DM does nothave to worry about the objective function ranges,but all the objective function weights may be givenin the range of 0–1. In this application, whereevery building has its own characteristics andevery optimisation task differs from its predeces-sor, this is an essential benefit and requirement.

The orthodox approach to tackle the MO prob-lem is to utilise some of the developed non-domi-nance rank based evolutionary MO method,obtain a large set of non-dominated solutions andpick the onewhich best satisfies theDMutility func-tion. The big obstacle with this approach is the com-putational load compared to the available timeframe to obtain the control actions and computingresources in the target control hardware. In addi-tion, these methods are not totally free of applica-tion-dependent tuning parameters. Moreover, inthe end, only one solution is used and the othersare discarded. In away, this is awaste of scarce com-putational resources in the target hardware. Be-cause of that, the decision to study the use of thecomputationally effective WA method was taken.

Now, the question still remains why the WAmethod gives good results here although, referringto Fig. 9, the problem clearly has concave regionsand the WA method is able to find only a few dis-tinct solutions and apparently shouldn�t workproperly. If the optimisation task consisted of thissingle one, then the performance would be intoler-able. However, here the optimisation task is anendless procedure triggered twice a second to solvecontinually varying problems. There is no final an-swer and no final Pareto-set that should be ob-tained. In these circumstances, in the longrun, although there are regions that are hiddenfrom the straightforward WA method, the DM isable to guide the optimiser and the process sothat the set goal will be satisfied sufficiently. The


standard interactive process described in MO liter-ature to solve one optimisation problem is herespread over the time. In that context, the successof applying theWAmethod to solve a problemwithapparently concave regions can be understood.

9. Conclusions

The present paper introduced an approach tothe control type to be used in optimisation applica-tions. The focus in this paper was to enhance theformer single-objective elevator group controlmethod to bi-objective control with two conflictingobjectives—the consumption of energy of the ele-vator routes and the system service level in termsof average call time. The bi-objective optimisationis performed in real time by the EvolutionaryStandardised Objective Weighted Aggregationmethod presented here. Because of the real timeand stand-alone requirements, special attention ispaid to the computational efficiency and automaticscalability to the problem being optimised. An in-ner control loop was established to regulate theservice level of the elevator group. Within theinner loop, a PI-controller interacts as a DecisionMaker with the optimiser. Simulations with high-rise office building as a test case ensured the feasi-bility of the approach. The results indicate that theapproach is able to maintain the specified passen-ger service level with minimum consumption of en-ergy. The reduction in the energy consumptioncomes from asymmetric properties of the elevator�shoisting system, potential energy the passengersposses and careful and economising usage of trans-portation resources. The control approach alsoprovides positive side effects on system wear andmaintenance costs. Now, with the presented ap-proach, for the first time in the elevator industry,it is possible to specify and maintain the service le-vel the transportation system should provide in anunderstandable and simple way.

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