Multiobjective Optimization of Operational Responses for Contaminant Flushing in Water Distribution...

Multiobjective Optimization of Operational Responsesfor Contaminant Flushing in Water Distribution Networks

Leonardo Alfonso, Ph.D.1; Andreja Jonoski2; and Dimitri Solomatine3

Abstract: Contamination emergency in water distribution systems is a complex situation where optimal operation becomes important forpublic health. In case of emergency corrective operational actions for flushing the pollutant out of the network are needed, which have tobe fast and accurate. Under such a stressful situation, trial-and-error simulation experiments with the hydrodynamic and water qualitymodels cannot be applied since significant number of model evaluations may be required to identify the optimal solution. This paperpresents a methodology for finding sets of operational interventions in a supply network for flushing a contaminant by minimizing theimpact on the population. The situation is treated as both single- and multiobjective optimization problem, which is solved by usingevolutionary optimization approaches, in combination with the EPANET solver engine. The methodology is tested on a simple imaginarynetwork configuration, as well as on a real case study for the city of Villavicencio in Colombia. The results prove the usefulness of theapproach for advising the operators and decision makers.

DOI: 10.1061/�ASCE�0733-9496�2010�136:1�48�

CE Database subject headings: Water distribution systems; Water pollution; Optimization; Algorithms.

Author keywords: Flushing; Operation; Optimization; Valves; Globe; COPA.

Background

Problems related to water distribution networks �WDNs� can bebroadly attributed to two large classes: design and operational.Solutions of most problems can be simplified by using math-ematical and optimization models. Optimization methods usedmay depend on the complexity of the problem and amount of timeavailable for solving it. For example, in operation, time con-straints may prevent the full exhaustive search of the optimalsolutions, whereas in design such constraints could be relaxed.Typically, optimization problem do not allow analytical formula-tion �since objective function calculation relies upon model runs�,thus they can be solved only by using relatively inefficient ran-domized direct search methods, like a popular genetic algorithm�GA� �see Goldberg �1989� and Holland �1975��. A brief overviewof the relevant research is given below.

For solving design problems, during the past three decades anumber of optimization techniques for minimizing the overallcosts of a network have been suggested and tested. Simpson et al.�1994� solved first the least cost design problem using GAs and

1Research Fellow, UNESCO-IHE Institute for Water Education, P.O.Box 3015, 2601DA Delft, The Netherlands �corresponding author�.E-mail: [email protected]

2Senior Lecturer, UNESCO-IHE Institute for Water Education, P.O.Box 3015, 2601DA Delft, The Netherlands. E-mail: [email protected]

3Professor, UNESCO-IHE Institute for Water Education, P.O.Box 3015, 2601DA Delft, The Netherlands; and, Water ResourcesSection, Delft Univ. of Technology, The Netherlands. E-mail:[email protected]

Note. This manuscript was submitted on September 22, 2006; ap-proved on June 3, 2009; published online on December 15, 2009. Dis-cussion period open until June 1, 2010; separate discussions must besubmitted for individual papers. This paper is part of the Journal ofWater Resources Planning and Management, Vol. 136, No. 1, January
1, 2010. ©ASCE, ISSN 0733-9496/2010/1-48–58/$25.00.
48 / JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT

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later Savic and Walters �1997� exposed the GAs for single-objective optimization of pipe costs related to pipe size. Similarproblem was explored by Abebe and Solomatine �1998� who ap-plied and compared two optimization approaches, adaptive clustercovering and GAs, enabling a choice between the accuracy andthe required computer time. Hewitson and Dandy �2000� includeda water quality penalty cost within the overall cost function toensure acceptable disinfectant levels in the network and opti-mized this single objective by means of the GAs approach. Inorder to prioritize budget investments in system expansions, Wuand Simpson �1996, 2001� introduced the fast messy GA in theleast cost design of pipe networks. Later, Wu et al. �2005� pre-sented a case study where the fast messy GA method was used foroptimizing a network expansion, minimizing costs and maximiz-ing benefits, using multiobjective approach. Reis et al. �1997�considered the use of GAs for maximizing the leakage reductionby finding an optimal location of isolation valves, posing it as asingle optimization problem. The water quality issue was alsotackled by Tryby et al. �2002� with the optimal location of boost-ers for secondary disinfection, formulated as a mixed integer lin-ear programming problem. Other important multiobjectiveevolutionary-based optimal pipe network design are Farmani etal. �2005�, Prasad and Nam-Sik �2004�, and Prasad et al. �2004�.

For solving operational problems, optimization methods havebeen applied to deal with different issues, such as leakage reduc-tion �Savic and Walters 1995; Pezzinga and Petitto 2005�, bothusing GA for solving single-objective problems; pump scheduling�Jowitt and Germanopoulus 1992; Pezeshk and Helweg 1996�, byusing linear programming and discrete adaptive search algo-rithms, respectively, for solving the single objective of minimiz-ing energy costs; and network disruption for repairs �Simão et al.2004�, using a logic process knowledge algorithm to find out thebest set of valves to close when a disruption of service is needed.

The real time reaction during emergency is, however, a spe-cific operational problem for which the worldwide awareness has
increased dramatically after the terrorists’ attacks of the past years
© ASCE / JANUARY/FEBRUARY 2010

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�see, e.g., Ostfeld �2006��. This operational problem should besolved, in principle in two steps:1. Identify the exact sources of contamination, moment of in-

trusion, and its duration, if possible; and2. Determine the corrective actions minimizing the propagation

of contaminant or, in more general terms, damage to publichealth.

Approaches to solve Problem 1 are presented, e.g., by Laird etal. �2005� and Preis and Ostfeld �2006�. The major results re-ported in this paper have been achieved already in 2006 in theframework of the masters study at the hydroinformatics core ofthe UNESCO-IHE Institute for Water Education �Alfonso �2006�,available at http://www.ihe.nl/hi/MSc_abstracts/2006/06-04%20Alfonso%20Segura%20Leonardo.htm�. When the paperwas submitted to ASCE in September 2006, to our knowledgethere were no published approaches dealing with Step 2. Duringthe reviewing period, Baranowski and LeBoeuf �2008� presenteda procedure to resolve Step 2. Their objective was to minimize thetotal contaminant concentration in all nodes for all times stepsafter the detection by manipulating pipe status and node demands.Their approach is characterized by the following: single-objectiveoptimization �rather than multiobjective�, nonrealistic assumptionthat flushing can be done at any node and every pipe can beclosed, lack of pressure-dependent demands, and pumps were notconsidered to be active elements in the flushing procedure. On theother hand, the writers introduced an interesting analysis of im-pact in terms of reaction time and explicitly used informationfrom sensors which is more realistic than assuming varioussources of pollution �which is, however, more general�.

In January 2007, one of the reviewers of the present paperpointed to an earlier work by Ostfeld �2006�. During the finalround of reviewing, in November 2008 we were glad to see thepublication by Preis and Ostfeld �2008� that also presented anapproach similar to ours. Their approach, however, is less generaldue to several limiting assumptions: it assumes constant-flow hy-drants for the flushing, does not consider occurrence of negativepressures, does not use pumps to assist flushing, and assumes thatonly one point in the network is polluted. It uses only the multi-objective approach, not considering the procedures for making thefinal choice of the optimal strategy.

Yet another approach for dealing with Step 2 was introducedby Poulin et al. �2008�. This heuristic approach isolates the pol-luted water by closing proper valves and leaves one pipe to letclean water to come into the isolated area, which is flushed byhydrants. Heuristic rules are applied for choosing which valves toclose, which, at the same time limit the extent of isolated areas,ensure the fast operational response and meet prespecified opera-tional constraints. Although the approach assumes static demandanalysis �a strong assumption�, it is interesting since it considersthe way the operation teams carry out the actual response.

The present paper addresses the problem of minimizing thedamage from network contamination �to be posed formally later�for situations when an operator would not have enough informa-tion to identify the sources of contamination with the adequateaccuracy. For example, these are cases when there is informationabout the high concentration of a pollutant only from one moni-toring node �sensor�. In such cases Problem 1 cannot be reliablysolved �until more information is collected� but Problem 2 stillhas to be solved quickly. This paper addresses Problem 2 and formodeling purposes it is simply assumed that the contaminant isintroduced at the monitoring node.

When contamination events take place in a WDN, the opera-
tor’s reaction must be quick and accurate �to avoid contamination
JOURNAL OF WATER RESOURCES PLANN


propagation�. However, under emergency conditions the processof decision making is very difficult and often stressing. From oneside, the rational decision about the operation actions to be takenis not easy, even if a hydraulic and quality model of the systemare available; from another side, such decision must be taken in ashort period of time, with the associated stress.

When the pollutant concentrations are extremely high andthere are imminent life losses, the utilities must shut the entiresystem down. Nevertheless, a different approach can be adoptedwhen less harmful contamination is found: isolating the contami-nant by operating valves in order to reduce the affected area of thesystem and simultaneously open accessories like hydrants, vents,or drains are used to flush out the contaminated water. Switchingpumps is also within the operational possibilities. However, theselection of the appropriate set of elements to be operated is amain issue because the hydraulic behavior and the water qualityin looped systems are quite complex and because a wrong selec-tion could make the situation worse.

On the other hand, the restricted time for reaction, and thestress associated with the public health concern, makes it impos-sible to conduct experiments at that particular moment with amodel in order to find a solution. It has to be pointed out that evenwith enough time for analysis and with a reliable model, a suit-able solution may not come up easily, simply because of the factthat the number of the system elements to be operated may bevery high.

In this paper, the problem of operational responses is ad-dressed by using currently available optimization methods to-gether with the hydraulic and quality solvers for pressurizednetworks, by solving an optimization problem in a multiobjectiveformulation by the nondominated sorting GA II, NSGA-II �Deb etal. 2002� and in a single-objective formulation with the criteriacombined by a GA. Both optimization approaches are applied tothe two case studies: a simple imaginary WDN and a real-worldsystem.

Formulation of the Operational Responseas an Optimization Problem

We consider a WDN with pipes �some of them represent valves�,nodes �some of them represent hydrants�, and pumps. Removal ofcontaminant is supposed to occur when flushing is performed by“interventions” �operational actions�—opening or closing certainvalves or hydrants or switching pumps. Such interventions areconsidered to be decision variables in this problem and theirnumber is equal to the number of elements �valves, pumps, orhydrants� to be operated. The problem is in identifying the valuesof decision variables �i.e., interventions� that prevent the pollutantpropagation �reducing associated damages�. At the same time thenumber of interventions, or network changes, which are associ-ated with costs, are to be minimized as well. Figs. 1 and 9 �casestudies� provide examples. Note that in this paper the terms “ob-jective” and “criterion” are used interchangeably.

Criteria „Objectives…

The problem is considered to be a multicriteria �multiobjective�and involves two main criteria: criterion C1 characterizing dam-age to public health associated with the network contaminationand criterion C2 representing the costs associated with the opera-tional effort required to set the network to a desirable condition.
These criteria �objective functions� are characterized below.
ING AND MANAGEMENT © ASCE / JANUARY/FEBRUARY 2010 / 49


Criterion C1 relates to the damage to public health associatedwith the network contamination �measured by the total cost in-curred by contamination�. The value of this criterion depends onthe existence of certain pollutant concentrations in the networkand has to be minimized. There are various ways to formulate thiscriterion.

Formulation �1� considers the damage at any given node to becalculated as the function of the number of nodes polluted at leastat one time step during the entire simulation period �referred to as“number of polluted nodes,” npn�. By a “polluted node” we un-derstand a node with pollution concentration above a specifiedthreshold. When minimizing C1, indirectly two key issues areaddressed: first, reducing the pollution extent �contaminated area�in the network and second, reducing the time of exposure of con-centrations above the threshold. Formulation �2� considers dam-age at any given node that is calculated as the sum of damages ateach time step and the latter is calculated as a nonlinear “nodaldamage function” of the concentration �a version of the sigmoidfunction which has to be calibrated for every situation can be

P1 P

P5 P

P9 P1

P13 P1

P17 P1

P33

P34

P35

P36P37

P38

P39

P40

P41 J2 J3

J8J9

J10 J11

J16J17

J18 J19

J1

Pollution sourcefor scenariosSc1, Sc2, Sc3

Pollutionfor s

Pollution sourcefor scenario

Sc2

Valve Pollu

Fig. 1. Distribution network of Case S

used�. The total network damage could be defined as the sum of



the damages of each node in the network for all time steps of thesimulation. Note that these formulations are crude and of coursedo not contain all the factors allowing for accurate assessment ofthe damage to public health. Moreover, it is clear that some nodeshave bigger impact on public health than others if they becomecontaminated, e.g., supply nodes for schools, hospitals, anddensely populated areas. However, in this paper, it is assumed thatthe population density is equally distributed over the nodes so allnodes are equally important in terms of impact.

In principle we may introduce other formulations as well, forexample, to consider the risk of contamination, understanding byrisk the potential damage multiplied by the probability of therealization of this damage �for example, associated with prob-abilities of contaminant intrusion at various nodes and times�.However, it is not a trivial task to accurately assess these prob-abilities �see, e.g., Ostfeld et al. �2006�� so full model of risk isnot considered here.

We performed experiments using formulations �1� and �2� forC1 but for the sake of testing the optimization methodology only

P3 P4

P7 P8

P11 P12

P15 P16

P19 P20

P21

P22

P23

P24

P25

P26

P27

P28

P29

P30

P31

P32

J4 J5

J6J7

J12 J13

J14J15

J20 J21 J22

J23

J24

J25

J26Day 1, 2:00 AM

eo3

ource Hydrant Reservoir

with scenarios of pollution considered

2

6

0

4

8

sourccenari

Sc

tion s

tudy 1

the results using formulation �1� will be presented, so C1=npn.



The reason to use this simplistic formulation is that it does notdepend on the choice of damage functions, which is often verydifficult to construct and which have influence on the optimiza-tion results. Of course, in real-life applications, each particularcase needs studies to identify the appropriate class of damagefunctions assessing public health risk, which is a considerableproblem in itself; �see, e.g., National Research Council NRC�2005��, and this should be a topic of further studies.

Criterion C2 �to be minimized� represents the costs associatedwith the operational effort required to set the network to a desir-able condition, e.g., closing certain valves and/or opening hy-drants for flushing the contaminant. There are also various waysto formulate this criterion, but in this paper we consider its valueto be the number of the operational interventions �oi� needed. Inreal-life applications the appropriate cost function that would re-flect the actual costs associated with the oi should be used.

Constraints

A number of constraints are considered: positive nodal pressures,topological checking to ensure network connectivity, and techni-cal operational capacity to implement interventions.

Approaches to Solving an Optimization Problem

The posed multiobjective optimization problem can be solvedusing two approaches:• Multiobjective optimization: when a number of solutions are

generated, such that each of them is better than at least oneother solution on at least one objective �so in this respect nosolution can be formally preferred to another one�, and it is upto the decision maker to make a selection between them;

• Single-objective optimization: when several objectives arecombined �for example, as a weighted sum or by measuringthe distance to the “ideal point”� into one composite objectiveand a solution is sought that minimizes this objective.

Methods and Tools

Multiobjective Formulation

The multiobjective optimization problem can be defined as theproblem of finding a vector of decision variables that satisfiesconstraints and optimizes a vector function whose elements rep-resent the objective functions. Since these objective functions areusually in conflict with each other, the term “optimize” meansfinding such a solution that would give the values of all the ob-jective functions acceptable to the decision maker.

Vector of decision variables �X�� is optimal if there is no fea-sible vector of decision variables �X� which would improve someobjective without causing a simultaneous degrading in at least oneother objective �see, e.g., Tang et al. �2005��. Formally, for aminimization problem, �X�� is Pareto optimal if for each�X�� and I= �1,2 , . . . ,k�, either

f i��X�� f i��X��, ∀ i � I �1�

or there is at least one i� I so that

f i��X�� f i��X�� 2�

where I=set of integers that range from one to the number of total�
objectives; �X� and �X �=vectors of decision variables; �


=decision space; k=number of objectives; and f =objectivefunction.

In the problem addressed, the costs C1 and C2 mentionedabove are considered as separate objectives to be minimized in-dependently. An example where a number of generated solutionsare displayed in two-criteria space is presented in Fig. 2. Thepoints represent states resulting from particular operational con-figurations of the network; the dark points represent the Pareto-optimal set of solutions.

Single-Objective Formulation

The multiobjective problem can be transformed into a single-objective one, by combining all the objectives Ci �i=1, . . . ,N�into one objective C. This can be done in a number of ways, forexample, by weighing the N objectives

C = �i=1

NwiCi �3�

where

�i=1

Nwi = 1 �4�

in the case of two criteria N=2 and C=wC1+ �1−w�C2, note thatthe criteria values have to be normalized to prevent the domina-tion of objectives with high values over other objectives and, forthis, additional study is needed to identify the possible minimumand maximum values of all objective functions.

Another way of combining the objectives is by measuring thedistance to the ideal point where all criteria take the minimumvalue. If such a point is at the origin of the criteria space �corre-sponding to no contamination and no operational costs� then thecomposite objective is �Fig. 2�

C = ��i=1

NCi

2 �5�

For the problem considered N=2 and

C = �C12 + C2

2 �6�

where C1 relates to damage due to contamination and C2 relatesto the cost of the oi required to set the network to a desirablecondition. This objective function ensures damage and interven-tions in the network �costs� receive the same weight. In the case

Fig. 2. Definition of objectives for single- and multiobjective opti-mization

studies below we used Eq. �6�.



Tools Used and Experimental Setup

Due to the fact that the objective function values are calculated byrunning a model, it is not possible to apply the gradient-basedmethods of optimization. In such cases the methods based onrandomized search are typically applied. The advantage is alsothat such methods do not typically assume existence of a singleextremum �minimum� so they are referred to as global �multiex-tremum� optimization methods. One of the ideas widely used inrandomized search is the idea of evolutionary optimization �see,e.g., Deb �2001��. For single-objective approach the global opti-mization methods implemented in GLOBE software �Solomatine1999� are used, and the optimization process is organized in afashion similar to the one used by Abebe and Solomatine �1998�.For multiobjective approach the NSGA-II method �Deb et al.2002� implemented in the NSGAX software �Barreto et al. 2006�is used. The function to be optimized is encapsulated in the ex-ecutable program called changing operation in pollutant affecta-tion �COPA�, which is presented below.

GLOBE. GLOBE �Solomatine 1999� is an optimization toolthat can find the minimum of a function dependent on multiplevariables, the value of which is given by an external program or adynamic link library. It is possible to impose box constraints�bounds� on the variables’ values. No special properties of thefunction are assumed. There are seven �with variations—nine�algorithms of randomized search implemented so that the user cantune to his/her problem and that can be run in a batch for the samefunction. The algorithm used for this paper was GA.

COPA module and interaction with GLOBE. The COPA mod-ule was developed as a console application in Borland Delphi andit runs the EPANET hydraulic and quality engine solver for dis-tribution networks �Rossman 2000�. Note that to calculate objec-tive functions once, COPA may need to run EPANET in extendedperiod simulation mode and with short time step and long simu-lation time this could be a computationally intensive task. Given anew operational network state it calculates the objective functions

Calculatenumber ofoperational

interventions, oi

Rhydrand qsimumo

Update inputfile of

simulator

Read elementsstatus and

parameter files EPANET.INP

File containingpotential solutions(element status)

Optimal so

S

S

GLOBE/NSGAX

COPA MODULE

no

Fig. 3. Interaction COPA op

C1 and C2 �and aggregates them into C�. These outputs are stored



in a text file which can then be read by optimization tool �GLOBEor NSGAX�. The communication between the optimization tool,COPA and EPANET �Fig. 3� employ the EPANET programmertoolkit.

The role of an optimization tool is to generate an input vector�characterizing the operational intervention and, hence, the newnetwork status� and supply it to COPA module. Dimension of thisvector is equal to the number of elements �valves, pumps, orhydrants� to be operated, and its values are binary numbers �0sand 1s� indicating the operational status of each element: 1 indi-cates that the corresponding element is open �switched on� and0—closed �switched off�. The following two sections cover thecase studies, along with the obtained results and discussions.

Case Study 1

A simple WDN is considered �Fig. 1�. It consists of a system of41 pipes with the same diameter, length, and Manning roughness�0.20 m, 1,000 m, and 0.01, respectively�, 25 junctions with zeroelevation and 0.5 L/s of base demand which are affected by atypical consumption pattern. The reservoir provides the systemwith a constant head of 50 m. Valves are located in the pipes P2,P6, P10, P14, and P18 �all initially opened� while the hydrants,originally closed, are located in the nodes J9 and J13. The systemis polluted by a conservative contaminant that is injected underthree possible scenarios Sc1 �one node—J9�; Sc2 �two nodesclose to each other—J9 and J10�, and Sc3 �two nodes far fromeach other—J9 and J15�.

In each scenario it is assumed that the location of the contami-nation sources become known after applying some availablemethod �see, e.g., Preis and Ostfeld �2006��, from which the lo-cation of the pollutant injection, the time ti when injection tookplace, and the concentration of c are known. The duration of theinjection di, however, is an additional variable that requires to be

Count number ofpolluted nodes inthe simulationtime, npn

Calculatecombined

objective C forSingle-Obj.Opt.(GLOBE)

Write C forSingle-Obj.Opt.(GLOBE)

found?

Write oi, npn forMulti-Obj Opt.(NSGAX)

tion tool �GLOBE/NSGAX�

unaulicualitylationdel

NET

lution

tart

top

yes

timiza

assumed. The initial status for all valves is considered to be 1



�opened� and for all hydrants to be equal to 0 �closed�. A node isconsidered polluted when its concentration exceeds the thresholdvalue ct. A conservative pollutant is also assumed.

In EPANET flow through an open hydrant is simulated as anemitter, with pressure-driven demand Q given by Q=K�P, whereK is the emitter coefficient and P is the pressure drop across theemitter. In order to simulate the opening of a hydrant a patterndemand was introduced so that it starts flowing tr hours after theinjection takes place. This time of reaction includes the time re-quired for detection, simulation, personnel transportation, and op-eration of the accessories in question. Additionally, a minimalresidual Pmin pressure in the network has been set as a constraintin the optimization problem. Certainly, there might be networkconfigurations in which the pressure in one or more nodesdropped so low that back-siphonage effects with the associatedwater quality problems may be generated. For simplicity, param-eters tr and Pmin are user defined. For all three scenarios thefollowing parameters values were used: ti=02:00; c=100 mg /L; ct=5 mg /L; di=3 h; tr=4 h; K=10 l /s /m0.5; andPmin=1 m.

It must be noted that the considered problem is quite simple interms of optimization: the number of evaluations required tocover the full solution space is only 27=128. Therefore, the GAwas set to run with the relatively small population �20� and thenumber of generations �5� resulting in 100 evaluations �COPAruns� which constitutes 78% of the solution space.

Single-Objective Optimization

Eq. �6� is used to calculate the �single� objective characterizingthe quality of the solution from the two objectives C1 and C2. Inthis case there are seven variables, which can be either 0 or 1, andthe network has the initial status 1111100 for the elements P2, P6,P10, P14, P18, J13, and J17. This means that initially all valvesare opened and the two hydrants are closed. The solutions ob-tained for each scenario are shown in Fig. 4, where the opera-tional status of the network for each scenario is shown togetherwith their values for C. It must be added that for this case nonormalization of C1 and C2 was carried out because, for thissimple case, both npn and oi are numerically similar. This situa-

Single-objective optimization C→ minSolutions for t i=02:00, d i=3h, t r=4h

0

2

4

6

8

10

12

0 1 2 3 4 5

Number of operational interventions, oi

Numberofpollutednodes,npn

Sc 1: J9 pollutedSc 2: J9, J10 pollutedSc 3: J9, J15 polluted

P2: 1P6: 0P10: 0P14: 0P18: 1J17: 1J13: 0C=8.06

P2: 1P6: 0P10: 1P14: 1P18: 0J17: 1J13: 0C=10.44

P2: 1P6: 0P10: 0P14: 1P18: 1J17: 1J13: 0C=7.62

Fig. 4. Single-objective optimization solutions for Sc1, Sc2, and Sc3of Case Study 1, presented in the npn-oi solution space

tion is different for bigger networks, as discussed in the next



section. �It is worth mentioning that for the considered simplenetwork the optimal solution found by GA coincides with the oneobtained by exhaustive search.�

In spite of the apparent simplicity of the problem for the firstscenario, the solution found is not trivial. Indeed, for scenariosSc1 and Sc2 an intuitive solution would be, probably, to close P6,P10, P14, and P18—in order to isolate the contaminated area—and to open J17 to flush the contaminant out. However, this so-lution requires five oi and the npn is nine, yielding a functionvalue of C=10.29, which, obviously, is far from being an optimalsolution. This proves the difficulty of choosing the best configu-ration even in a simple network, with enough time available fortrial-and-error analysis. Note that the mentioned intuitive solutioncan be obtained in the optimization process if a very low concen-tration value is considered as threshold. In this case, one portionof the network will be highly contaminated while the rest of itwill be completely clean. This shows that the suggested method-ology is flexible to be used under different scenarios.

Solutions obtained for the first two scenarios are similar: pipesP6 and P10 are selected for closure and J17 is the hydrant to beopened. The only difference between them is that for Sc2 pipeP14 is also closed. The value of C is a bit higher in the secondscenario due to the fact that two nodes are contaminating thenetwork. The impact of the solutions for each scenario can beobserved by comparing the resultant concentrations in the mostaffected �closest to the source� nodes �J8, J10, J11, and J12� withthe concentrations when no oi are carried out. For Sc1, the statusof the system when no oi are made is presented in Fig. 5�a�. J10and J12 are suffering the most as they are immediately after thepollution of 100 mg/L during 3 h occurring in J9. Fig. 5�b� showsthe effects of closing P6, P10, and opening J17: even though nodeJ10 has the same performance �due to the reaction time of 4 h�, inall mentioned nodes the pollution is under the threshold of 5 mg/Lafter 08:00. On the other hand, people demanding water from J12are exposed only 1 h to a higher concentration, whereas in theoriginal situation the exposure was lasting from 8:00 to 14:00 h.Figs. 6 and 7 show the same effects �reduction of exposure timeand concentrations� when analyzing the solutions obtained forscenarios Sc2 and Sc3, correspondingly.

Multiobjective Optimization

As mentioned before, the multiobjective problem was defined asminimization of the damage to public health C1, �in this papermeasured as npn, as explained in “Criteria �Objectives�”� and theassociated operational costs C2 �measured as the number of oi� inthe network as separate objectives.

The algorithm was applied for the problem posed, using thesame evolutionary parameters as in the case of the single-objective optimization. In Fig. 8 Pareto-optimal solutions for eachscenario are presented. The dashed ovals indicate that for a par-ticular number of oi the same solution was found. It is interestingthat for the three scenarios, one of the possible solutions is tomake no interventions at all, pipe P6 is always included �as in thesingle-objective optimization approach� and that opening the hy-drant J13 is not considered in any of these solutions.

Additionally it can be noted that if only one intervention isconsidered �oi=1�, this action, which is to close P6 in all threescenarios, does not reduce significantly the npn value: it is re-duced only by 1 if compared to the “do-nothing” option. Thisaction isolates the pollutant and facilitates its dilution but since noflushing is involved, the pollutant remains in the network affect-
ing almost the same number of nodes. Consider now the solution


with oi=2 for Sc1 and Sc2: it includes flushing through hydrantJ17—an action quite consistent with an engineering judgment.These two actions already lead to a considerable reduction of npn.For the case of oi=3, closing pipe P14 is now added to the set ofpreviously mentioned interventions and the value of npn ishalved. Note that for oi=3 the same solution was obtained withthe single-objective optimization approach for Sc1 when two ob-jectives were aggregated �Fig. 4� and therefore the analysis ofpollutant concentrations in time presented in Fig. 5 is valid forthis case as well. This analysis demonstrates the usefulness ofhaving several solutions to be considered by a decision maker inthe process of selection of the best one.

The results obtained with both single and multiobjective opti-mization demonstrate that the use of the npn across all simulationtime as objective function helps in reducing both exposure timeand pollutant concentrations, as can be noted from Figs. 5–7.These variables affect directly the damage in public health,which, however, is not quantified explicitly in this paper.

Case Study 2—Villavicencio, Colombia

A case study in Villavicencio, Colombia is considered. A source

(a)

(b)

Fig. 5. Effect of the solution for Sc1, Case Study 1, on pollutantconcentrations at selected nodes: �a� do-nothing alternative; �b� solu-tion of Sc1, Fig. 4

of pollution is supposed to be identified in a node of the hydraulic



Sector 11 of the Villavicencio supply network �Aquadatos 2000�and the best options for operating the system have to be found. InEPANET model of the Sector 11 there are 247 junctions �fromwhich 30 are considered hydrants initially closed�, 367 pipes�from which 60 are considered to contain valves, all initiallyopened�, and two pump stations, initially switched off �Fig. 9�.This means that 92 elements are possible to be operated andtherefore this is an optimization problem with 92 variables. Asin the first case study, a conservative contaminant is injectedunder three possible scenarios: Sc1 �one node—J2119�; Sc2�two nodes close to each other—J2119 and J2120�, and Sc3�two nodes far from each other—J2119 and J2164�. For allthree scenarios the following parameters values were used: ti

=02:00; c=230,000 mg /L; ct=0.3 mg /L; di=4 h; tr=5 h; K=10 l /s /m0.5; and Pmin=1 m.

With 92 binary variables, this problem needs a serious compu-tational efforts. The total number of possible solutions �searchspace� is 2924.95�1027. With such an enormous search space nooptimization algorithm will guarantee the convergence to a globaloptimum so we have adopted a two-phase procedure. First, afterseveral experiments aimed at optimizing the convergence and ac-curacy of the algorithms, we have adopted the GA and NSGA-IIparameters, according to Table 1. Then we ran GA and NSGA-II

(a)

Pollutant concentration at selected nodesSolution for Sc2: P6, P10 and P14 closed; J17 open

4 interventions, 7 affected nodes

0102030405060708090100

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (h)

Concentration(mg/L)

Node J8

Node J9 (polluted)

Node J10 (polluted)

Node J11

Node J12

Threshold = 5mg/L

(b)


and found a number of feasible �hopefully close-to-optimal� so-



lutions. We analyzed the sets of oi present in these solutions andfigured it is worth considering further only 18 elements to beoperated. With these 18 binary variables �and much smallersearch space with only 2182.62�105 possible solutions� we ranGA and NSGA-II again with the same GA parameters �requiring

(a)Pollutant concentration at selected nodes

Solution for Sc3: P6 and P18 closed; J17 open3 interventions, 9 affected nodes

0102030405060708090100

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (h)

Concentration(mg/L)

Node J8

Node J9

Node J10

Node J11

Node J12

Threshold = 5mg/L

(b)


Multi-objective optimizationSolutions for t i=02:00, d i=3h, t r=4h

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4


Numberofpollutednodes,npn Sc 1: J9 pollutedSc 2: J9, J10 pollutedSc 3: J9, J15 polluted

P2: 1P6: 0P10: 0P14: 1P18: 1J17: 1J13: 0

P2: 1P6: 0P10: 1P14: 1P18: 1J17: 0J13: 0

P2: 1P6: 0P10: 1P14: 1P18: 1J17: 1J13: 0

Fig. 8. Pareto-optimal solutions of the multiobjective optimizationfor Sc1, Sc2, and Sc3, Case Study 1



5,000 COPA model runs and 89 min of running time on a 2.4-GHz PC�. The identified solutions are reported below. We realizethat the choice of optimization algorithms’ parameters may needfurther attention �we just used the order of values generally rec-ommended in the literature� but due to the computational com-plexity of this exercise we leave this for further research.

Single-Objective Optimization

Fig. 10 presents the solutions for the three scenarios. As in thefirst case study, Eq. �6� is used to calculate the single-objective Cfrom C1 and C2, again with C1=oi and C2=npn. In order to giveequal weights to these criteria, both have been normalized duringthe optimization process by dividing them by the maximum pos-sible values for each one. Note that for comparison purposes inFig. 10 the nonnormalized criteria values are used. For this casestudy the solutions that require more than 15 oi have been ne-glected. There are two reasons for that: first, it represents a ver-sion of “operational capacity constraint” and, second, this allowsfor saving a considerable amount of computational time.

It is possible to see that solutions for scenarios Sc1 and Sc2 arethe same because the pollution spreading is similar in both cases.

J2119Pollution source

for scenarios

Sc1, Sc2, Sc3

J2164

Pollution sourcefor scenario

Sc3

J2120Pollution source

for scenario

Sc2

Pump 1

Pump 2

Pump station Valve Pollution source Hydrant Reservoir

P1304

P1439

J1199

P2814

J2118

P1408

P1463

P1342

P1461

Fig. 9. WDN of Sector 11, Villavicencio

Table 1. GA Parameters Used for Single- and Multiobjective Optimiza-tion

Parameter

Single-objective GA Multiobjective NSGA-II

CS 1 CS 2 CS 1 CS 2

Selector FR FR FR FR

Population size 20 100 20 100

Number of generations 5 50 5 50

Crossover probability 0.9 0.9 0.9 0.9

Mutation probability 0.1 0.1 0.1 0.1

Elitism BCK BCK BCK BCK

Note: CS�case study; FR�fitness rank; and PCK�best chromosomekept.



The solution that gives the minimum value of C requires three oiand affects eight nodes. This improves the situation significantlyif compared to the do-nothing alternative, as a npn reduction of88% is obtained �see Table 2�. Moreover, the results for Sc3 alsoshows a good performance: with just five interventions the npngoes down to 13 �reduction of 84%�.

A number of interesting observations are worth mentioning�see Fig. 9 and Table 2�. First, the closure of pipe P1439 and theopening of J2118 �Fig. 9� are the unique oi that are common tothe solution of all three scenarios. Second, no pump operation isconsidered in these solutions. Third, in order to avoid the pollut-ant propagation to the southern part of the network, P1408 be-comes an important element in the solution for Sc3. For thisscenario, the closure of P1500 is important: if it is not operatedtogether with the other four elements, the npn value is increasedup to 90, which is worse than the do-nothing alternative. It can besaid that without the optimization tools it would be very difficultto find that the closure of P1500 �not a trivial choice!� leads to aconsiderable reduction in pollutant spread.

Multiobjective Optimization

In this case the objectives C1=oi and C2=npn are to be mini-mized as well. Before the results of optimization are analyzed, apossible “intuitive” solution for Sc1 is presented: closed pipesP1342, P1461, P2814, and P1463 and open hydrants J1199 and

Single-objective optimizationSolutions for t i=02:00, d i=3h, t r=4h

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6


Numberofpollutednodesnpn

Sc 1: J2119 polluted

Sc 2: J2119, J2120 polluted


P1408=0P1439=0P1500=0P1428=0J2118=1

C=0.27

P1304=0P1439=0J2118=1

C=0.16

Fig. 10. Multiobjective optimization solutions for Sc1, Sc2, and Sc3of Case Study 2, presented in the npn-oi solution space

Table 2. Solutions for Sc1, Sc2, and Sc3 for Single- and Multiobjective

Element

Initial status

Single

Sc1

npnSc1=69npnSc2=69npnSc3=84 C=0.16npn=8oi=3 C

PMP-1 0

J2118 0 1

P1304 1 0

P1408 1

P1439 1 0

P1500 1

P2814 1

Note: 0�closed/off and 1�opened/on.



J2118, in order to isolate the pollution and flush it �Fig. 9�. Thisconfiguration yields npn=83 with oi=6, which, as our furtheranalysis shows, is not optimal. Even more, this solution rises thenpn value by 16% with respect to the do-nothing alternative,which is patently unacceptable. A detailed analysis of this solu-tion shows that the closure of P1342 and P1461 indeed stops thepollution spread toward the east but, at the same time, these clo-sures increment the velocities of the pipe nearby the pollutionsource with the consequent pollutant propagation to the west,where there are not enough valves available to completely stop it.This demonstrates how dangerous it is to follow intuitivesolutions—which are also not easy to find in large networks.

Referring to the results of optimization presented on Fig. 11and Table 2, a number of interesting outcomes from our experi-ments that can be mentioned are:• If solutions with oi=1 are considered, the following can be

observed. In Sc1 and Sc2, the npn reduces by 40% just byclosing pipe P1304 �Fig. 9�, which is a nontrivial solutionsince it is far away from where pollutant has been injected.Although the reason for this is that pollutant is not spreadbecause flow velocities in the area drop considerably, it isalmost impossible to come up with this solution just by play-ing manually with the model. Similar situation occurs for Sc3,in which npn drops by 40% just by switching on the pump 1.

• For Sc1 a solution with an npn=1 was found, with oi=4, inwhich closing P2814, P1439, and P1500, together with open-

ization of Case Study 2

tive optimizationMultiobjective optimization

�solution for oi=1�

Sc2 Sc3 Sc1 Sc2 Sc3

npn=8oi=3 C=0.27npn=13oi=5 npn=42 npn=42 npn=56

1

1

0 0

0

0

0

0

Multi-objective optimizationSolutions for t i=02:00, d i=3h, t r=4h

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6


Numberofpollutednodes,npn Sc 1: J2119 polluted



P1304=0P1439=0J2118=1

P1408=0P1439=0P1500=0P1428=0J2118=1

Fig. 11. Pareto-optimal solutions of the multiobjective optimizationfor Sc1, Sc2, and Sc3, Case Study 2

Optim

-objec

=0.16

1

0

0



ing J2118 are the interventions to make. In this case, only thenode J2119 �the pollution source� is contaminated. The mini-mum value for Sc2 is also obtained with the previously men-tioned solution, yielding npn=4, which represents a reductionof 94% with respect to the do-nothing alternative.

• Due to the complexity of the pollution scenario Sc3 the num-ber of oi is higher than is needed for Sc1 and Sc2: to reducenpn significantly �from 84 to 13� five interventions are needed.The elements to operate in this case are J2118, P1439, andP2814 �selected in previous solutions�, having in addition tomodify P1408 and P1500. This yields npn=13; note that thissolution was also found as a result of single-objective optimi-zation.

• The solutions found for Sc1 and Sc2 with oi=3 are the samethat were obtained with the single-objective approach �see Fig.10� and therefore the analysis presented in Single-ObjectiveOptimization applies as well.

• It is very interesting that in all the solutions that yield the leastvalue of npn, only one hydrant, J2118, was included, even forthe complex case of Sc3.Now, possibly exhausted, the reader will be happy to move to

the next section.

Conclusions and Recommendations

From this study the following conclusions can be drawn:• With respect to earlier research reviewed in Background, the

present work introduced new methods enhancing contamina-tion management of WDNs.

• Three basic factors are present in all the solutions found inboth case studies: they all tend to isolate the contaminant, toflush it out, and/or to dilute it.

• The results revealed that there exist combinations of oi thatcould be even more dangerous than the do-nothing alternative,in terms of network damage. For example, in some cases theuse of pump stations for accelerating the flushing process isnot always a good idea.

• Although isolation, flush, and dilution are considered whentrying to come up with an intuitive solution that solves theproblem properly, this is a very difficult task. For the first casestudy the presented intuitive solution was relatively easy toobtain due to its simplicity but still that solution was notamong the optimal solutions. For the second complex casestudy, a good intuitive solution �such that at least reduces npnif compared to the do-nothing solution� could not be evensuggested.

• Results demonstrate that using the npn as an objective functioncharacterizing the impact on public health is a simple androbust way to deal with the extension of the contamination, thetime of exposure of the nodes to the pollutant, and its concen-tration values. Additionally, this concept provides a straight-forward picture of the state of the network for the decisionmaker.

• A multicriteria approach �as opposed to single-criterion one�makes it possible to generate several solutions from which themost appropriate one can be chosen based on additional analy-sis; such involvement of a decision maker may improve theacceptance of the system by managers and practitioners.

• Model-based optimization for real-life problems requires con-siderable computational effort and the adopted two-phase pro-
cedure helped to arrive to optimal �or close-to-optimal�


solutions even with PC-level computing power and quite stan-dard optimization algorithms.

• The framework �COPA—EPANET—optimization toolsGLOBE and NSGAX� can be used for other case studies and itis flexible enough to incorporate various pollution scenarios.The following recommendations can be suggested:

• Since the damage function used in this paper was simplistic�albeit robust�, more sophisticated definitions would be worthformulating based on the following possible approaches �notmutually exclusive�:

• To separate the contamination impact into more objectivefunctions, in particular, extension of contamination, pollutantconcentration, and time of exposure;

• To formulate a suitable definition of contamination risk to beused as an objective function, in order to consider all the pos-sible factors that can affect the public health.

• The objective function associated with the operational costs�in this paper being simply the number of oi� could be modi-fied to consider the travel time of the operators from the watersupply station to the place where the interventions are re-quired, the time needed by the operators for closing a particu-lar type of valve, as well as the optimal path that must be takenby the operators to operate the network. For this purpose, theelements with the higher impact in the network should be thefirst to intervene.

• Some of the assumptions made in this paper could be relaxedor dropped and it is recommended to do so. For example: �1�allow for scenarios with pollution occurring at different times;�2� allow for situation with unknown pollution sources �anddevelop methods including the approach suggested by Preisand Ostfeld �2006��; and �3� allow for oi to be phased in time.

• It would be useful to develop the rules for selecting a limitedset of elements to be changed since this will decrease the sizeof the optimization problem.

• For large networks, this methodology can be used to generatein advance the optimal interventions for various possible con-tamination scenarios. In this way they would be available im-mediately when a contamination event is detected.

• In this research, only the evolutionary optimization algorithms�GA and NSGA-II� were employed. However, for large net-works their running times may be prohibitively long. Thisprompts for the development of other more efficient randomsearch methods requiring less model runs.

Notation

The following symbols are used in this paper:C � composite objective;Ci � single-objective i;c � concentration of the pollutant at the source

�mg/L�;ct � concentration of the pollutant that is considered

harmful �mg/L�;di � duration of the pollutant injection �h�;K � emitter coefficient for pressure-dependent

flow in hydrants �l /s /m0.5�;N � number of objectives;

Pmin � minimal residual pressure allowed in thenetwork �m�;

ti � time at which pollution has been injected
�hh:mm�;


tr � time of reaction for operational responsesince ti �h�;

wi � weight value for the objective i;�X� � any vector of decision variables; and

�X�� optimal vector of decision variables.

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