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Environmental Engineering and Management Journal February 2010, Vol.9, No.2, 239-247 http://omicron.ch.tuiasi.ro/EEMJ/

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OPTIMIZATION BY NN GA TECHNIQUE OF THE METALCOMPLEXING PROCESS.

POTENTIAL APPLICATION IN WASTEWATER TREATMENT

Ciprian-George Piuleac 1, Silvia Curteanu 1 , Maria Cazacu 2 1Gh eorghe Asachi Technical University Iasi, De partment of Chemical Engineering,

71 Mangeron Blvd., 700050, Iasi, Romania2Petru Poni Institute of Macromolecular Chemistry, Iasi, Romania

Abstract

Some samples consisting in silica functionalized in different degrees with dihydroxy-azomethine groups have been tested assorbents for copper (II) ions from aqueous solutions in different conditions. An indirect monitoring procedure for the complexingprocess was approached: UV-VIS absorption intensity time variation for the metal-containing solution in which complexingsilica was soaked. In order to find the conditions in which the maximum efficiency in the metal absorption can be obtained(maximum decreasing of the UV absorbance), a method based on neural networks and genetic algorithms (NN-GA) was applied.The model included into the optimization procedure was a feedforward neural network with one hidden layer. The optimization

problem was solved with a standard genetic algorithm, which computed the optimal values for reaction conditions (CuCl 2 solutionconcentration, pH, complexing groups density in silica) leading to minimum relative absorbance of the metal in shortest time.

Key words: complexed metals, functionalized silica, genetic algorithm optimization, neural network modeling

Author to whom all correspondence should be addressed: e-mail: [email protected]

1. Introduction

Chelating polymers play an important role inthe decontamination of aqueous systems such aswastewater treatment, sludge and noble metalrecovery (Liu and Cheng, 1993). Chelating groupsimmobilized on the surface of inorganic solid

supports are gained increasing importance as low costsorbents for separation and preconcentration of metalions. Advantages of such supports are welldocumented (Singh and Mishra, 1991).

Silica gel, the inorganic polymer containinginternal siloxane groups (Si-O-Si) and silanol groups(Si-OH) distributed on the surface, is currently beingused as a support for various functional groups (Deyet al., 2006). When these possess complexing ability,then such silica gel can be used to retain metal tracesfrom wastewater (Bowe and Martin, 2004; Dudler etal., 1987). The immobilization of chelating moietiescontaining donor atoms on the silica gel surface can

occur via chemical bond formation between organic

modifiers like amino or chloro- and silica support orthrough simple physical adsorption processes(Mahmoud and Gohar, 2000). The chemicalmodification of silica gel surfaces with donor atomssuch as N, S, O and P is primarily aimed to improvethe adsorption and exchange properties of the silicagel, as well as selectivity towards certain metal ions

(Seshadri and Haupt, 1988). Several new chemicallymodified silica gels were synthesized, and applied asnormal or selective solid phase extractor for manytoxic and other metal ions. They were found to besuperior to the conventional ion exchange resins intheir ability to extract and selectively preconcentratethe heavy metal ions from solutions containing highconcentrations of alkali and alkaline earth metal ions(Jal et al., 2004; Kocjan and Prezeszlakowski, 1992;Prado and Airoldi, 2001). Advantages of the modifiedsolid phase extractors compared with the classicalliquid extractors were reported in many references(Blain and Treguer, 1995; Mahmoud and Gohar,

2000). A number of complexing and chelating

Gheorghe Asachi Technical University of Iasi, Romania

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systems immobilized on silica gel are available.Between them, Schiff bases, having multidentatecoordination sites, are known to form complexes withtransition metal ions readily (Che and Cheng, 1986;Ueno and Martell, 1955).

Silica xerogels functionalized in differentdegrees with hydroxyazomethyne groups linkedthrough a propylene moiety to silica network weretested in this paper for the uptake of copper (II) fromaqueous solutions. An indirect monitoring procedurefor the complexing process was approached: UV-VISabsorption intensity time variation for the metal-containing solution in which complexing silica wassoaked.

For complex chemical processes, neuralnetworks (NN), which posses the ability to recognizeand reproduce cause effect relationships, has gainedpopularity in various areas of environmentalapproaching (Karatzas and Kaltsatos, 2007;Manolakos et al., 2007; Mjalli et al., 2007). Neuralnetworks are efficient modelling tool for complexprocesses where the chemical and physical laws arenot completely known because they are black boxesbased on input output data.

Genetic algorthms (GA) are part of the so-called evolutionary algorithms and represent anoptimization instrument with increasing application inscientific problems. These kinds of approaching donot require any piece of information about the searchspace area, just being necessary an objective/fitnessfunction that assigns a value to any solution (Deb,1999).

The basic algorithm, simple GA (SGA), hasthe advantages that it does not require good initialguesses for the values of the decision variables, liketraditional methods. It uses a population of severalpoints simultaneously along with probabilisticoperators (reproduction, crossover and mutation),inspired by natural genetics. Additionally, SGA hasthe advantage of using only the values of theobjective functions and not any derivatives, asrequired by gradient search techniques (Guria et al.,2005).

The applicability of these algorithms hascovered a wide variety of problems because of theirflexibility, ease of operation, minimal requirementsand global perspective that they offer (Deb, 2001).GAs have found various applications in chemicalengineering including process control, gas pipelinedesign, pattern recognition of multivariate chemicaldata, optimization of reaction rate parameters,multipurpose chemical batch plant design, andscheduling (Yan et al., 2003). Details about differenttypes of genetic algorithms and a series of theirapplications in optimization of the chemical processeshave been given in the reviews of Bhaskar et al.(2000) and Nandasana et al. (2003).

Our group applied GA optimization method

for different chemical systems (Caliman et al., 2008;Curteanu et al., 2006; Curteanu and Leon, 2007;Curteanu and Cazacu, 2007).

In a previous paper (Piuleac et al., 2008)details of preparing silica xerogels with differentcontents in chelating groups and its use to extractmetal ions (Cu 2+) from aqueous solution werepresented. In order to find the conditions in which amaximum efficiency in the metal absorption can bereached and to study the evolution in time of theabsorbance as a function of others process parameters(saturation time, concentration of the solution,chelating groups content and pH), a series of experiments have been performed in differentconditions. The acquired data were used for processmodeling based on artificial intelligence instruments.It was emphasized the option of using simple neuralnetworks or stacked neural networks with differentarchitectures to model the wastewater treatmentprocess based on silica xerogels functionalized withhydroxyl-azomethine groups.

The main goal of the present paper is todevelop a general procedure based on neural networksand genetic algorithms, which could be applied to thecomplex optimization problems. Neural networks areused as efficient modeling tools and geneticalgorithms as solving methods of optimization; aneural model of the process is included in theoptimization procedure. In this herein case study, theestimation of the metal absorbance is analyzed as afunction of the process parameters: time, CuCl 2solution concentration, values of complexing groupsdensity in silica and pH values. There is followed amaximum value of the absorbance decreasing in thecontext of using minimum resources. It wasdemonstrated that GA optimization procedure is easyto apply and provides accurate results.

2. Experimental

2.1. Materials

Some solutions differing by copper dichlorideconcentration (5.5 and 11 g /L) and pH (4, 5 and 6)were prepared by using adequate buffer solutions.

Silica functionalized withdihydroxyazomethine groups (Fig. 1) in differentdegrees (Table 1) was prepared, as already described(Cazacu et al., 2008), by one-pot procedure, bothsilica formation and its functionalization occurring inthe same sol-gel system.

OHN = HC -O - Si

O

OHO

Fig.1. The silica functionalized with dihydroxyazomethine

groups

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Table 1 . The functional groups content in the preparedsilica

Sample Functional groups content in silica (mol/g)FS1 4.35 x 10 -4

FS2 8.70 x 10 -4

FS3 13.04 x 10 -4

2.2. Metal uptake experiments

UV-VIS spectrum was registered for eachCuCl 2 solution. A certain amount of functional silicagel bringing a certain amount of chelating groups wasintroduced in such a solution and UV-VIS spectrumwas registered (by using SPECORD M42spectrophotometer with quartz cells of 1 cmthickness) at certain time intervals until the maximumabsorbance remains constant. The corresponding

time, saturation time, was denoted as t s, when eithersorption equilibrium was reached or all functionalgroups were occupied by metal complexing (Cazacuet al., 2008).

2.3. Formulation of the optimization problem

The general solution of an optimizationproblem implies a dependency of the following fourelements: an accurate model of the process, aselected number of control variables, an objectivefunction and a suitable numerical method for solvingthe specified optimization problem.

A good process model is a prerequisite forapplication in the optimal control strategy.

The feed-forward, multilayered neural network is the most used type of network because of thesimplicity of the theory, ease of programming, goodresults provided and for its character of universalfunction in the sense that if topology of the network isallowed to vary freely it can take the shape of anybroken curve .

One major problem in the development of neural network model is the determination of thenetwork architecture, i.e. the number of hidden layersand the number of neurons in each hidden layer. The

most used method is the trial-and-error, done bytesting several topologies and comparing theprediction errors. Lower errors indicate potentiallygood architectures, i.e. neural network topologieswith chances to train well and to output good results(Fernandes and Lona, 2005).

Based on the experimental data, a neuralnetwork modeling methodology was developed todescribe the dependency of the absorbance as afunction of reaction conditions: time (minutes), CuCl 2 solution concentrati on (gL -1), complexing groupsdensity in silica (molg -1) and pH. Consequently, 4inputs corresponding to the 4 variables mentionedbefore are presented as input of the neural model,along to one output absorbance. Trial and errormethod applied for feedforward neural networks leads

to a multilayer perceptron having one hidden layerwith 6 neurons, MLP(4:6:1). Before using, the neuralmodel was tested in training and validation phases.Good agreement between experimental data andneural network predictions (average relative errorsless than 0.3298 % and correlation over 0.9939)

registered against unseen data (validation phase).Maximum absorbance at every time is noted

At and reported to the absorbance of the initialsolution (A 0). For a better comparability of theresults, eliminating the influence of the ratio betweensorbent and solution amounts, the relative absorbance,Ar=A t /A 0, can be used.

In this study, the optimization problemincludes the neural model, which is represented as:

NN [Inputs: Time, CuCl 2 solution concentration,complexing groups density in silica, pH; Output:

Absorbance] (1)

The vector of decision variables, u, has thecomponents:

u = [Time, CuCl 2 solution concentration, complexinggroups density in silica, pH] (2)

An admissible control input u* should beformed in such a way that the performance index, J ,defined by the following equation, to be minimized:

r A J (3)

subjected to:

6 pH 4

gmol1013silicaindensitygroups1044

Lg11CuCl5.5

min2200time0

uuu

145

12

maxmin

(4)

The absorbance is a measure of the ionselimination from wastewater, with values between1.017 and 3.01. The objective function supposes theminimization of the relative absorbance value, whichmeans the maximization of the decrease of the

absorbance.The constraints (4) are very important todefine the range of variation of parameters and todisregard possible solutions that could be interestingin a theoretical approach to the problem.

GA posses several characteristics that makethem attractive to solve optimization problems wherethe model is only available in an implicit form(black-box model). Firstly, due to the fact that it isbased on a direct search method, it is not necessary tohave explicit information of the mathematical modelor its derivatives. Secondly, the search for theoptimal solution is not limited to one point, but it

rather relies on several points simultaneously,therefore the knowledge of initial feasible points is

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not required and such points do not influence thefinal solution (Leboreiro and Acevedo, 2004).

The optimization procedure includes theneural model MLP(4:6:1) and it is solved with asimple genetic algorithm. Genetic algorithmprovides, after an iterative calculus, the optimalvalues for decision variables (time, CuCl 2 solutionconcentration, complexing groups density in silica,pH), which are the inputs for the neural network model. With these inputs, the neural network computes the final value of the relative absorbance. If the two values are identical or there is a very tightdifference between them, it can be conclude that thetask of the optimization, represented by minimum of the objective function, J , is achieved. Fig. 2illustrates this optimization procedure.

Fig. 2. The optimization method based on NN and GA

2.4. GA optimization technique

Genetic algorithms are intelligent stochasticoptimization techniques based on the mechanism of natural selection and genetics. GAs start with aninitial set of solutions, called population. Eachsolution in the population is called chromosome (orindividual), which represents a point in the searchspace. The chromosomes are evolved throughsuccessive iterations, called generations, by geneticoperators (selection, crossover and mutation) that

mimic the principle of natural evolution. A set of solutions are analyzed and modified by geneticoperations simultaneously, where selection operatorcan select some good solutions as seeds, crossover operator can generate new solutions hopefullyretaining good features from parents, and mutationoperator can enhance diversity and provide a chanceto escape from local optima (Wang et al., 2006).

In a GA, a fitness value is assigned to eachindividual according to a problem-specific objectivefunction. Generation by generation, the newindividuals, called offspring, are created and survivewith chromosome in the current population, called

parents, to form a new population.In the GA model, They were used real values

encoding for the chromosomes. There are other

approaches for genetic algorithm based optimizationwhich use binary solution representation, as it is thesimplest type of encoding, in which chromosomes arecomposed only of 1s and 0s. Even the number of alleles is thus rather small (two), this encoding is verycommon, because it is very easy to use. However,value encoding is more general, because genes arereal numbers. Some experiments (Michalewicz, 1996)have shown that real value encoding is more timeefficient, with better precision of the solutions.

The initial population is generated randomly.Offspring is created by genetic operators and it isstored in a population pool that is a collection of offspring and their parents.

Selection compares the chromosomes in thepopulation aiming to choose those which will takepart in the reproduction process. The selection occurswith a given probability on the base of fitnessfunctions. The fitness function plays a role of theenvironment to distinguish between good and badsolutions. The individuals with higher fitness musthave more chances to reproduce. For each individualto be created in the next generation, two parents arethus selected.

There are different methods for selectionphase; our paper uses rank selection which first ranksthe population and then every chromosome receivesfitness from this ranking. The worst will have fitness1, second worst 2 etc. and the best will have fitness n (number of chromosomes in the population).

The recombination (crossover ) has as mainpurpose the recombination the features of tworandomly selected parents from the mating pool withthe aim of producing better offspring. The variant of crossover used in this study supposes different pointsfor all genes, which means that the new individualwill no longer be on the line segment that links itsparents. The offspring will look more like one parentregarding a feature and less regarding another.

After recombination, offspring undergoes tomutation . Generally, the mutation refers to thecreation of a new chromosome from one and onlyone individual with predefined probability. Mutationis used to produce small perturbations onchromosomes to promote diversity of the population.Our GA includes a variant of mutation namedresetting.

A gene value is reset to a random value in itssearch interval. The purpose is to refresh the searchprocess, in case when the genetic diversity of thepopulation decreases (so no longer converges to thesolution) or the algorithm has converged into a localoptimum. Each gene is independently considered,and mutation gives it a new random value in theinitialization interval. Only some genes change(possibly all, but unlikely).

After the three operators are carried, theoffspring is inserted into the population, replacing

the parent chromosomes in which they were derivedfrom, producing a new generation. The bestindividual is copied directly into the new population(the elitism technique) and the rest of the individuals

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are replaced by the new generations. So, in order tokeep the best solution, there were considered anelitism factor f e = 1, that is the best individual iscopied directly in the new generation. That ensuresthat the overall solution of the GA will not get worse.

The stopping criterion determines when GA

will break. In other words, the genetic operations arerepeated until a termination condition is finding. Inthis implementation GA was stopped if the maximumnumber of generations has been executed or the pre-set number of generations without improvement in thelast best solution has been reached.

3. Results and discussion

Due to the presence in positions favourable toclosing the chelate ring, the azomethine and hydroxylgroups attached to the silica can co-ordinate the metalions from an aqueous solution forming complex like

that showed in Fig. 3 and proved by the spectralmethods (Piuleac et al., 2008). The Si-OH groups onthe surface permit the silica wetability and the metalion access to the chelating groups (Piuleac et al.,2008).

OHN = HC -O - Si

O

OO

Si - O

O

O

- CH = NHO

O Cu

Fig.3 . The copper complexed by functionalized silica

Three variables were involved in this process:functional groups content in silica, metalconcentration and pH of the solutions. UV spectrumfor each initial solution was registered, the maximumabsorbance being A 0. A determined amount of functional silica gel was introduced in such a solution

and UV spectrum was registered at certain timeintervals. Thus, the concentration of the copper ionsin solution decreases and, by consequence, the UVabsorbance also decreases Figs. 4 and 5 present someexamples. Maximum absorbance at every time (A t)was determined from the spectra as an indirectmeasure of the metal content and reported to theabsorbance of the initial solution (A 0). The time atwhich the absorbance remained constant wasconsidered the saturation time.

The good agreement between experimental andsimulation data obtained with neural model invalidation phase is shown in Fig. 6. The neural

network MLP(4:6:1) has a good capacity of generalization, therefore it can be used trustily in theoptimization procedure.

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0 500 1000 1500 2000 2500

Time, min

R e l a

t i v e a

b s o r b a n c e

G1_exp

G1_net

G2_exp

G2_net

G3_exp

G3_net

G4_exp

G4_net

Fig. 4. Evolution of the relative absorbance in time(samples G1, G2, G3, G4) obtained experimentally and

predicted with MLP(4:6:1) on training data

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0 200 400 600 800 1000 1200 1400 1600

Time, min

R e l a

t i v e a

b s o r b a n c e

G5_exp

G5_net

G6_exp

G6_net

G7_exp

G7_net

G8_exp

G8_net

Fig. 5. Evolution of the relative absorbance in time(samples G5, G6, G7, G8), obtained experimentally and

predicted with MLP(4:6:1) on training data

0.8

0.9

0.9

1.0

1.0

1.1

1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25.0

Exemples

R e l a

t i v e a

b s o r

b a n c e

Experimental

Modeling

Fig. 6. Relative absorbance obtained experimentallyand predicted with MLP(4:6:1) on testing data

Population size, number of generations,crossover probability and mutation probability areknown as the control parameters of genetic

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algorithms. The values of these parameters must bespecified before the execution of GA and they dependon the nature of the objective function. One importantthing in using GA as solving method is to adjust itsparameters to the particular problem approached, soas to obtain good solutions and to preserve thealgorithm from a preliminary convergence.

The fitness function in GA is the objectivefunction of the optimization procedure. The results of the optimization are represented by the values of thedecision variables (time, CuCl 2 solutionconcentration, complexing groups density in silica,pH) that lead to a minimum value of the objectivefunction, which means the achievement of minimumvalue for the relative absorbance (maximum decreaseof the absorbance).

The optimization procedure is implemented in Matlab 7.5 with original software, as specificfunctions were programmed for each phase of thegenetic algorithm.

Since GA is a stochastic algorithm, it was runfor many times, for each situation (each row in thetables of results) to get statistically meaningful valuesfor the time taken. Longer runs are not necessary asGA is already a population based procedure thatworks with multiple solutions. One of the solutions(the best solution) is chosen and inserted into theresults Tables.

Table 2 shows the influence of initialpopulation. There is known that the grower parameteris the better results of optimization are obtained, butthis kind of rule is applied until one certain limit.

Table 2. The influence of population dimension on the performance of GA optimization

No. Dimension of

population

Number of

generation

GA method Decision variables Values of objective

function

1 50 100 Cross rate =0.4Mutation rate=0.04

Time = 2125.4214Conc = 5.5007

Gr_dens = 0.0010pH = 5.5017

0.9433

2 100 100

Time = 2199.3954Conc = 5.5111

Gr_dens = 0.0010pH = 5.5008

0.9427

3 150 100

Time = 2173.9741Conc = 5.5024 Gr_dens =

0.0010pH = 5.5003

0.9428

4 200 100

Time = 2194.5754Conc = 5.5082 Gr_dens =

0.0010pH = 5.5018

0.9429

5 300 100

Time = 2190.0300Conc = 5.5062

Gr_dens = 0.0010pH = 5.5005

0.9428

6 400 100

Time = 2187.1616Conc = 5.5092 Gr_dens =

0.0010pH = 5.5015

0.9429

7 500 100

Time = 2190.0520

Conc = 5.5039 Gr_dens =0.0010

pH = 5.50320.9429

8 600 100

Time = 2198.7309Conc = 5.5191

Gr_dens = 0.0010pH = 5.5024

0.9429

9 800 100

Time = 2186.6470Conc = 5.5005 Gr_dens =

0.0010pH = 5.5023

0.9429

10 1000 100

Time = 2193.6061Conc = 5.5072

Gr_dens = 0.0010pH = 5.5006

0.9427

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Table 4. Optimization with different restrictions imposed to the time interval

No Imposed interval of

time

Dimension. of iniial

population

No. of generations

GA Method Decision variables Output of neural model

Values of objective function

1 02200 50 50 Rata_cross =0.9Rata_mut=0.03

Time = 2043.6148Conc = 5.5002Gr_dens = 0.0010

pH = 5.5005

0.9438 0.9438

2 02000 Time = 1997.6259Conc = 5.5060Gr_dens = 0.0010

pH = 5.5007

0.9442 0.9442

3 01800 Time = 1798.9703Conc = 5.5035

Gr_dens = 0.0010pH = 5.5001

0.9471 0.9471

4 01000 Time = 265.0295Conc = 6.9988Gr_dens = 0.0010

pH = 5.9999

0.9518 0.9518

5 0500 Time = 265.1145Conc = 6.9996Gr_dens = 0.0010pH = 5.9991

0.9518 0.9518

6 0200 Time = 199.5373Conc = 6.9991Gr_dens = 0.0010

pH = 5.9993

0.9536 0.9536

7 0150 Time = 149.9525Conc = 6.9978Gr_dens = 0.0010pH = 5.9998

0.9590 0.9590

8 0100 Time = 99.9194Conc = 5.5005

Gr_dens = 0.0010pH = 6.0000

0.9692 0.9692

9 050 Time = 49.9311Conc = 5.5045Gr_dens = 0.0010 pH = 5.9994

0.9845 0.9845

One can see that a minimum relativeabsorbance is associated with maximum time.Consequently, a compromise between the limitsituations presented in Fig. 5 supposes the values of relative absorbance of 0.950 0.955 with time around250 minutes.

0.94

0.945

0.95

0.955

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0 500 1000 1500 2000 2500

Time, min

R e l a

t i v e a

b s o r b a n c e

Fig. 7. Relative absorbance vs. time at optimum point

4. Conclusions

This paper provides a general and simpleoptimization methodology, based on genetic

algorithms and neural networks, applied to awastewater treatment by implying silica xerogelcompounds.

The genetic algorithm solves the optimizationproblem and the neural network constitutes the modelincluded in the optimization procedure. Simplearchitecture of the neural network is proposed forprocess modeling: a simple feed forward neuralnetwork with one hidden layer. The simple geneticalgorithm proves to be a good tool for solving theoptimization problem, providing importantinformation useful in experimental practice.

The method can be easily extended andadapted to other environmental oriented processes,with high chances of providing accurate results bysimple handling.

AcknoledgementsThis work was done by financial support provided byRomanian Ministry of Education and Research throughNational Program for Research, Development andInnovation II, project 71-006/2007.

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