GAPinch : Genetic Algorithm Toolbox for Water Pinch Technology
Detchasit PRAKOTPOL
Chemical Engineering Practice School, Department of Chemical Engineering,
Faculty of Engineering, King Mongkut's University of Technology Thonburi,
Bangkok 10140, THAILAND
Thongchai SRINOPHAKUN*
Department of Chemical Engineering, Faculty of Engineering,
Kasetsart University, Bangkok 10903, THAILAND
* To whom all correspondence should be addressed.
* Tel. 66-2-9428555 ext. 1214
* Fax. 66-2-5792083
* E-mail: fengtcs@ku.ac.th
Abstract
Wastewater in the chemical industry can be minimized by water reuse. The
optimum water usage network leads to a minimum freshwater consumption and
wastewater treatment. Genetic algorithm, an objective of this work, is developed for
solving the wastewater minimization problem. The optimization model is formulated
for both single and multiple contaminants in the class of mixed integer nonlinear
programming (MINLP). In this model, there is a set of equality constraints from mass
balance that drives the genetic algorithm from addressing the feasible solution. To
elucidate this problem, all of variables have to be divided into 2 groups; independent
and dependent variables. The values of independent variables come from
randomization whereas the values of dependent variables come from simultaneous
solutions of a set of equality constraints after assigning the values of independent
variables. This method is applied to the steps of Initialization, Crossover and
Mutation.
The developed program is the MATLAB toolbox that consists of 29 m-file.
The graphic user interface was created in order to make the program can be used
easily and conveniently. After a user inputs the process condition of the problem into
the blank form of GUI, the program will formulate the optimization model and solve
for the solution automatically. Then, the optimum results are returned to the user. The
program is tested with a process that contains a certain number of water-using
operations in which water is used to remove a fixed content of contaminant. In the
single contaminant system, this program and Lingo can find the minimum freshwater
consumption but the solutions are different in the configuration of water usage
network. These alternative configurations give a wide-vision on the analysis of the
system. In the multiple contaminants system, this program can find the same or better
results in some test problems.
Keywords
Wastewater Minimization, Genetic Algorithm
Introduction
In the chemical industry, wastewater is generated from many sources in the
process. Because of environmental impact, wastewater must be reduced to an
acceptable level before being discharged. Large amounts of wastewater cause high
cost for effluent treatments. Prior to focusing on wastewater treatment, wastewater
production should be minimized. In addition to reducing treatment cost, wastewater
minimization can also reduce the freshwater costs.
There are three approaches to reduce wastewater excluding process changes
that reduce the inherent demand for water [1]; Re-use, Regeneration re-use and
Regeneration recycling.
Several studies have been reported showing the application of these
approaches. Wang and Smith [1] addressed the case study of minimization of
wastewater in the petroleum refinery. Through re-use, freshwater consumption,
wastewater generation and total cost was reduced by 20 percent. Adding regeneration
process without recycle reduced freshwater and wastewater flowrate by nearly 60
percent and reduced cost by more than 60 percent. In Suriyaprapadilok’s work [2],
nonlinear programming (NLP) was formulated to solve for the optimum water-using
network in tapioca plant. At the optimum, the freshwater consumption is minimum. A
13.22 percent reduction of freshwater usage is obtained.
In developing an optimal design of water using network target to minimize
wastewater, engineers face selection of the best choice from a vast number of process
alternatives. This is an optimization problem that requires an appropriate technique to
identify the best result. In wastewater minimization problem involving single key
contaminant, the optimization programming can be formulated as a linear
programming (LP) problem. For multiple contaminants, the mathematical
representation is in the class of nonlinear programming (NLP). This class of problem
has more than one local optimum. The accuracy and efficiency of conventional
techniques for finding the global optimum depend on the initial guess. The
inappropriate one leads to the solution getting stuck at the local optimum. A wellknown technique for avoiding local optima in improving search is genetic algorithms
(GAs).
Genetic algorithms (GAs) are search algorithms based on the mechanics of
natural selection and natural genetics. They are a direct search method based on
principle of evolution and heredity [3]. GAs have been developed by John Holland,
his colleagues and his students at the University of Michigan since 1960s. GAs have
been successfully applied to a wide variety of problems including multimodal
function optimization.
Algorithm is started with a set of random solutions called population.
Individual solution is represented in encoded form called chromosome. Each
chromosome comprises of individual structures called genes. Solutions from one
population are used to form a new population. This is motivated by a hope that the
new population will be better than an old one. In order to form a new population, GAs
use genetic operators and selection process. Genetic operators are used to generate the
new solutions (offspring) from the current solutions (parents). Selection is the process
of keeping and deleting some solutions from both parents and offspring for the same
number of next population. Moreover, selection is the process of choosing some
parents to generate offspring also. In the selection process, the solutions are selected
according to their values of objective function (fitness). The more fitness has, the
more chance of be selected. The algorithms will repeat until a termination condition is
satisfied. The best solution is returned to represent the optimum solution.
The procedure of GAs can be described in the following steps [4].
1. Choose a randomly generated population (feasible candidate solution).
2. Calculate the fitness at each chromosome in the population.
3. Selection process with the chosen population to evolve for new
population by genetic operation.
4. Create a new population by genetic operator: crossover and mutation.
5. Check termination condition.
In 2000, Wasanapradit [4] developed a new effective method of
genetic algorithm to solve general MINLP problem. The specific methods for each
step of genetic algorithms are as follow:
 Real Number Representation
Real number representation is used to represent the solutions. For the example,
the solution has 4 variables, x1 = 20.22, x2 = 1.55, x3 = 0, x4 = 5.09. The vector that
represents this solution is < 20.22 1.55 0 5.09>.

Arithmetical Crossover
Arithmetical Crossover is defined as a linear combination of two vectors. For
example, if v1 and v2 are selected to undergo a crossover, then the offspring can be
calculated from equations (1) and (2).
(1)
v1  a  v1  (1  a)  v 2
v2  a  v 2  (1  a)  v1
v1 = < 5.22 14.05>; v2 = < 9.95 4.31>; a = 0.4

v1 = 0.4 <5.22 14.05> + (1-0.4) < 9.95
= <8.058 8.206>
v2 = <7.112 10.154>
(2)
4.31>

Transformation Based Mutation
By transformation based mutation, a chromosome is selected the positions of
genes undergoing mutation randomly. After that, these genes are replaced with new
values between the lower and upper bound of those genes.

Repair Strategy
Repair Strategy is used to convert the infeasible solutions to the feasible ones.
The general form of in equality constraints is
gi(x)  bi
In order to repair any solution, the feasibility of any solution is calculated first by
equation:
S(x) = max(gi(x) – bi)
(3)
If S(x) is negative that means this solution is feasible. It stays in the feasible
area of the problem. The positive sign means this solution cannot satisfy some or all
the inequality constraints. It is an infeasible solution. Zero value of S(x) means this
solution stay on the constraint boundary.
The purpose of repair algorithm is to convert a solution with S(x) > 0 to one
S(x) = 0. Such procedure corresponds to the root finding of equation with a numerical
method. Therefore, secant method incorporating the bisection method was modified to
achieve this goal. The secant method was selected because of its high speed in
equation root finding. However, it often diverges when the initial points were not
suitable. Thus, the bisection method, the promising method but slower, was combined
in order to find the new suitable initial points for secant method.
The simultaneous secant and bisection method can calculate the new solution
by using equations (4) and (5), respectively.
xi 1  xi 
S ( xi )( x x 1  xi )
S ( xi 1 )  S ( xi )
x i1  x i2
x i 1 
2
(4)
(5)
This is bisection formula. i is number of iteration. Each iteration, there are two
solution and the new solution is the middle of these two points that are the solution
from the latest iteration ( xi1 and x i2 ). Therefore, xi1 is a solution of iteration ith and
x i2 is an another solution of iteration ith.
The procedure of the program of the secant method combined with the
bisection method is given in Figure 1[4].
Begin
Xl , Xr, Fl , Fr, Ib=1
Set iter_maxb
i=1,BiS=0
Input max_iter, tol
Xnew = 0.5(xl+xr)
Input xi-1 xI,
Calculate fnew
Ib=Ib+1
Calculate f(xi-1), f(xi)
Yes
No
Fnew*fl > 0
Calculate xI+1 , f(xI+1)
xl = xnew
Fl=fnew
i=i+1
f(xI)tol
Yes
No
Yes
Fnew  tol
No
I
max_iter
i max_iter
No
Bis = 1
Yes
xr = xnew
Fr=fnew
No
No
Bis =1
Yes
Return
Figure 1
The Program of Secant Method Combine with Bisection Method [4]
Yes

Cross-Generation Probabilistic Survival Selection (CPSS)
CPSS is the selection method that can keep the diversity of population. This
method is developed to prevent a premature convergence problem in traditional
genetic algorithms. By CPSS, a selection possibility does not depend on the fitness of
solution only. It also depends on the structure of the solutions. A selection probability
for each solution can be calculated by using equation (6).
h 

p s  (1  m )  m 

L 
(6)
Where h is the hamming distance between the candidate solution and the
solution with the best fitness value. L is the length of the string representing the
chromosome. m is the shape coefficient and  is the exponent.
The hamming distance (h) can be calculated by this equation.
h  ( v1  v1 ) 2  ...  ( v k  vk ) 2
(7)
Where v i and v i are i gene of the candidate solution and the fittest solution.
For the length of string representing the solution (L), it can express as follow.
L = max ( h j ); j = 1, …, number of population
th
For mixed integer problems, the calculation of h and L must be separated
between real and integer variables. After that, the results are combined together with a
weight factor. Therefore, h and L for mixed integer problems can be determined by
using the following equations.
(8)
h  w  hR  (1  w )hI
L  w  LR  (1  w ) LI
(9)
Where w is the weight factor. Its value depends on the importance of variables.
In this work, a value of 0.5 for the weight factor is used. The subscript R and I
indicate real and integer variables, respectively. The procedure of CPSS is as follows:
1.
Eliminate duplicated structure (new population) from the combined
population of parent and offspring.
2. The best solution is kept first.
3. Calculate a selection probability (ps) for each solution.
4. Generate a random number for each solution. If the generated random
number is smaller than ps, the solution is selected. Otherwise it is deleted.
5. If the number of current population is smaller than population size, the new
structures are generated randomly by the insufficient number. If the number of current
population is greater than population size, the fitter ones are selected.
2. Problem Statement
The process contains a certain amount of water to reduce a fixed content of
contaminant. This water is considered as a contaminant-rich stream. It transfers some
contaminants to a contaminant-lean stream; the water. The contaminants may
correspond to suspended solid (SS), chemical oxygen demand (COD), or similar
quantities whose concentration levels limit the reuse of the effluent water in the other
operations. The water using operation represented by the mass transfer of these two
streams is shown in Figure 2.
Rich Stream
Mass Transfer
Lean Stream (water)
Figure 2 The Process Stream Representation of Water Using Operation
From Figure 2, the contaminant concentration of the water inlet and outlet is
limited by the concentration at the outlet and inlet of the rich stream, respectively. The
lean stream (water) entering any unit operation must have a lower contaminant
concentration than the concentration of the rich stream outlet and the wastewater
leaving must have a lower concentration than the concentration of the rich stream
inlet.
Mann and Liu [3] addressed the method to formulate the water networks as
linear programming (LP) and nonlinear programming (NLP) for single and multiple
contaminants system, respectively. The solution of those models is the optimal
allocation of species and streams throughout the process with minimum freshwater
flowrate target.

Single Contaminant-Water Reuse
Figure 3 illustrates the superstructure model of any water using operation in
water reuse process.
Fi   X i , j
Xi, j
Cj, out
i j
C i ,in
Xj, i
Ci, out
Operation i
Wi
F
i
Ci, out
Figure 3 Superstructure Model of Any Operation of Water Reuse Process
The objective function which is the minimum total freshwater flowrate can be
defined as equation (10).
F =  Fi
; number of i is equal to number of unit operation (10)
i
Then, the constraints of the mass balance and maximum inlet concentration
are formulated. The water mass balance around each unit operation i in Figure 3 is
(11)
Fi   X i , j  Wi   X j ,i  0
j i
j i
The contaminant mass balance around each operation can be formulated as
follows:
(12)
 C j ,out X i , j  mi  C i ,out (Wi   X j ,i )  0
j i
j i
The average inlet concentration must be smaller than or equal to minimum
allowable concentration at the inlet, C imax
, in . This constraint is formulated as follows:
Ci ,in 
X
j i
i, j
X
j i
C i j ,out
i, j
 Cimax
,in
 Fi
(13)
The outlet concentration is the sum of the average inlet concentration and the
change in concentration due to the fixed mass load of contaminant transferred. To
maximize water reuse, the outlet concentration is forced to reach the limiting outlet
concentration. Then, equations (12) and (13) become equations (14) and (15),
respectively.
max
j
 C j ,out X i , j  mi  C i ,out (Wi   X j ,i )  0
j i
X
i, j
X
i, j
j i
j i
(14)
j i
C ij ,out
 Fi
 Cimax
,in
(15)
Finally, an LP is formulated. The objective is to minimize equation (10) with
the constraints of equations (11), (14) and (15).

Single Contaminant-Regeneration Recycle
The superstructure model with the regeneration process included can be shown
in Figure 4.
Xi, j
Cj, out
Fi 
Fi
C i , in
Xi,j
ij
Xj, i
Ci, out
 X i ,r
Wi
Ci, out
Operation i
Xi, r
Co
Xr, i
Ci, out
Xr, i
Ci, out
Regeneration Process
Xi, r
Co
Figure 4 The Superstructure Model of Regeneration Recycle Process
According to Figure 4, a water balance around the regeneration process is as
follows:
; number of j is equal to number of unit operation (16)
 X j ,r   X r , j
j
j
In order to handle this type of process, equations (11), (14) and (15) should be
modified to become equations (17) to (19)
(17)
Fi   X i , j  X i ,r Wi   X j ,i  X r ,i  0
j i
max
 C j ,out X i , j
j i
j i
 C o X i ,r  mi  Cimax
,out (Wi   X j ,i  X r ,i )  0
X C  X C
X F  X
j i
j i
i, j
i, j
max
j ,out
i ,r
i
(18)
j i
o
 Cimax
,in
(19)
i ,r
The linear programming to optimize the water network including the
regeneration process is to minimize equation (10) subject to equations (16) to (19).

Multiple Contaminants-Water Reuse
The superstructure model of water reuse process that is multiple contaminants
system is illustrated in Figure 5.
Xi, j
Cj ,k, out
Fi   X i , j
i j
C i ,k ,in
Fi
Xj, i
Ci,k, out
Operation i
Wi
Ci, k, out
Figure 5 Superstructure Model of Multiple Contaminants-Water Reuse
In the multiple contaminants system, water balance around each process is the
same as equation (11) for single contaminant but the contaminant balance and
constraints from maximum inlet concentration have to be modified for each type of
contaminant. The contaminant k balance around operation i is:
 C j , k , out X i , j  mi , k  C i , k , out (Wi   X j ,i )  0
j i
j i
(20)
The constraints from the maximum inlet concentration of contaminant k to
operation i is:
X i , j C j ,k ,out

j i
(21)
 Cimax
,k ,in
X

F
 i, j i
j i
For the multiple contaminants system, the outlet concentration of each
contaminant from any operations cannot be fixed. Since, they are unknown then
equations (20) and (21) are nonlinear. Therefore, the nonlinear programming is used
to minimize equation (10) subject to equations (11), (20) and (21).
The mathematical formulations of the single and multiple contaminants
system are LP and NLP, respectively. These models target the minimum total fresh
water feed subject to water and contaminant balance and maximum allowable
concentration at inlet of each unit operation.
Methodology
In this paper, these following assumptions are made to the process.
1. The mass separating agent (MSA) is water only. It is used in any unit
operation throughout the process industries.
2. The mass flowrate of each stream are constant as it passes through the
network.
3. Mass load of each contaminant in any unit operation is held at constant.
4. No equilibrium relation governs the distribution of contaminants in water.
5. In single contaminant system, the outlet concentration of any unit operation
is equal to the limiting outlet concentration in order to maximize water reuse.
6. In multiple contaminants system, the transfer of any contaminant is
proportional to the transfer of the others.
In some optimization techniques, such as linear programming, inequality
constraints are converted into equality constraints by the addition of slack or surplus
variables. In contrast, for genetic algorithms that generate solutions randomly, such
equality constraints are a bother. GAs cannot produce solutions that satisfy these
constraints randomly and wastewater minimization confronts this problem because of
mass balance. Therefore, the problem of this equality constraints has to be handled
before the optimization model is solved by GAs.
The equality constraints in each type of process can be handled by these
techniques.

Degree of freedom (DOF) for Single Contaminant-Water Reuse Model
In this kind of problem, all of the variables can be divided into three groups
1. Freshwater flowrate (Fi)
2. Wastewater flowrate (Wi)
3. Reused water flowrate (Xi,j)
The possible number of freshwater and wastewater stream is equal to the
number of unit operation. So, there are 2N variables that represent the flowrate of
these streams. They are:
F = [F1, F2, . . ., FN]
W = [W1, W2, . . ., WN]
There are N2-N variables that represent the flowrates of reused stream. All of
the possible reused streams from any operations to the others can be represented by
this matrix.
0

 X 2,1
X   X 3,1



 X N,1
X1,2 X 1,3 ... X 1,N 

0
X 2,3 ... X 2,N 
X 3,2 0 ... X 3,N 


 ...  

X N,2 X N,3 ... 0 
Hence, the total number of variables is N + N + N2-N = N2 + N variables.
The optimization model of this process contains N equality constraints from water
balance and N equality constraints from contaminant balance around each operation.
Hence, there are 2N equations of N2 + N variables. If the values of N2 – N variables
are fixed, the rest 2N variables can be determined by solving the 2N equations
simultaneously. In the other words, the value of 2N variables depends on the others.
As mentioned early, the number of variables, which are reused water flowrate,
is N2 – N. This number is equal to the number of variables that must be fixed.
Moreover, after assigned the value of reused water flowrate, the 2N equations are still
independent and can be solved simultaneously. Thus, reused water flowrate is
selected to be the independent variables from randomization by GAs. The remainders
are the dependent variables. Their values come from the solution of the equality
constraints after assigned the random value of independent variables.

Single Contaminant-Regeneration Recycle
When regeneration process is included, there are 2N variables more than water
reuse without regeneration. These adding variables are the flowrate of regenerated
water to each operation and wastewater from each operation to regeneration process.
These variables can be represented by this matrix:
 R1,r
R
2 ,r
R


 R N ,r
Rr ,1 
Rr , 2 

 

Rr ,N 
Although there are 2N variables more, there is only one equation excessed. It
is the mass balance around regeneration process. So, in regeneration recycle process,
there are 2N+1 equality constraints of N2 + 3N variables. In this case, the values of
N2+N-1 variables have to be known before solving 2N+1 equations simultaneously.
Same as in water reuse, the flowrate of reused water (N2-N variables) is selected to be
the independent variables. The rest of independent variables come from matrix R
except Rr, N (2N-1 variables).

Multiple Contaminants-Water Reuse
In multiple contaminants system that contains N operations and M
contaminants, there are N+NM equality constraints. They come from N water balance
and NM contaminant balance around each operation. These variables can be divided
into 4 groups. The first three groups are same as in the single contaminant system.
They are the flowrate of freshwater, wastewater and reused water. The number of
variables in these groups is N2+N variables which are equal to the single contaminant.
The fourth group of variable is the outlet concentration of each contaminant of each
operation. The number of these variables is NM variables. Therefore, the total number
of variables for multiple contaminants system is N2+N+NM variables. So, the number
of independent variable is equal to N2.
In this work, the freshwater flowrate and reused water are selected to be the
independent variables.
4. Model Set Up
According to the previous mention, the wastewater minimization problem of
single and multiple contaminants can be formulated as LP and NLP, respectively. In
this paper, the problem formulation was developed to be suitable for using with
genetic algorithms.
Binary variables are introduced to the problem. These variables represent any
possible streams in the process. The mathematical representation of these problems is
in the class of mixed integer nonlinear programming (MINLP). Binary variable is
applied to only independent variables. It is not necessary to apply on dependent
variables because the values of dependent variable come from calculations. Binary
variables can be included in the optimization model by multiplying the binary variable
and the independent variable together.
Example
An industrial system with three separate water-using operations; called
operations 1, 2, and 3 is considered. In this process, only one contaminant is diluted
during transferred through those operations. Table 1 shows the limiting process data
of the water reuse process of a single contaminant system.
Table 1
Limiting Process Data of the process [3; page 36]
m
lim
Operation
C
(ppm)
in
(kg/hr)
1
3.75
0
2
1
50
3
1
75
lim
C out
(ppm)
75
100
125
Then the optimization model is the following:
 Objective Function
F = F1 + F2 + F3

(22)
Constraints:
1) Mass Balance around each unit Operation
F1  B1, 2 X1, 2  B1,3 X1,3 W1  B2,1 X 2,1  B3,1 X 3,1  0
F2  B2,1 X 2,1  B2,3 X 2,3 W2  B1, 2 X 1, 2  B3, 2 X 3, 2  0
F3  B3,1 X 3,1  B3, 2 X 3, 2 W3  B1,3 X 1,3  B2,3 X 2,3  0
(23)
(24)
(25)
Where Bi, j is binary variable. Bi, j equals one when the reused stream from
operation j to i appears in the process, otherwise it is zero.
2) Contaminant Balance around each unit Operation
3750  100 B1, 2 X 1, 2  125B1,3 X 1,3  75(W1  B2,1 X 2,1  B3,1 X 3,1 )  0
1000  75B2,1 X 2,1  125B2,3 X 2,3 100(W2  B1, 2 X 1, 2  B3, 2 X 3, 2 )  0
1000  75B3,1 X 3,1  100 B3, 2 X 3, 2 125(W3  B1,3 X1,3  B2,3 X 2,3 )  0
(26)
(27)
(28)
3) Maximum inlet concentration of each operation
100 B1, 2 X 1, 2  125 B1,3 X 1,3
0
F1  B1, 2 X 1, 2  B1,3 X 1,3
75 B2 ,1 X 2 ,1  125 B2 ,3 X 2 ,3
 50
F2  B2 ,1 X 2 ,1  B2 ,3 X 2 ,3
75 B3,1 X 3,1  100 B3, 2 X 3, 2
 75
F3  B3,1 X 3,1  B3, 2 X 3, 2
(29)
(30)
(31)
Then, MINLP can be set up by minimizing equation (22), subject to equations
(23) – (31) and boundary limits of all variables.

Initialization
Initialization is the first step of genetic algorithms. It generates a group of
initial solutions randomly. For the wastewater minimization problems that have a lot
of equality constraints, it is impossible to produce the feasible solution by randomly
generating the value of every variable. Thus, the initialization in this work is divided
into 3 steps. The first step is to generate the value of X ij (i  j ) as independent
variables, randomly. They give the correspondent values to the binary variables for
the model. Then, the second step is to calculate the values of dependent variables.
A solution that is produced by this method will be guaranteed satisfy all the equality
constraints. Finally, the feasibility of the solution should be checked by the inequality
constraints and boundary limit of each variable.

Crossover and Mutation
Crossover and mutation are the methods for producing a new solution from the
old one. Because of equality constraints, the new solutions from changing the values
of some variables will break the equalities. This new solutions are always infeasible.
Thus, crossover and mutation must be requested only on the independent variables.
And then, these variables should be used to calculate the dependent variables.

Graphic User Interface (GUI)
In this work, graphic user interface was built. The user just give the input of
the limiting process data and the program will formulate the optimization
programming automatically.
By this methodology, the GAs based program can be developed. The
wastewater minimization problem is formulated as MINLP. By classifying the
variables into independent and dependent variables, the initialization, crossover and
mutation produce the feasible solutions.
After the GAs based program is developed, it is used to solve the wastewater
minimization problem. Then, the results are compared to either from Lingo or from
literatures.
The genetic parameters and the method of genetic operator used in the testing
are concluded in Table 2.
Table 2 Genetic Parameters and Genetic Operators
Genetic Parameters/Operators
Value/Method
Population size
15
Probability of crossover, Pc
0.3
Probability of mutation, Pm
0.1
Crossover
Arithmetical crossover
Mutation
Transformation based mutation
Handling constraint strategy
CPSS
Selection
Selection
These parameters are used in GAs toolbox [5] and the series of case study are
implemented as in the following sections and in the appendix. Note that the solution
of Table 1 is the problem no.1 in the appendix.
Results

Single Contaminant – Water Reuse
The limiting process data for an example problem of water reuse process of
the single contaminant system are shown in Figure 6. The results from GAs based
program are shown in Figure 7. Then, the results are used to construct the optimum
water-using network and compared to the results from [3] as shown in Figure 8.
Figure 6
Figure 7
Limiting Process Data for an Example Problem of Single
Contaminant – Water Reuse [6]
Results of Single Contaminant – Water Reuse Problem
As one can see that the minimum freshwater consumption and minimum
wastewater generated are the same at 89.375 tons/hr. However, there are some
differences in parts of stream and configuration. In the water-using network from
Lingo, wastewater from operation 1 is reused in operations 2 and 3 but it is reused in
every operation according to the results from GAs. Moreover, GAs allows the
wastewater from operation 2 to be reused in operation 3 while this stream does not
occur in Lingo’s result. This test problem seems to indicate that the result from Lingo
is better because of lower capital cost investment especially a piping.
12 t/hr
25 t/hr
25 (250) 30 (150 ppm)
Operation 1
7 (250)
89.375 t/hr
(0 ppm)
19.375 t/hr
30 (400)
10.625
55.833 (31.3 ppm)
48.833 t/hr
Operation 3
(a)
55.833
(500)
Operation 2
70 t/hr (500 ppm)
70 (300)
Operation 4
3.542 t/hr
13.8038
7.1813
25
Operation 1
3.6853 (250 ppm)
89.375
(0 ppm)
53.0711 (17.36)
49.3858
Operation 2
1.1854
Figure 8
29.9978 (149.98)
(b)
Operation 3
29.9978
(400)
19.375
9.0127
14.1333
53.071
(300)
10.6228
Operation 4
89.375
(478.32 ppm)
70 (500 ppm)
70 (300)
Optimum Water-Using Network for an Example Problem of Single
Contaminant – Water Reuse
(a) Results from Lingo [3]
(b) Results from GAs Based Program

Single Contaminant – Regeneration Recycle
The limiting process data for an example problem of regeneration recycle
process of the single contaminant system are shown in Figure 9. The outlet
concentration of regeneration process is 25 ppm.
Figure 9
Limiting Process Data for an Example Problem of Single
Contaminant – Regeneration Recycle[3]
The optimum water-using networks that are constructed from the results from
Lingo and GAs based program are shown in
Figure 10.
35.57
13.33
75
0.5
26.67
Operation 1
39.30
Operation 2
Regeneration
0.70
Operation 4
39.43
13.92
4.01
3.82
13.33
21.50
8.17
Operation 3
(a)
13.27
39.04
75
Operation 1
50
Operation 4
40.64
11.73
Figure 10
Regeneration
13.33
Operation 3
Operation 2
13.33
(b)
9.36
Optimum Water-Using Network for an Example Problem of Single
Contaminant – Regeneration Recycle
(a) Results from Lingo [3]
(b) Results from GAs Based Program
Even the total amount of flow is the same, complicated network or piping has to be
set when simulates with Lingo.

Multiple Contaminants – Water Reuse
The limiting process data for an example problem of water reuse process of
the multiple contaminants system are shown in Figure 11.
Limiting Process Data for an Example Problem of Multiple Contaminants –
Water Reuse [1]
The optimum water-using networks from GAs based program and Lingo are
compared in Figure 12.
Figure 11
45
Operation 1
45
(15,400,35)
19.5
25.5
108.32
8.5
54.82
8.45
(a)
105.62
(0 ppm.)
Operation 2
Operation 3
Operation 2
108.32
34
(111.25,12500,161.25)
54.82
(102.15,25.54,9500)
34 (111.3,12500,161.3)
25.55 (15,400,35)
45
Operation 1
16.79
105.62
2.66 (15,400,35)
(b)
Figure 12
52.17
Operation 3
54.83
(102.9,45,9500)
Optimum Water-
Using Network for an Example Problem of Multiple
Contaminants – Water Reuse Problem
(a) Results from Lingo
(b) Results from GAs Based Program
From Figure 12, the minimum freshwater consumption from the two programs
are different. The results from GAs is 105.82 tons/hr while the results from Lingo is
108.32 tons/hr. The optimum water-using network from GAs based program has the
reused stream from operation 1 to operation 3 but the one from Lingo does not has
this stream. It shows the freshwater requirement from GAs is less than from Lingo
because of the more amount of water reused.

The Other Test Problems
Several problems are used to validate this GAs based program. The program
runs on an AMD Athlon 1000 MHz. computer. Table 3 shows the comparison of
minimum freshwater used from this program with the well-known optimization
software, Lingo, and the other tools or techniques from literatures such as GAMS,
graphical method and the other proposed methods.
Table 3
The Results Summary of the Other Test Problems
Minimum freshwater
Number
(tons/hour)
Problem
Computational
Process type
of
number.
GAs
Lingo Literature* time (minute)
operation
[3]
1
Single/reuse
3
56.67 56.67 56.67 [3]
0.15
2
Single/reuse
4
90.00 90.00 90.00 [1]
0.19
3
Single/reuse
4
89.375 89.375 89.375 [6]
3.24
4
Single/reuse
4
63.33 63.33 63.33 [3]
12.26
5
Single/reuse
5
30
30
30 [3]
14.58
6
Single/recycle
3
30
30
30 [3]
0.65
7
Single/recycle
3
60
60
60 [3]
0.52
8
Single/recycle
4
75
75
75 [3]
1.07
9
Single/recycle
4
60
60
60 [3]
1.79
10
Multiple/reuse
2
60
65
60 [3]
6.28
11
Multiple/reuse
2
54
63.33
54 [1]
20.39
12
Multiple/reuse
2
100.57 100.57 104 [6]
14.02
13
Multiple/reuse
3
70
79.67
70 [3]
206.18
14
Multiple/reuse
3
105.62 108.32 106 [1]
215.15
*
[ _ ] : references.
Discussion
The results from test problems show that GAs based program can be used to
solve the wastewater minimization problem. It can be found that the minimum
freshwater consumption or wastewater generated is equal to the other authors but with
different configurations. These alternative configurations give the wide-vision on the
analysis of the system. To decide which one is better, all the capital and operating cost
must be included in the optimization. In some multiple contaminants problems, GAs
give usually better results because genetic operators have the ability to avoid getting
stuck in a local optimum like it occurs sometimes in the conventional optimization
techniques. This ability leads the GAs based program to obtain global optimum or
near the global optimum.
For the computational time, GAs spend quite a long time when used with
multiple contaminants problems. In some problems, it spends more than an hour to
obtain the optimum. So, the algorithm should be improved to overcome this
deficiency
Conclusion
In this work, a genetic algorithms (GAs) based program; GAPinch, is
developed to solve the wastewater minimization problem. This prototype covers both
single and multiple contaminants system. For single contaminant, it can be used for
water reuse and regeneration recycle process. For multiple contaminants, it can be
used for water reuse process. The optimization model of wastewater minimization
problem can be formulated as MINLP. This MINLP targets to minimize the total
freshwater feed to the process subject to water and contaminant mass balance around
each operation and maximum inlet concentration of each operation.
This problem of equality constraints are handled by dividing all variables
into two groups, independent and dependent variables. The value of independent
variables come from randomization according to genetic methods and the value of
dependent variables come from solving a set of equality constraints simultaneously
after assigning the value of independent variables into these equations. By this
method, initialization, crossover and mutation can guarantee the feasible solutions.
After that, GUI is created in order to make this program can be used easily.
Then, GAPinch is tested and the results are compared to the ones given by
Lingo. For single contaminant, the results from GAPinch and Lingo reach the same
value of minimum freshwater consumption but they present different configurations.
For multiple contaminants, GAPinch gives better than or equal minimum freshwater
consumption when compared to Lingo because this package could stuck in a local
optimum while GAs has an ability to escape from there. The development is still
undergoing to put on more conceptual design; such as cost constraints of piping and
pump, in this prototype.
Nomenclature
a
b
Bi,j
Ci, out
Random value between 0 and 1
Set of right hand side of inequality constraint
Binary variable
Outlet concentration of water leaving operation i in ppm
Outlet concentration from operation i to operation j
Cimax
,in
C imax
,out
Maximum inlet concentration to operation i in ppm
C imax
, k ,in
Maximum inlet concentration of contaminant k to operation i in ppm
C imax
,k ,out
Maximum outlet concentration of contaminant k to operation i in ppm
Ci, in
Ci, k, in
Ci, k, out
Ci, out
Co
Fi
g(x)
Pc
Pm
Ps
S(x)
Average inlet concentration to operation i in ppm
Average inlet concentration of contaminant k to operation i in ppm.
Outlet concentration of contaminant k water leaving operation i in ppm
Outlet concentration of water leaving operation i in ppm
Outlet concentration from regeneration in ppm
Flowrate of freshwater entering operation i in tons/hr
Set of left hand side of inequality constraints
Crossover rate
Mutation rate
Selection Probability
A function from the set of inequality constraints that returns the maximum
value.
Flowrate of wastewater leaving operation i in tons/hr
Solution of any function at iteration ith
Flowrate to operation i from operation j in tons/hr
Flowrate of operation i after Regeneration Process in tons/hr
Flowrate from operation i next to operation j in tons/hr
Flowrate to regeneration from operation i in tons/hr
Shape factor of CPSS
Total mass load of contaminant transfer from operation i in kg/hr
Total mass load of contaminant k transfer from operation i in kg/hr
C ij,out
Wi
xi
Xi,j
Xi,r
Xj,i
Xr,i

i
i, k
Maximum outlet concentration to operation I in ppm
References
[1]
[2]
[3]
[4]
Wang, Y.P. and Smith R., 1994, “Wastewater Minimization,” Chemical
Engineering Science, Vol. 49, 981 p.
Suriyapraphadilok, U., 1998, Network Prototype of Water-Wastewater
Management, Master of Engineering Thesis, Chemical Engineering Practice
School, King Monkut’s University of Technology Thonburi, 113 p.
Mann, J.G. and Liu, Y.A., 1999, Industrial Water Reuse and Wastewater
Minimization, New York, McGraw-Hill, 523 p.
Wasanapradit, T., 2000, Solving Nonlinear Mixed Integer Programming Using
Genetic Algorithm, Master of Engineering Thesis, Chemical Engineering
Practice School, King Monkut’s University of Technology Thonburi, 90 p.
[5]
[6]
Prakotpol, D., 2001, “Development of MATLAB Toolbok with Genetic
Algorithm for Water Pinch Technology”, Master of Engineering Thesis,
Chemical Engineering Practice School, King Mongkut’s University of
Technology Thonburi, 113 p.
Castro, P., Matos, H., Fernandes, M.C. and Nunes, C.P., 1999, “Improvements
for Mass-Exchange Networks Design,” Chemical Engineering Scince, Vol.
54, pp. 1649-1665.
Appendix
Problem
no.
1
2
3
4
Limiting Process Data
Results
5
6
7
8
9
10
11
12
13
14
----------------------------------------------