57 optimizing water quality monitoring stations using genetic ...

OPTIMIZING WATER QUALITY MONITORING STATIONS
USING GENETIC ALGORITHMS
Muhammad A. Al-Zahrani * and Khurram Moied
King Fahd University of Petroleum & Minerals
Department of Civil Engineering
Dhahran 31261, Saudi Arabia
: ﺔــﺻﻼﺨﻟا
ﻚﻟذو ،ﻊﻳزﻮﺘﻟا
ﺔﻜﺒﺷ لﻼﺧ ﻖﻓﺪﺘﻤﻟا ءﺎﻤﻟا
ﻦﻣ تﺎﻨﻴﻋ
ﺬﺧأ ﺐﻠﻄﺘﺗ ﺎﻬﺘﻤﻈﻧأو ﺔﻴﻤﻟﺎﻌﻟا بﺮﺸﻟا ﻩﺎﻴﻣ ﻦﻴﻧاﻮﻗ
نإ
ﻰﻠﻋ ءﺎﻨﺑو
. ﺔﻴﻤﻟﺎﻌﻟاو ﺔﻴﻠﺤﻤﻟا تﺎﻔﺻاﻮﻤﻠﻟ ﺎﻬﺘﻘﺑﺎﻄﻣو ﺎﻬﺗدﻮﺟو بﺮﺸﻠﻟ ﻩﺎﻴﻤﻟا ﻩﺬه ﺔﻴﺣﻼﺻ ﻦﻣ ﺪآﺄﺘﻟا ﻢﺘﻳ ﻲﻜﻟ
رﺎﺒﺘﻋﻻا ﻲﻓ ﺬﺧﻷا ﻊﻣ ﺔﻴﻤﻠﻌﻟا قﺮﻄﻟﺎﺑ
ﻩﺎﻴﻤﻠﻟ ﻲﻋﻮﻨﻟا ﺪﺻﺮﻟا تﺎﻄﺤﻤﻟ ﻰﻠﺜﻤﻟا ﻊﻗاﻮﻤﻟا ﺪﻳﺪﺤﺗ ﻢﺘﻳ نأ ﺐﺠﻳ ﻚﻟذ
. ﺔﻳدﺎﺼﺘﻗﻻا ﻞﻣاﻮﻌﻟا
Genetic ) ﺔﻴﻨﻴﺠﻟا
بﺎﺴﺤﻟا ﺔﻘﻳﺮﻃ ماﺪﺨﺘﺳﺎﺑ ﻲﺿﺎﻳر جذﻮﻤﻧ ﺮﻳﻮﻄﺗ ﺔﺳارﺪﻟا ﻩﺬه ﻲﻓ ﻢﺗ ﺪﻗو
ﻰﻠﻋ ﺪﻋﺎﺴﻳ ﺎﻤﻣ ،ﻩﺎﻴﻤﻠﻟ
ﻲﻋﻮﻨﻟا ﺪﺻﺮﻟا تﺎﻄﺤﻤﻟ ﻰﻠﺜﻤﻟا ﻊﻗاﻮﻤﻟا ﻦﻴﻴﻌﺗ ﻪﺘﻃﺎﺳﻮﺑ
ﻢﺘﻳ يﺬﻟا ،(
Algorithm
ﻢﺗ يﺬﻟا جذﻮﻤﻨﻟا حﺮﺷ و ﺢﻴﺿﻮﺗ ﻢﺗ ﺪﻗو . ﺎﻬﺗدﻮﺟو ﺔﻜﺒﺸﻟا ﻲﻓ ﺔﻟﻮﻘﻨﻤﻟا
ﻩﺎﻴﻤﻟا ﺔﻴﻋﻮﻧ ﻦﻋ ﺔﻠﻣﺎآ ةرﻮﺻ ءﺎﻄﻋإ
ةرﺪﻗ ﻦﻣ ﺪآﺄﺘﻠﻟ ﻚﻟذ و ،ﺔﻴﺿﺮﻔﻟا
ﻩﺎﻴﻤﻟا تﺎﻜﺒﺷ ﺾﻌﺑ ﻰﻠﻋ رﻮﻄﻤﻟا جذﻮﻤﻨﻟا ﻖﻴﺒﻄﺗ ﺎﻀﻳأ ﻢﺗ ﺎﻤآ ، ﻩﺮﻳﻮﻄﺗ
ﺬﺧأ
حُﺮﺘﻗ
ُا ﻲﺘﻟا
ﻰﻠﺜﻤﻟا ﻊﻗاﻮﻤﻟا ﺪﻳﺪﺤﺗ ﺚﻴﺣ ﻦﻣ ةزﺎﺘﻤﻣ ةءﺎﻔآ رﻮﱠـﻄﻤﻟا
جذﻮﻤﻨﻟا ﺖﺒﺛا ﺪﻗ و . ﻪﺗءﺎﻔآ و جذﻮﻤﻨﻟا
. ﺔﻜﺒﺸﻟا ﻲﻓ ﺔﻘﻓﺪﺘﻤﻟا ﻩﺎﻴﻤﻟا ةدﻮﺟ ﻦﻣ ﺪآﺄﺘﻠﻟ
ﺎﻬﻨﻣ ت ﺎﻨﻴﻋ
* Address for correspondence:
KFUPM Box 686
King Fahd University of Petroleum & Minerals
Dhahran 31261
Saudi Arabia
E-mail address: mzahrani@kfupm.edu.sa
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58
ABSTRACT
Monitoring of drinking water transported by a water distribution network is an
essential step to ensure the safeguard of human health and the compliance of drinking
water quality with local and international standards. The Safe Drinking Water Act requires
that water quality in a water distribution network be sampled at locations which are
representative of the whole network system. Different tools based on optimization
techniques can be employed for identifying water quality monitoring stations in a water
distribution network. In this paper, a Genetic Algorithm (GA) is applied for this purpose.
The steps involved in the developed methodology are presented with an application on
hypothetical networks. Then its validity was tested against two cases presented in the
literature and gave similar results.
Keywords: Water quality, Water distribution network, Optimization, Genetic Algorithm (GA).
M. A. Al-Zahrani and K. Moied
The Arabian Journal for Science and Engineering, Volume 28, Number 1B April 2003

M. A. Al-Zahrani and K. Moied
OPTIMIZING WATER QUALITY MONITORING STATIONS
USING GENETIC ALGORITHMS
LIST OF SYMBOLS
C1 Scaled fitness constant
C2 Scaled fitness constant
d Nodal demand
fn Water fraction
Fr Raw fitness
Fs Scaled fitness
n Number of nodes in the water distribution network
NFS Number of feasible solutions
P Number of generations
Q The demand coverage that a possible solution can achieve in the distribution network
R Rate of mutation
S Number of monitoring stations
W Quantity of water
X Size of population
yi Yes/No signal, suggesting if the node “i” is covered or not
Z Best fitness value
1. INTRODUCTION
Drinking water quality can deteriorate during distribution to the consumer. Many factors, which can be external or
internal, cause the deterioration of water quality between treatment and consumption. Some of the major causes are: source
water, treatment processes, operation of systems, transport and transformations, water distribution network condition, and
storage.
In order to have a general picture about the water quality situation in a water distribution network, sampling locations need
to be identified to monitor water quality parameters. Convenience and spatial representativeness are the two major factors in
selecting the sampling locations [1,2].
Once appropriate sampling locations are identified, then regular monitoring of water quality at these locations in addition
to monitoring of source quality is needed. Monitoring should include sufficient parameters to indicate all quality concerns and
should be conducted at appropriate locations throughout the source of supply. The monitoring program should include
protocols for frequency of sampling and methodology of analysis and should be designed to establish baseline data to indicate
both short-term and long-term trends. Such monitoring can serve as a trigger mechanism to detect the occurrence of water
contamination problems at their earliest stages [3].
The current practice of water sampling is based on taking water samples from locations that are easy to reach. The types of
locations used for collecting water samples include: fire hydrants, storage tanks, pumping stations, commercial buildings,
public buildings and private residences. Thus, no guidelines exist on how to locate sampling stations.
Recent methodologies have been developed to locate sampling stations (monitoring stations) based on scientific methods.
Lee and Deininger [2] developed such a scientific approach based on the concept of demand coverage (DC). The term DC
was used to represent the percentage of network demand monitored by a particular monitoring station. The objective of this
methodology was to allocate monitoring stations that provide maximum information about water quality condition within a
distribution network. The solution suggested by Lee and Deininger [2] was based on the general feature that water quality
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M. A. Al-Zahrani and K. Moied
parameters decrease with time and distance from the source. That is, if the water quality at a sampled node is good, then it
must be good at an immediate upstream node. The term “covered node” was used to denote that water quality at a particular
node can be inferred by the water sampled at some downstream nodes. Lee and Deininger [2] used the information obtained
from hydraulic analysis of the network to identify the pathways, such that the water quality of a large portion of the network is
assessed by installing a few sampling stations. The information obtained from the pathways, in terms of a water fraction
matrix, was then converted into an integer-programming problem under a chosen coverage criterion. By this method, the
lowest level of knowledge occurred when only a very small fraction of the water passed through the node that was called “any
fraction”. For a large network however, this method became highly cumbersome and difficult to handle because of the large
dimensionality of the problem.
Kumar et al. [4] enhanced the work of Lee and Deininger [2] to resolve the problem of dimensionality and proposed a few
changes in the methodology. Kumar et al. [4] used the same coverage matrix as developed by Lee and Deininger. After
calculating the flow direction in each pipe of the network, nodes are renumbered in ascending order of flow, and then the
monitoring station with maximum coverage of upstream nodes is selected. Next, the row corresponding to the selected station
is deleted from the coverage matrix. The subsequent monitoring stations were selected by repeating the same process for the
number of times the monitoring stations were required from the preceding coverage matrix. The methodology proposed by
Kumar et al. [4] was simpler than that of Lee and Deininger [2] as far as construction of the coverage matrix was concerned;
however, extensive computer programming was required to optimize the monitoring locations even with simple mathematical
calculations for a large distribution network.
Based on the concept of Lee and Deininger [2], Kessler et al. [5] developed a methodology that is capable of locating
optimal water quality monitoring stations in a distribution network under the situation of accidental intrusion of contaminants.
Kessler et al. [5] defined a “level of service” as the maximum allowable quantity of water to flow through a certain node
before the detection of contaminant in relation to the time of detection. After hydraulically simulating the network using
extended period simulation, an auxiliary network is developed in the form of a graph consisting of nodes and directed arcs,
such that the length of arc represents the travel time between the nodes. All shortest paths were calculated using the auxiliary
network and a pollution matrix was constructed with 0–1 coefficients.
The current study involves an extension of the model developed by Lee and Deininger [2] to help in identifying water
quality monitoring stations in a water distribution network using a Genetic Algorithm.
2. MONITORING STATIONS AND OPTIMIZATION
The main objective of optimization is to determine appropriate locations of water quality monitoring stations such that they
are representative of the whole network. So, water quality examined at these monitoring stations will represent the quality of
the whole network. For a water distribution network, the size of the space domain as well as the number of monitoring
stations required increases exponentially with an increasing number of nodes in the network. Thus, the number of feasible
solutions, assuming that any node within the distribution network is a candidate monitoring sampling station, is defined as:
NFS = N S (1)
where NFS=Number of feasible solutions,
N=is the number of nodes in the network and
S=is the number of monitoring stations required
For example, in order to locate 4 monitoring stations in a network of 100 nodes, the number of feasible solutions are on the
order of 100 4 . However, out of these 100 million feasible solutions, there is only one optimal. To locate this optimal solution
from a large number of feasible solutions a powerful algorithm is required. A Genetic Algorithm (GA) is one such algorithm
which can solve this problem. Described briefly in the next section, GAs have been successfully used in other areas involving
water networks. Meier et al. [7] used GAs to optimize the flow test locations needed for network model calibration. Savic and
Walters [11] illustrated the use of GAs for least-cost selection of pipe sizes.
3. OPTIMIZATION BY GENETIC ALGORITHM
3.1 Outline of Genetic Algorithm (GA)
A GA starts with a randomly generated set of coded strings representing potential solutions to variables that point to one
location in the solution domain. The variables encoded in these chromosomes are called “genes” or “alleles”. Natural
evolution takes place in chromosomes that are the microscopic threadlike part of the cell nucleus that carries hereditary
information in the form of genes [6]. Concentration of decision variable (genes) values usually forms the strings [7]. This is
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M. A. Al-Zahrani and K. Moied
most often done using binary representation of those values, but in this study integer values have been used, which represent
the number of nodes in the distribution network, thus shortening the length of possible solution strings (chromosome). From
the initial population, the fittest strings (as measured by their objective function values) are selected to pass their “genetic
information” to the next generation. This operation is called “selection” which resembles the survival of the fittest in natural
systems. There are many different schemes for selecting survivors; however, all of them share the common goal that more fit
members replace the less fit ones in the population to advance the searching operation. After selection, the population is, on
average, more fit than it was before selection.
Selection is then accompanied by an operation called “crossover” which creates, from the survivors, new strings that
contain distinguished properties of the survivors from which they are created. In some cases the new strings will have lower
fitness, in other cases they will have higher fitness, and in a certain percentage of cases the children will resemble their parents
and thus have the same fitness values as of their parents
Since crossover simply recombines existing strings into new combinations, successive generations will carry the
characteristics contained in the previous populations. It is possible that some desirable strings were not included in the initial
(randomly generated) population or have been lost because individuals possessing those desirable qualities got unfit and
disappeared from the population. An operation called “mutation” is therefore used to occasionally alter a string (chromosome)
to recover desirable qualities or to create new qualities in the strings (chromosomes).
Figure 1 shows the necessary steps involved while applying a Genetic Algorithm for locating optimum water quality
monitoring stations
Figure 1. Genetic algorithm flowchart
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M. A. Al-Zahrani and K. Moied
3.2 Hydraulic Simulation & Demand Coverage
A prior step before applying the GA is to hydraulically simulate the water distribution network. Hydraulic simulation is
achieved once all the directions of flow in the links along with demands at each node are known, such that all head losses
around the closed loops are added to zero in order to satisfy the mass balance equation. The formulation is carried out for
single or multi-demand patterns of the water distribution network. This will help while optimizing water quality monitoring
stations under multiple flow scenarios.
Once the hydraulic features of the network are known, the logic that water quality at an upstream node is better than the
downstream nodes is applied. It comes from the fact that water quality deteriorates with the passage of time as water starts
flowing away from the source of supply. Matrices are therefore developed for this purpose to analyze the maximum coverage
of the distribution network. The matrix developed for this purpose is called the “Demand Coverage Matrix”. Thus, demand
covered at each downstream node is computed by considering the demands of all the upstream nodes en-rout to that node.
Since the direction of flow in links changes with the change of demand pattern, coverage matrices are required to be
constructed for each demand scenario separately. The above concept will be presented later when the developed methodology
is applied on a hypothetical water distribution network.
4. APPLICATION OF GA
To illustrate the application of the above concept, a hypothetical water distribution network consisting of 15 nodes, 23
links, and 3 sources of supply (A, B, and C) is proposed [8]. Water distribution networks use interconnected elements such as
pipes, pumps and reservoir to convey treated water from one or more sources to consumers spread over a wide area. For this
hypothetical network, hydraulic simulation of the network for a specific scenario is determined using EPANET [9]. Thus,
quantities, directions of flow and nodal demands are determined. These quantities and directions of flow in the links along
with demands at each node are shown in Figure 2 for Scenario 1. The total supply to the network from the source is set to 415
units.
Figure 2. Hypothetical water distribution network (scenario 1) (after Boul s and Altman, [8])
Nodes have to be identified in order to determine the routing of water in the distribution network. Considering a
downstream node, evaluation is carried out in the upstream direction to identify the nodes, which contribute water supply to
the considered downstream node. For the hypothetical network, it is quite obvious that node 9 receives water from node 1,
node 5 receives water supply from node 2, and node 4 receives water from nodes 1 and 2. Similarly, node 10 receives water
supply from nodes 4 and 9. In this way, all downstream nodes are evaluated to determine the contributing upstream nodes of
the network.
Once the nodes are identified, water fraction matrices are constructed. For this purpose, the fractions of total water
received at a particular downstream node from the contributing upstream nodes are determined and inserted in the water
fraction matrix. For example, if (wnk + wnl + wnm) is the total water supplied to a downstream node n from the upstream nodes
k, l, and m, then the fractions fn are calculated by [4]:
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M. A. Al-Zahrani and K. Moied
where
f
f
f
w
nk
nk = (2)
wnk
+ wnl
+ wnm
w
nl
nl = (3)
wnk
+ wnl
+ wnm
w
nm
nm = (4)
wnk
+ wnl
+ wnm
fnk is the fraction of water received at node n from node k,
fnl is the fraction of water received at node n from node l, and
fnm is the fraction of water received at node n from node m.
Since nodes k, l, and m are also getting supplies from further upstream nodes 1,2,3,4........., the water fraction of all these
upstream nodes to the monitoring node n is the vector fn , which will be:
n
( f f , f ,....., f , f , f ,....., f f )
f ,
= . (5)
n1,
n2
n3
nk nl nm n(
n−1)
Elements of the vector fn can be computed as
f n = [ ( f nk * f k ) + ( f nl * f l ) + ( f nm * f m ) ] , (6)
and water coverage matrix is represented by
[ f ]
⎡ f
⎢
= ⎢
⎢
⎢
⎣
11
f
f
12
22
:
:
:
f
f
f
1n
2n
:
nn
⎤
⎥
⎥
⎥
⎥
⎦
April 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 1B 63
nn
. (7)
Since a node always covers itself, all the fnn entries are set equal to ‘1’ in the water fraction matrix. Table 1 represents the
computed water fraction matrix for the hypothetical network of Scenario 1.
After the construction of the water fraction matrix, a coverage criterion is established. If ‘d’ is the total demand of the
entire network and ‘di’ is the demand of a particular node, then by monitoring node i, the fraction di/d of the network can be
covered. Thus, in order to cover the entire network, logically every node of the network must be monitored but it might not be
possible due to economical reasons. Therefore, in order to make the selection process easy, a coverage criterion has to be set.
In the current study, a coverage criterion of 50% is used. Under 50% coverage criteria, those upstream nodes which deliver
more than or equal to 50% of the water to a downstream node are considered as covered and marked as ‘1’ in the water
coverage matrix. Otherwise, they are marked as ‘0’. The coverage criterion plays a role in establishing a tradeoff between the
number of monitoring stations and the demand coverage of the network. A small value of the coverage criteria may suggest
less number of stations to be monitored in order to achieve a desired level of the demand coverage. Consequently, a large
value of this coverage criterion may suggest a large number of monitoring stations to ensure that the same level of demand
coverage has been achieved.
Under the 50% criteria of coverage, the water fraction matrix, Table 1, is then converted into a water coverage matrix,
Table 2. An entry equal to ‘1’ indicates that the node has been covered while an entry of ‘0’ indicates that the particular node
is not covered by a certain monitoring station.
It is shown in Table 2 that node 1 in the hypothetical network covers only itself, node 5 covers nodes 2 and 5, whereas
node 12 covers nodes 2, 5, and 12. Similar analyses are made for all nodes of the network. The demand vector of the network
is constructed as d = di, where d is the demand of node and i represents the number of nodes in the distribution network. The

64
M. A. Al-Zahrani and K. Moied
demand vector is the vector of known nodal demands. Hypothetical values were assumed for the hypothetical network.
However, for the real networks, the values for demand vector can be determined from design sheets or water bills.
Table 1. Water Fraction Matrix (Scenario 1).
Sample
at node
Water Fraction through Nodes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 0 0 0.67 0 0 0 0.61 0.79 0.71 0.08 0.19 0.19 0 0.19
2 0 1 0 0.33 1 0 0 0.39 0 0.21 0.03 0.68 0.68 0 0.68
3 0 0 1 0 0 1 1 0 0.22 0.09 0.89 0.12 0.12 0 0.12
4 0 0 0 1 0 0 0 0.9 0 0.64 0.08 0.27 0.27 0 0.27
5 0 0 0 0 1 0 0 0.09 0 0 0 0.61 0.61 0 0.61
6 0 0 0 0 0 1 0 0 0.22 0 0.40 0.05 0.05 0 0.05
7 0 0 0 0 0 0 1 0 0 0 0.48 0.06 0.06 0 0.06
8 0 0 0 0 0 0 0 1 0 0 0 0.29 0.29 0 0.29
9 0 0 0 0 0 0 0 0 1 0.36 0.04 0.01 0.01 0 0.01
10 0 0 0 0 0 0 0 0 0 1 0.12 0.02 0.02 0 0.02
11 0 0 0 0 0 0 0 0 0 0 1 0.13 0.13 0 0.13
12 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
13 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
For the hypothetical network, where i = 15, the demand vector is constructed as follows:
( 30 25 30 30 30 30 30 45 30 30 35 50 0 0 20)
.
4.1 Multiple Flow Scenarios
The flow demands in a water distribution network vary more than once during the day. To incorporate this effect, multiple
flow scenarios are considered. For our purpose, the hypothetical model is modified to represent a flow scenario other than
Scenario 1. Figure 3 shows the modified quantities and directions of flow as well as demands at each node for Scenario 2.
The corresponding water coverage matrix and nodal demand vector for Scenario 2 can be calculated similar to Scenario 1.
Figure 3. Hypothetical water distribution network (scenario 1) (after Boulos and Altman, [8])
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T

M. A. Al-Zahrani and K. Moied
Once the coverage matrix is developed, the developed Genetic Algorithm model can be applied to identify the optimum
water quality stations in a water distribution network for both single flow (Scenario 1) and multiple flows (the combination of
both Scenario 1 and Scenario 2). The following (Sections 4.2–4.9) are the steps involved when applying the GA.
4.2 Raw Fitness Evaluation
Unlike other optimization techniques, the objective function is formulated as a “fitness function” in a Genetic Algorithm.
This fitness function is derived based on either maximization or minimization of the objective(s). The first fitness value of a
possible solution is called the “raw fitness value”, which is determined by Equation (8).
⎡Z − Q ⎤
= 100 − ⎢ * 100⎥
⎣ Z ⎦
F r (8)
Where Fr is the raw fitness, Z is the best fitness, and Q is the demand coverage that a particular solution can achieve.
An initial step prior to the process of optimization using GA is to define an ideal or “best” solution. All possible solutions
generated during optimization are then compared with this “best” value to determine their relative goodness. The closer the
fitness value of a possible solution falls near the “best”, the greater is the chance of its selection. In this study, the “best” value
is set to equal the total supply of water in the distribution network. This value can also be set greater than or equal to the total
input supply of water to the network. For the hypothetical water distribution network, Scenario 1, the total input supply is 415
units, and the “best” is set equal to 500. It can be set to a value equal to 415, but not less. Therefore:
Z ≥ W , (9)
where, W is the total input supply.
Based on the maximization function
n ⎛ ⎞
⎜max dy ⎟
∑
, Q is evaluated from Table 2 (Water Coverage Matrix). The
i i
⎝ i = 1 ⎠
resultant coverage matrix is constructed for this purpose, which is obtained after “ORING” those columns of the coverage
matrix, which are indicated by the possible solution. This process of “ORING” is similar to taking the union of 1’s in these
column vectors. Q is evaluated by adding the product of the resultant coverage vector with the corresponding nodal demand
vector. For example, if ( 3 8 11 15 ) is the first possible solution for the hypothetical network (Scenario 1), then the resulting
coverage vector is constructed after “ORING” the columns 3, 8, 11 and 15 of the coverage matrix shown in Table 2. The value
of Q is then calculated by adding the product of the resultant coverage vector with the nodal demand vector. Table 3 shows
the evaluation of raw fitness of a possible solution for Scenario 1.
Table 2. Water Coverage Matrix (Scenario 1).
Sample
Water fraction through nodes
at node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0
2 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1
3 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0
4 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0
5 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1
6 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
13 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
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66
m
n
M. A. Al-Zahrani and K. Moied
Similarly, based on the maximum function ( ∑ ∑d
ik yik
) defined for multiple scenarios, Q is first evaluated for the first
k = 1 i=
1
scenario and then for the 2 nd , 3 rd , and so on. Total Q is then evaluated by adding all the Q values such that:
Q =
m
∑
k = 1
Q
where, m is the number of scenarios.
k
, (10)
Columns obtained from Table 2
Table 3. Evaluation of “Q”.
Resultant
coverage
vector after
“ORING”
(5)
Nodal
demand
vector
(6)
Q
(5)*(6)
Node 3 Node 8 Node 11 Node 15
(1)
(2)
(3)
(4)
0 1 0 0 1 30 30
0 0 0 1 1 25 25
1 0 1 0 1 30 30
0 0 0 1 1 30 30
0 0 0 1 1 30 30
0 0 0 0 0 30 0
0 0 0 0 0 30 0
0 1 0 0 1 45 45
0 0 0 0 0 30 0
0 0 0 0 0 30 0
0 0 1 0 1 35 35
0 0 0 1 1 50 50
0 0 0 1 1 0 0
0 0 0 0 0 0 0
0 0 0 1 1 20 20
∑ Q = 295
For multiple scenarios, the total Q is 510 and the best be defined as equal to or greater than 955 units (i.e it represents the
summation of the total water supply of Scenario 1, which is 415 units, and the total water supply of Scenario 2, which is 540).
4.3 Scaled Fitness Evaluation
Though, the goal of GA is to dominate the population pool, the same has to be supported by increasing the search space for
the truly fit members to be identified. This can be achieved by scaling of fitness values, so as to add further security to avoid
premature member dominance in the population. This premature member can also be termed as unhealthy or weak member,
which could not be otherwise identified. This phenomenon is extremely important in higher order populations where the
average and maximum fitness values fall very close to each other and search space needs to be increased. This could further
mean a little delay in convergence of algorithm since enough members fall under examination.
A simple linear scaling is proposed by Goldberg [10] and is adopted in this study, such that the average scaled fitness is
kept equal to the average raw fitness. Thus, the scaled fitness, Fs, of a possible solution can be defined as:
Fs = Fr
∗ C1
+ C2
(11)
where Fs is the scaled fitness and C1 and C2 are the constants for the linear scaling. Appendix I shows how the linear
constants C1 and C2 are evaluated [10].
4.4 Random Generation of Initial Population
After writing the fitness function, the next step is to generate an initial population of possible solutions. Here, analogy with
nature is established by creating within a computer a set of solutions called the “population” [11]. Each solution string called a
“chromosome”, consists of decision variables called genes or alleles. The number of chromosomes required to be generated,
The Arabian Journal for Science and Engineering, Volume 28, Number 1B April 2003

M. A. Al-Zahrani and K. Moied
depends on the decision regarding the size of population. As there is no set guided rule to define the exact size of the
population; artistic judgment of the GA user is employed. The judgment comes from experience and relative knowledge of
GA implementation.
In this study, X numbers of chromosomes (possible solutions) are randomly generated in the first population. These
chromosomes generated at random serve as parents for selection. The length of chromosomes (i.e. the number of genes) is
kept equal to the number of monitoring stations required. A “gene” is set to have an integer value between 1 and n, where n is
the total number of nodes in the distribution network. However, during the random generation of chromosomes, care is
exercised to ensure that all the genes in a chromosome must have different values defined in the range of 1 and n. Table 4
shows the randomly generated initial population consisting of 10 numbers of chromosomes for locating “four” monitoring
water quality stations in the hypothetical network.
Table 4. Initial Population.
Index Number
(1)
1
2
3
4
5
6
7
8
9
10
Initial Population
(2)
12 15 5 3
2 15 13 3
11 15 5 1
3 15 4 10
8 4 1 7
9 3 1 7
10 6 1 13
15 12 9 2
4 14 1 7
9 11 7 2
4.5 Selection of Parents
Randomly generated chromosomes are required to be selected, such that only fitter ones can mate to produce children for
the subsequent populations. In this study, tournament selection is used as the method of selection.
In this method of selection, the whole population of chromosomes is divided into subgroups, such that each subgroup
contains two or more chromosomes. Then, a highly fit chromosome is selected from each subgroup. To select the remaining
members of the population, the source population is shuffled and the same process is repeated till all the members of the new
population are selected, such that the size of the population must remain constant throughout the simulation. Table 5 shows
the tournament selection of the parents for the hypothetical network.
In this method of selection, a parent can twice get a chance of being selected, based on its higher fitness value, whereas the
less-fit parent also receives a good probability of being selected for mating.
4.6 Crossover
Natural process of evolution describes the evolution of children from their parents; when they mate together and their
chromosomes cross to produce children. Concatenation of chromosomes takes place at the point of crossover and new
chromosomes (children) are produced. These chromosomes are different in structure from their parent chromosomes but
inherit characteristic behavior from them. A similar concept is induced in GA, which is called “crossover operation”.
In this operation of Genetic Algorithms, parents are made to produce children. Several methods are available to accomplish
this task. The simple idea is to generate children from their parents, such that they bear the characteristics inherited by their
parents. Every GA user can develop his own technique to produce children from parents depending on the specific constraints,
such that the objective of creating new from the old is achieved.
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68
M. A. Al-Zahrani and K. Moied
Once the parents are selected by tournament selection, they are made to mate and hence produce children. In the current
study, two parents are made to produce two children and single point crossover is adopted for this purpose. Random selection
of crossover point is performed using built-in Matlab function called “randint”. Random integer number is generated in the
range of 1 to (S–1) for each crossover operation, where S is the number of monitoring stations.
A child produced is termed as “perfect” if all of its genes appear to be dissimilar. In terms of our problem a “faulty child”
is a solution that contains a particular node more than once, which would imply a duplication of monitoring point. However, if
any two or more number of genes appears to be the same after crossover, the child is termed as “faulty”. By the end of the
crossover operation, only perfect children are allowed to enter the mutation pool, whereas in the case of a faulty child, the
corresponding parent (instead of faulty child) is made to enter the mutation pool. The whole mutation pool therefore consists
of perfect children only. In this study a “faulty child” is a solution that contains a particular node more than once, which
would imply a duplication of monitoring point. Table 6 shows the application of crossover to the parents obtained in Table 5.
Table 5. Tournament Selection of Parents for Scenario 1.
1
2
3
4
5
6
7
8
9
10
Source Population
12 15 5 3 X
2 15 13 3 2 15 13 3
11 15 5 1 X
3 15 4 10 3 15 4 10
8 4 1 7
9 3 1 7 X 8 4 1 7
10 6 1 13
15 12 9 2 X 10 6 1 13
4 14 1 7 X
9 11 7 2 9 11 7 2
11 15 5 1 X
3 15 4 10 3 15 4 10
4 14 1 7 X
10 6 1 13 10 6 1 13
9 3 1 7 X
2 15 13 3 2 15 13 3
12 15 5 3 X
15 12 9 2 15 12 9 2
9 11 7 2
8 4 1 7 X 9 11 7 2
4.7 Mutation
After crossover, an operation called “mutation” is applied. Since the fundamental principle of GA is its randomness, it is
quite possible that the solution appearing in the initial populations will not appear for several successive populations ahead.
This is due to the fact that fitter parents forced it to die, and hence not to appear ever again. This disappeared solution can help
in making the most optimal solution in GA runs. An operator called “mutation” is therefore applied, which randomly alters
the structure of the chromosome, and hence gives the chance to the disappeared feasible solutions to appear again and
participate towards the generation of the most optimal solution in the forthcoming populations. The rate at which this
mutation is applied needs to be very low. It is suggested to be within the range of 1–3%, however, studies conducted by Tate
and Smith [12] suggested a high rate of mutation for non-binary encoding of strings. Thus, in this study the mutation is carried
out at a rate of 5%.
During the mutation pool, a random real number is generated in the range of 0 to 1, corresponding to every gene of the
chromosome. If the random number generated is less than 0.05 then the corresponding value of the gene is changed randomly,
such that it is different from the values of the remaining genes in the same chromosome. Table 7 summarizes the application
of mutation to the crossed population obtained in Table 6.
The Arabian Journal for Science and Engineering, Volume 28, Number 1B April 2003

M. A. Al-Zahrani and K. Moied
Index Number
(1)
1
2
3
4
5
6
7
8
9
10
Index Number
(1)
1
Random Numbers
2
Random Numbers
3
Random Numbers
4
Random Numbers
5
Random Numbers
6
Random Numbers
7
Random Numbers
8
Random Numbers
9
Random Numbers
10
Random Numbers
Parents from
Table 5 with
crossov er point
2 15↓ 13 3
3 15↓ 4 10
8 4 1↓ 7
10 6 1↓ 13
9 11↓ 7 2
3 15↓ 4 10
10↓ 6 1 13
2↓ 15 13 3
15 12↓ 9 2
9 11↓ 7 2
Table 6. Crossover for Scenario 1.
Children
produced after
crossover
2 15 4 10
3 15 13 3
8 4 1 13
10 6 1 7
9 11 4 10
3 15 7 2
10 15 13 3
2 6 1 13
15 12 7 2
9 11 9 2
Selection Status
(4)
Perfect
Faulty
Perfect
Perfect
Perfect
Perfect
Perfect
Perfect
Perfect
Faulty
The ( ↓ ) sign represents the point where crossover operation is performed.
Table 7. Mutation Pool for Scenario 1.
2
0.752
3
0.545
8
0.458
10
0.329
9
0.215
3
0.033
10
0.354
2
0.214
15
0.325
9
0.215
Mutation Pool from Table 6
(2)
15
0.255
15
0.458
4
0.214
6
0.010
11
0.859
15
0.782
15
0.857
6
0.354
12
0.024
11
0.710
Mutation Pool
(5)
2 15 4 10
3 15 4 10
8 4 1 13
10 6 1 7
9 11 4 10
3 15 7 2
10 15 13 3
2 6 1 13
15 12 7 2
9 11 7 2
Mutated Population
(3)
April 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 1B 69
4
0.625
4
0.015
1
0.958
1
0.385
4
0.438
7
0.529
13
0.081
1
0.852
7
0.665
7
0.257
10
0.859
10
0.075
13
0.245
7
0.495
10
0.215
2
0.125
3
0.958
13
0.756
2
0.682
2
0.045
2 15 4 10
3 15 6 10
8 4 1 13
10 2 1 7
9 11 4 10
12 15 7 2
10 15 13 3
2 6 1 13
15 14 7 2
9 11 7 5
* Bold numbers represent generated random numbers which are less than the adopted mutation rate of 5%.
4.8 Construction of Array of Best Solutions
Once the operation of mutation is completed, the best member of the population is selected and stored in an “array of best
solutions”. In this way, an array is obtained, which contains only the best solutions from each population. These best
solutions therefore represent the solutions, which were selected from a population based on their highest fitness among the
other members.

70
Population Number
(1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Table 8. Array of Best Solutions for Scenario 1.
Array of Best Solution
(2)
3 15 4 10
15 4 10 6
8 10 3 15
8 10 3 15
10 6 15 8
6 15 8 10
15 8 10 6
6 15 8 10
6 15 8 10
11 15 8 10
8 10 11 15
8 10 11 15
8 10 11 15
15 8 10 11
11 15 8 10
11 15 8 10
15 8 10 11
15 8 10 11
15 8 10 11
15 8 10 11
*Maximum Scale Fitness
Solution Fitness
(3)
59.55
65.55
68.55
69.30
71.85
72.90
77.85
81.30
81.45
86.40
89.10
84.30
93.75
96.90*
96.45
95.55
95.40
87.90
87.45
93.30
M. A. Al-Zahrani and K. Moied
For the hypothetical network, a tentative array of best solutions is shown in Table 8 after running the program for 20
iterations (population), four monitoring stations, and a population size of 10.
4.9 Selection of Optimal Solution
Once the “array of best solutions” is obtained, the optimal solution can be identified based on the highest fitness among the
best selected in this array. It is quite obvious that the best or optimal solution after 20 populations is ( 15 8 10 11 ) which is
selected based on its highest fitness value of 96.90 among all members of this array.
Figure 4. Generations vs. maximum scaled fitness of single flow scenario
The Arabian Journal for Science and Engineering, Volume 28, Number 1B April 2003

M. A. Al-Zahrani and K. Moied
The hypothetical network was run using a program named QUDIS developed in MATLAB, for identifying 4 monitoring
stations (S). For this purpose 500 populations (P) were set for both single and multiple scenarios. Simulation was carried out
for the two cases (single flow and multiple flow) independently. The best values for fitness (Z) were selected as 500 for the
single scenario and 1000 for the multiple scenarios. The population size (X) was kept constant at 100 with mutation rate (R) at
5% in both cases.
Figure 5. Generations vs. maximum scaled fitness of multiple flow
It took about 1 minute and 56 seconds to run 500 iterations using PC-1400 MHz machine and ( 11 15 8 10 ) was selected as
the optimal or best identified water quality monitoring stations for single flow (Scenario 1). Figure 4 shows the maximum
scaled fitness plotted against generations (P). As can be seen from the figure, the maximum scaled fitness of the population
increases until it gets stable after about 40 generations.
For multiple flows (Scenario 1 and Scenario 2), it took about 2 minutes and 3 seconds to run the 500 iterations using PC-
1400 MHz machine. Stations ( 8 6 15 10 ) was identified as the optimal water quality monitoring stations. Figure 5 shows the
maximum scaled fitness plotted against generations. As can be revealed from the figure, the maximum scaled fitness increases
until it gets stable after about 45 generations.
5. MODEL VERIFICATION
To check the validity of the developed model, it was applied to two cases presented in the literature. The application of the
developed methodology and the result comparison are presented in the following paragraphs.
Case I
The first case is taken from Lee and Deininger [2]. The water distribution network consists of 7 nodes with only one
source of supply as shown in Figure 6(a). The model was run based on 50% coverage demand criteria.
Simulation was run for X = 100, P = 500, S = 2, Z = 200, N = 7, and R = 0.05. The simulation time was about 52 seconds
for 500 generations. Stations ( 5 6 ) were identified to be the optimal water quality monitoring stations. This conclusion was
similar to the findings of Lee and Deininger [2]. Simulated results are shown in Figure 6(b).
Case II
The second case is taken from Kumar et al. [4]. The water network consists of 19 nodes with two sources of supply as
shown in the Figure 7(a).
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72
M. A. Al-Zahrani and K. Moied
The Arabian Journal for Science and Engineering, Volume 28, Number 1B April 2003

M. A. Al-Zahrani and K. Moied
Figure 6. (a) Water distribution network of Case I (after Lee and Deininger, [2]), (b) generations vs. maximum scaled fitness for Case I.
April 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 1B 73

74
M. A. Al-Zahrani and K. Moied
Figure 7. (a) Water distribution network of Case 2 (after Kumar et al., [4] (b) generations vs. maximum scaled fitness for case2
Simulation was run for X = 100, P = 500, Z = 25000, N = 19, and R = 0.05. The simulation time took about 2 minutes and
14 seconds to run 500 generations. Stations ( 5 17 18 19 ) were identified to be the optimal water quality monitoring stations,
which were similar to those identified by Kumar et al. [4]. Simulated results are shown in Figure 7(b).
Model verification implies to the application of developed methodology based on Genetic Algorithm to the studies carried
out by Lee and Deininger [2] and Kumar et al. [4]. Two monitoring stations were identified for example network, as proposed
by Lee and Deininger [2]. Similarly, four monitoring stations were identified for the example network, as proposed by Kumar
et al. [4].
This finding gives confidence in applying the developed model for identifying water quality monitoring stations in any
water distribution network.
6. CONCLUSION AND RECOMMENDATIONS
A methodology based on GA was developed and illustrated with the help of a hypothetical case to identify water quality
monitoring stations in a water distribution network and verified with two examples from the literature.
The results of this research can contribute significantly in assuring safe and better water quality to be delivered to the
consumers through the water distribution network by identifying proper locations of monitoring stations over the entire water
distribution network, thus ensuring safe water provided to the consumers.
In this paper, water quality monitoring stations were located based on the quantity of the flow assuming that water quality
at a downstream node is less than water quality at an upstream node. This research can be extended in the future to consider
multiple reasons for water quality variation when identifying water quality monitoring stations such as water distribution
network condition, constituent concentration, and age of water.
ACKNOWLEDGEMENTS
The authors express their thanks to King Abdulaziz City of Science and Technology (KACST) for the financial support and
to King Fahd University of Petroleum and Minerals (KFUPM) for providing the necessary help and research facility to
conduct the current study.
REFERENCES
[1] B. H. Lee, “Locating Monitoring Stations in Water Distribution Networks”, Ph.D. Dissertation, Environmental Health Sciences,
The University of Michigan, 1990.
[2] B. H. Lee, and R.A. Deininger, “Optimal Iocations of Monitoring Stations in Water Distribution system”, J. Envir. Engrg., ASCE,
118(1) (1992), pp. 4–16
[3] F.W. Pontius, Water Quality and Treatment. (4 th Edn), New York: (AWWA), McGraw-Hill, (1990).
[4] A., Kumar, M.L., Kansal, and G. Arora, “Identification of Monitoring Stations in Water Distribution System”, J. Envir. Engrg.,
ASCE, 123 (8) (1997). pp. 746–752.
[5] A. Kesseler, Ostfeld, and G. Sineri, “Detecting Accidental Contaminations in Municipal Water Networks”, J. Water Resour.
Planning and Management, ASCE, 124(4) (1998), pp. 192–198.
[6] L.F.R. Reis, R.M., Porto, and F.H. Chaudhry, “Optimal Location of Control Valves in Pipe Networks by Genetic Algorithm”,
Journal of Water Resources Planning and Management, ASCE, 123(6) (1997), 314–326.
[7] R.W. Meier, and B.D. Barkdoll, “Sampling design for network model calibration using Genetic Algorithm”, J. Water Resour.
Plang. and Mgmt., ASCE, 126(4) (2000), pp. 245-250.
[8] P.F., Boulos, and T. Altman, “Explicit Calculation of Water Quality Parameters in Pipe Distribution Network.” Journal of Civil
Engineering Systems, 10(1), (1993), pp. 187–206.
[9] L.A. Rossman, EPANET – User’s Manual. Cincinnati, Ohio: United States Environmental Protection Agency (USEPA), 2000.
[10] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, Mass. Addison – Wesley, (1989).
[11] D.A. Savic, and G.A. Walters, “Genetic Algorithms for Least–Cost Design of Water Qistribution Networks”, Journal of Water
Resources Planning and Management, ASCE, 123 (2) (1997), pp. 67–77.
[12] D.M. Tate, and A.E. Smith, Expected Allele Coverage and the Role of Mutation in Genetic Algorithms”, Proceedings of the Fifth
International Conference on Genetic Algorithm, University of Illinois at Urban-Champaign, July 17–21, 1993, pp. 31–37.
Paper Received 4 February 2002, Revised 2 June 2002; Accepted 23 October 2002.
The Arabian Journal for Science and Engineering, Volume 28, Number 1B April 2003

M. A. Al-Zahrani and K. Moied
APPENDIX I. Evaluation of the Linear Constants C1 & C2
If frmin >
Then C1 = >
If frmin <
Then C1 = >
Where
( 1.
5 * ( fravg − frmax
))
,
0.
5
0.
5 * fr
fr − fr
max
avg
avg
, and C2 =
( 1.
5 * ( fravg − frmax
))
,
0.
5
fr
avg
fr
avg
−
fr
min
, and C2 =
( fr
frmin = Minimum raw fitness of population
frmax = Maximum raw fitness of population
fravg = Average raw fitness of population
max
−1.
5 * fr
fr − fr
max
min
avg
avg
( − frmin
* fravg
) * fr
fr − fr
avg
) * fr
avg
April 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 1B 75
avg