Synthesis of Reuse Water Networks by PSO Approach
Mauro A. S. S. Ravagnani
1
, Daniela E. G. Trigueros
2
, Aparecido N. Módenes
2
and Fernando Espinosa-Quiñones
2
1
State University of Maringá, Av. Colombo 5790, Maringá, PR, Brazil
2
State University of Paraná West, Rua da Faculdade 645, Toledo, PR, Brazil
Keywords: Reuse Water Networks, PSO, MINLP, Optimization.
Abstract: In the present paper the problem of reuse water networks have been modeled and optimized by the
application of a modified Particle Swarm Optimization (PSO) algorithm. A proposed modified PSO method
lead with both discrete and continuous variables in Non-Linear Programming (NLP) and Mixed Integer
Non-Linear Programming (MINLP) formulations that represent the water allocation problems. Pinch
analysis concepts are used jointly with the improved PSO method. A literature problem was solved with the
developed systematic and results has shown excellent performance in the optimality of reuse water network
synthesis based on the criterion of minimization of annual total cost.
1 INTRODUCTION
In the last decades the studies in the minimization of
primary water consumption in industrial processes
and in the wastewater reduction from such processes
have contributed to the minimization of
environmental impacts. Instead of applying graphic
and algebraic technologies to solve the problems of
process integration, mathematical programming has
been used as a very convenient alternative method
when the subject can be formulated as an
optimization problem.
The problem of Water/Wastewater Allocation
Planning (WAP) can also consider both discrete and
continuous variables. A large group of WAP
problems have Mixed Integer Non-Linear
Programming (MINLP) and NLP formulations and a
great variety of algorithms has been proposed,
developed and improved.
The PSO algorithm was properly modified in
order to satisfy the requirements of leading with
discrete-type variables and other strategies were also
included to solve MINLP-based models. In addition,
as criteria for obtaining the synthesis of the reuse
water network, the minimization of the total cost
was applied.
2 WAP PROBLEM DEFINITION
AND MODEL FORMULATION
With regard to the total possible configurations of
mass transfer between the water streams and the
process streams and all the possibilities for reuse
water, a superstructure was built, as reported by
Trigueros et al. (2012), in order to attain
optimization of the mass exchange network project
in a simultaneous analysis procedure. A reduction in
the high contaminant loads of the process streams is
essentially performed by transferring mass to a
cleaner water stream, with the possibility of reusing
it in the other (N-1) process units.
In this work, maximum inlet and outlet pollutant
concentration data were used in the synthesis of the
reuse water network, calculating the maximum water
flow rate (Eq. 1) and demanding a global mass
balance (Eq. 2). The superstructure was fractioned in
small components corresponding to each process
unit, mixing and splitting nodes in which their
individual mass balances are defined by Equations
(3)–(5), respectively.
In addition, pollutant mass balances in the
process streams are also performed (Eqs. (6) and
(7)), and the maximum allowed pollutant
concentration constraints for the inlet and outlet of
each process unit, two inequalities (Eqs. 8 and 9). A
condition necessary to warrant no violation of the
minimum ΔCi, (see Eq.10), was demanded in each
226
A. S. S. Ravagnani M., E. G. Trigueros D., N. Módenes A. and Espinoza-Quiñones F..
Synthesis of Reuse Water Networks by PSO Approach.
DOI: 10.5220/0004157502260230
In Proceedings of the 4th International Joint Conference on Computational Intelligence (ECTA-2012), pages 226-230
ISBN: 978-989-8565-33-4
Copyright
c
 2012 SCITEPRESS (Science and Technology Publications, Lda.)

process unit (see Eq. 10). In addition, the pinch point
freshwater flow rate value was introduced in the
modeling as a physical restriction variable (Eq. 11),
among other non-negativity constraints (Eqs. (12–
17)). Finally, as an optimization criterion of the
reuse water network synthesis the total cost of the
industrial plant (Eq. (18)) was considered.
f
i


m
i
(C
j
out
max
C
j
in
max
)
(1)
0
111
,
1



N
i
wastewater
i
N
i
J
j
ji
N
i
freshwater
i
fmf

(2)
Nimff
J
j
ji
in
i
out
i
0
1
,




(3)
Nifff
in
i
N
ik
k
ki
freshwater
i
0
1
,




(4)
Nifff
out
i
N
ki
k
ik
wastewater
i
0
1
,




(5)
f
i
fr eshw at er
C
i
fr eshw at er
 f
i ,k
k1
ik
N

C
k, j
out
 f
i
in
C
i , j
in
 0
 i  N; j  J
(6)
f
i
in
C
i , j
in


m
i , j
 f
i
out
C
i , j
out
 0
 i  N; j  J
(7)
C
i , j
in
 C
i , j
in
max
 i  N; j  J
(8)
Jj N i CC
out
ji
out
ji
 ;
max
,,
(9)
N i ff
i
in
i
 0
max
(10)
0
1



Pinch
N
i
freshwater
i
ff
(11)
f
i
f r eshwat er
, f
i
wastewat er
, f
i
in
, f
i
out
, f
i ,k
, f
k,i
 0

i

N
(12-17)
Min(z)  AB f
i ,k
 f
i
fr eshwater
i1
ik
N











k1
N



CD f
i ,k
 f
i
fr eshwater
i1
ik
N











k1
N

CE f
i
freshwater
i1
N


 Fy
i ,k
i1
ik
N

k1
N

 y
i
fr eshwater

i1
N

y
i
wast ewat er
i1
N











(18)
2.1 PSO Proposed Algorithm
A PSO algorithm that was earlier reported by
Kennedy and Eberhart (2001) applied by Trigueros
et al. (2010) to solve problems with continuous
variables, was modified to consider also discrete
variables. A numeric generator function in the 0-1
range and a cut-off value condition were introduced
in the PSO algorithm (Eqs. 19-20), including a
complementary binary attribution test (Eqs. 21 and
22). Within the modified PSO algorithm, the
possible interference between discrete and
continuous variable positions as well as their
respective velocities was avoided by creating
another search space where binary particles are
moving with other velocity ranges. To avoid non-
viable solutions, the original objective function was
penalized by adding the inequality and equality
constraints that were previously violated as well as
assigning weights to each type of violation,
according to Eqs. (23-25).
)(
1
1
)(
k
i
e
sig
k
i
x
x



(19)
If
)(
k
i
k
i
sig xx 
then
1
k
i
x
else
x
i
k
 0
(20)
If
0
,

ki
y
then
0
,

ki
f
else
()
,
randf
ki

(21)
If
0
,

ki
f
then
y
i ,k
 0
else
1
,

ki
y
(22)
H(x,y) 
h(x,y) if h(x,y)
   0
0 if h(x,y)
   0





(23)
G(x,y) 
g(x,y) if g(x,y)  0
0 if g(x, y)  0



(24)
z
p
 z b
i
G
i
i1
m

 d
j
H
j
j1
n









(25)
In order to avoid the constrain search space and
the increasing computational time, two strategies
were considered: dependent and independent
variables were defined in the mathematical model
and adopting the fundamental concepts of pinch
analysis in order to achieve feasible or very near
feasible solutions.
3 CASE STUDY
An early proposition of Olsen and Polley (1997),
SynthesisofReuseWaterNetworksbyPSOApproach
227

summarized in Table 1, was used as a modified
PSO-method testing system in the optimization
procedure. Firstly, the pinch point flow rate was
estimated (157.14 ton/h) and required as a physical
criterion in the optimization procedure. A set of 51
equations (38 equality constraints and 12 inequality
constraints and one objective function), 73
continuous and 48 binary decision variables are
required to represent the WAP problem. By
redefining some variables as dependent in the PSO
algorithm, decision variables were reduced. All
financial parameter (A, α, B, C, D, E and F) values
were obtained from Wang and Smith (1994). As
some situations that are expected for the
minimization of the total cost, two strategies were
applied, being a fixed pinch point flow rate as first
strategy, whereas no constraint on the consumption
of freshwater was considered as second strategy.
Results from the use of the developed PSO
algorithm for the reuse water network synthesis are
shown in Fig1. When applying the first strategy, a
minimum water flowrate of 157.16 ton/h and an
annual total cost of US$ 2,217,101.70 were attained
The network contains 5 fresh water, 4 reuse water
and 5 wastewater streams (see Fig. 1a). By
considering a variation on the fresh water flowrate
near to the Pinch point, other reuse network
synthesis were obtained with different annual total
cost as shown in Fig. 2, where its behavior is
depending on the total fresh water (see Fig. 2a) and
reuse water flowrate (see Fig. 2b).
4 CONCLUSIONS
A modified PSO algorithm was proposed and tested
to optimize a WAP problem. It is possible to achieve













22.85
t
on h
-1
45 ton h
-1
7
t
on h
-1
18
t
on h
-1
44.40
t
on h
-1
5.6
t
on h
-1
5
0
t
on h
-1
1
6
.40 t h
-1
5
t
on h
-1
25
t
on h
-1
Proc1
Proc2
Proc3
Proc4
Proc5
Proc6
Wastewate
r
5
0
t
on h
-1
4
0
t
on h
-1
5
t
on h
-1
Freshwate
r
15.85
t
on h
-1
(a)

5
t
on h
-1
5
t
on h
-1
7
t
on h
-1
18 ton h
-1
44.40
t
on h
-1
5.6
t
on h
-1
22.86
t
on h
-1
50
t
on h
-1
16.40
t
on h
-1
25
t
on h
-1
Proc1
Proc2
Proc4
Proc5
Proc6
Wastewate
r
50
t
on h
-1
40
t
on h
-1
50
t
on h
-1
Freshwate
r
15.85
t
on h
-1
Proc3
(b)
Figure 1: Reuse network synthesis by the PSO method for the minimization of total cost, considering the (a) first and (b)
second strategies.
IJCCI2012-InternationalJointConferenceonComputationalIntelligence
228

R²=0,9835
2,10
2,30
2,50
2,70
2,90
3,10
3,30
186 196 206 216 226 236 246 256 266 276
Annual total cost (10
6
US$)
Total water flowrate (ton h
-1
)
0,00
0,50
1,00
1,50
2,00
2,50
3,00
0 0
12,82
30,6
36,33 36,42 36,75 37,03 37,37 37,38
38,2
41,84 45,63 46,83 51,94 56,36 56,42 81,56
Annual total cost
(10
6
US$)
Reuse water flowrate (ton h
-1
)
Pinch
Figure 2: Behavior of the total cost as a function of (a) total water flow rate and (b) reuse water flow rates.
Table 1: Problem data - Olesen and Polley (1997).
Process
max
in
C
(ppm)
out
C
max
(ppm) m (g h
-1
)
1 25 80 2000
2 25 100 5000
3 25 200 4000
4 50 100 5000
5 50 800 30000
6 400 800 4000
SynthesisofReuseWaterNetworksbyPSOApproach
229

different reuse water network synthesis by
demanding the minimum annual total cost as
criterion and requiring on fixing or assigning values
near the Pinch point for the fresh water flowrate, and
without any constraint in the fresh water flowrate. In
conclusion, the modified PSO algorithm has shown
high flexibility and capability to provide optimal
results for the reuse water network synthesis, being
independent of initial estimative for the decision
variables.
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Kennedy, J., and Eberhart, R., 2001. Swarm Intelligence.
Morgan Kaufmann Publishers, San Francisco, CA.
Trigueros, D. E. G., Módenes, A.N., Kroumov, A.D., &
Espinoza-Quiñones, F. R., 2010. Modeling of
biodegradation process of BTEX compounds: Kinetic
parameters estimation by using Particle Swarm Global
Optimizer. Process Biochemistry, 1355-1361.
Trigueros, D. E. G., Módenes, A. N., Ravagnani, M. A. S.
S., and Espinoza-Quiñones, F. R., 2012. Reuse Water
Network Synthesis by Modified PSO Approach.
Chemical Engineering Journal.
Wang, Y. P., and Smith, R., 1994. Wastewater
minimization, Chemical Engineering Science, 49, 981-
1006.
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