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IJCBS RESEARCH PAPER VOL. 1 [ISSUE 1] April, 2014 ISSN:- 2349–2724

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Optimization of Water-Allocation Networks with Multiple Contaminants using Genetic Algorithm

*Md. Alauddin Department of Petroleum Studies,

F/o Engineering & Technology, AMU, Aligarh, UP, India.

Email: [email protected]

ABSTRACT: This is to show that Genetic Algorithm can be used effectively to solve water allocation network problems. In this paper a multi-contaminant problem discussed by Li & Chang [1] has been taken and Genetic Algorithm is used to optimize the model for minimization of freshwater consumption. The freshwater consumption was found to be 104.91 (t/h) which is comparative to Li & Chang that reported as 105.67 (t/h). The model has been written in a different way to reduce the number of effective variables. In Li & Chang paper, there were 40 continuous variable in NLP and 40 continuous and 15 binary variables in MINLP while this paper requires only 12 continuous variable in NLP and 12 continuous and 12 binary variables in MINLP. In addition to this Chang used GAMS environment where it is necessary to initialize and the choice of this initialization has a wide role on the convergence of the solution, where as in this paper GA is used, where no initialization of the variable s is needed, its automatically set by the algorithm, we have to select some parameters like cross over fraction, mutation etc.

Keywords: Evolutionary Technique, GA, GAMS, MINLP, Multi Objective Optimization, Water Allocation Network 1. INTRODUCTION

Water is one of the most important natural

resource. It is widely used in most of the

industrial operations particularly in chemical,

petrochemical and paper & pulp industries.

Water is used in two types of operations. One is

mass transfer based operation in which

contaminants are transferred from process

stream to water streams e.g, in pulp washing in

paper mills. The second is non-mass transfer

operation in which water is generated or

consumed e.g, steam generation. The huge

volume of water usage can be figure out with

following data1.

To produce one kg of paper,

approximately 300 lit of water is

required

To manufacture one complete car,

including tires, 147,972 lit of water is

used.

It takes 215,000 lit of water to produce

one ton of steel

Figure 1.1 shows a typical water network

with m sources WW1, WW2,........WWm, n

processing units P1,P2....Pn, k treatment

units TTP1,TTP2,.......TTPk discharge units

and their interconnections.1

Fig. 1.1: Typical water network

Optimization can be defined as the search

for the best possible solution(s) to a given

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problem while satisfying all the constraints

[1]. Practical optimization problems,

especially the engineering design

optimization problems, seem to have a multi

objective nature much more frequently than

a single objective one. Typically, some

structural performance criteria are to be

maximized, while some others like weight of

the structure and the implementation costs

should be minimized simultaneously. For

example, consider designing a car, the

comfort for the passenger should be

maximized, while simultaneously cost is to

be minimized. But these two objectives are

conflicting to each other. If we want to

minimize the cost then comfort level should

be compromised and vice-versa. Hence

there is a trade-off between cost and

comfort level, as shown in fig 1.2 [2].

Fig. 1.2: Trade-off between cost and comfort

level

In MOP we have to deal with two types of

spaces: decision space as well as objective

space, as shown in fig. 1.3. These types of

problems result in a set of optimal solution

called Pareto Optimal Front, which is locus of

non-dominated points. That is, none of the

points from the set is the best with respect to all

objectives, there is no single optimal, rather,

and there exist a number of solutions which are

all optimal. Fig 1.4 shows a Pareto front of two

objectives – objective 1 and objective2, both are

to be minimized. Solutions A and B are non-

dominated solutions and therefore, they reside

on the non- dominated Pareto-optimal front.

Solution A dominates solution C because

Solution A results in an improvement in

Objective 1 with no change in Objective 2 when

compared with Solution C. Solution B dominates

solution C because Solution B results in an

improvement in Objective 2 with no change in

Objective 1 when compared with Solution C. As

a result, Solution C is dominated and thus, is not

part of the Pareto-optimal front.

Fig. 1.3 Decision and objective space

Fig. 1.4 Pareto front

2. Literature survey

Researchers in the field of water network, since

one and half a decade, a nice review is

presented in this regard by Bagajewicz [4], Foo

[5] and Jacek Jez’owski [6]. It is to minimize the

fresh water consumption that will result not

only the processing cost but also capital cost.

Saveleski and Bagajewics [7] reported, higher

the flow rate through the process, larger the

equipment size. Das et al.[8], shows simple

structure with fewest possible inter connection


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will result in high level of controllability,

operability and safety.

There are broadly two conventional methods

for design of water network as shown in figure

(2.1). One is graphical method associated with

pinch design and the other is mathematical

programming (Optimization based).

Fig. 2.1: Classification of design method of

water networks

The basis of pinch analysis for water network

was put forward by Wang & Smith [9]. This

focuses on to maximize water reuse and recycle

strategy. In this the limitation is that as the

number of contaminants increases, it becomes

more and more difficult. Mathematical

modeling, on the other hand handle multi

component problems and produce global or

near optimal solution. Takama et. al [10]

established a super structure of all possible

reuse and regeneration opportunities which

was then optimized by series of workers. Polley

[11], Yang et.al [12] and Poplewski et.al [13]

optimized the networks for fixed flow operation

and single component. These models were

linear in nature .The model were minimized

using LP for fresh water and MILP for minimum

interconnection. Smith ([14],[15]), Chang( [16],

[17],[18]) come up with multi-component

problems and NLP & MINLP as solution

strategies.

In this paper a multi contaminant problem

discussed by Chang[17] has been presented and

Genetic Algorithm is used to optimize the

model. GA is used prior to optimize over all

water network by some workers. Lavric[19]

that deals with the multi contaminant in which

every unit operation was recieving streams

from previous operations only. Motension [20]

used modified GA in water distribution

network. Wan [21] used advanced GA to reduce

the cost of water supply under the constraint

with hydraulic condition in annular pipe.

3 Mathematical modelling

Fig (3.3) shows general water using unit

network where W represents Water source, M

as mixing unit, S splitting unit and D as demand.

And fig (3.4) depicts a water using unit ‘i’ of the

network. Here a modified version of equations

is written for the Le and Chang Model which is

given in appendix A.

Fig. 3.3: A water using network

Fig. 3.4 A water using Unit

Writing Material Balances we get-

Total mass balance can be given as in (3.1)

∑ ∑

Partial mass balance, for k pollutant species is

written as in (3.2)


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∑

( ∑ )

The first set of constraints can be given as in

(3.3)

∑

∑

∑

∑

And the second set of constraints can be written

as in (3.4)

∑

∑

Objective Functions:

There are two objective functions one is

minimization of fresh water consumption ( )

and another is minimization of number of inter

connections (

Minimization of fresh water consumption-

∑

Minimization of number of interconnections-

=min[∑ ∑

∑ ∑

∑ ∑ ∑ ∑

] (3.6)

Indices

Sets

Parameters

Binary Variable

Positive Variables

Pollutant concentration k going to

operation i

Pollutant concentration of k coming

from operation j

Exit flow from unit operation i

Water flow from j to i operation (likewise

Xij)

3.4 Result & Discussion

The model was tested on a well-known

petroleum refining problem (given in table 3.1),

studied by many workers and currently by Li

Chang (2007 & 2011). The example was

modelled and executed on MATLAB 7.15a

(2008) using optimtool, GA- Genetic Algorithm

as solver. The parameters used were population

size as 120, number of generation as 100, Cross

over fraction as 0.8 and all the others are listed

in the table 4.2. The freshwater consumption

was found to be 104.91 t/h and there were 9

inter connections. The result is shown in


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matching matrix in table 3.2. We can see the

comparative results of this with that of the Li

Chang (in Table 3.3). Fig (3.5) and fig (3.6) show

the solver result for NLP and MINLP

respectively.

Table 2 (a): Current result using GA (MATLAB)

Fig. 3.5: Solver output for NLP


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Fig. 3.6: Solver output for MINLP

Table 3.1: Process limiting data

Table 3.2: GA Parameters settings


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5 Conclusions

The freshwater consumption was found

to be 104.91 t/h almost same as 105.67

as reported in Li & Chang [32] and

Number of interconnection was same as

in Li Chang.

In Li & Chang paper, there were 40

continuous variable in NLP and 40

continuous and 15 binary variables in

MINLP while this paper requires only

12 continuous variable in NLP and 12

continuous & 12 binary variables in

MINLP

In addition to this Chang used GAMS

environment where it is necessary to

initialize and the choice of this

initialization has a wide role on the

convergence of the solution, where as in

this paper GA is used, where no

initialization of the variable s is needed,

its automatically set by the algorithm,

we have to select some parameters like

cross over fraction, mutation etc.

The convergence is highly susceptible

on the choice of the parameter to be

selected particularly on Population size,

Ellite Counts, cross over fractions.

We cannot access the same random

number voluntarily if we want i,e., we

do not have control on the random

number

The constraints is not 100 % meet

though very small degree of violation

9.99*e-7.

We are not getting Pareto fronts- What

we are doing is that First minimization

of Fresh water and assuming the

obtained value as an additional

constraint we are minimizing the

Number of interconnections.

References

1. Thomas, B., Fogel, D. B., and

Michalewicz, Z.; editors. Handbook of Evolutionary Computation. Institute of Physics Publishing and Oxford University Press, 1997.

2. Deb, K.; Multi-objective optimization

using evolutionary algorithms. Wiley,

Chichester, UK, 2001.

3. Bleuler, S., Laumanns, M., Thiele, L., and Zitzler, E.; PISA - a platform and programming language independent interface for search algorithms. Technical Report 154, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Gloriastrasse 35, CH-8092 Zurich, Switzerland, October 2002. Submitted to the Second International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003).

4. Bagajewicz, M., “ A review of recent

design procedures for water networks in refineries and process plants” Comp. Chem. Eng., 24, (9-10), pp. 2093-2113, 2000.

5. Foo, D. C. Y., “State-of-the-art

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11. Polley, G. T., Polley, H. L., “ Design better water networks” Chem. Eng. Prog., 96, pp. 47–52, 2000.


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12. Liu, Z. Y., Yang, Y., Wan, L. Z., Wang,

X., Hou, K. H., “A heuristic design procedure for water-using networks with multiple contaminants” AIChE J., 55 (2), pp. 374–382, 2009.

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J., “ Optimization-based method for calculating water networks with user specified characteristics” Chem. Eng. Res. Des., 88, pp. 109–120, 2010.

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