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Journal of Manufacturing Systems 32 (2013) 197– 205

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Technical Paper

Normal-boundary intersection based parametric multi-objective optimization ofgreen sand mould system

T. Ganesana, P. Vasantb,∗, I. Elamvazuthic

a Chemical Engineering Department, University Technology Petronas, Malaysiab Fundamental & Applied Sciences Department, University Technology Petronas, Malaysiac Electrical & Electronic Engineering Department, University Technology Petronas, Malaysia

a r t i c l e i n f o

Article history:Received 27 April 2012Received in revised form 26 October 2012Accepted 30 October 2012Available online 20 November 2012

Keywords:Multi-objective (MO)Green sand mould systemNormal Boundary Intersection (NBI)Genetic algorithm (GA)Particle Swarm Optimization (PSO)Uniform spreadPareto frontier

a b s t r a c t

In manufacturing engineering optimization, it is often that one encounters scenarios that are multi-objective (where each of the objectives portray different aspects of the problem). Thus, it is crucial forthe engineer to have access to multiple solution choices before selecting of the best solution. In this work,a novel approach that merges meta-heuristic algorithms with the Normal Boundary Intersection (NBI)method is introduced. This method then is used generate optimal solution options to the green sandmould system problem. This NBI based method provides a near-uniform spread of the Pareto frontier inwhich multiple solutions with gradual trade-offs in the objectives are obtained. Some comparative studieswere then carried out with the algorithms developed and used in this work and that from some previouswork. Analysis on the performance as well as the quality of the solutions produced by the algorithms ispresented here.

© 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Most issues encountered when dealing with emerging tech-nologies in engineering are multi-objective (MO) in nature [1,2].Strategies in multi-objective optimization (MO) can be crudelyclassified into two classes. First being methods that use the con-cept of Pareto optimality to trace the non-dominated solutionsat the Pareto curve (for instance, Zitzler and Thiele’s [3] StrengthPareto Evolutionary Algorithm (SPEA) and Non-dominated Sor-ting Genetic Algorithm II (NSGA-II) by Deb et al. [4]). The othertype of methods is known as the weighted (or scalarization) tech-niques. In these methods, the objective functions in the problemare aggregated into a single objective function which is then solvedfor various scalar (weight) values. Some known scalarization tech-niques include the Weighted Sum method [5,6], Goal Programming[7] and Normal-Boundary Intersection (NBI) method [8]. Usingthese techniques, the scalars (or weights) are used to consign rela-tive trade-offs to the objectives during the aggregation procedure.Hence, alternative near-optimal solution options are generated forvarious values of the scalars.

A unique and ideal solution that explains all the features of a MOproblem in engineering are rarely encountered [9,10]. Nevertheless

∗ Corresponding author.E-mail address: [email protected] (P. Vasant).

in more practical scenarios, the decision maker (DM) is only inter-ested in a single optimal solution. To select this unique optimum,the DM utilizes some supplementary knowledge which is usuallyvery heuristic and too complex to be represented mathematically[11]. Therefore, it is very useful for the DM to have access to numer-ous solution options with a variety of significance with respect tothe objectives prior to the selection the best optimal solution. See[1,12,13] for more detail investigations and explanations on MOtechniques in engineering optimization.

In optimization problems of this kind, it is required that the solu-tion method caters for the multiobjective nature of the problem.Thus, in this work the MO issue is tackled using the NBI method forgeometrical trade-offs of the weights while the GA-PSO is used toiteratively improve the solutions for each respective weight. Thiswork aims to generate a series of Pareto-optimal solutions thatobtain a near-complete trade-off among the objective functions forthe green mould sand system. This problem was presented andsolved in Surekha et al. [14] by the application of genetic algo-rithm (GA) and Particle Swarm Optimization (PSO) techniques inconjunction with the Weighted Sum approach.

The difference between sand mould and green sand mould isthat green sand mould has green compression strength, permeabil-ity, hardness and bulk density requirements where as sand mouldhas the same properties without the green constraints. In greenmould systems, the quality of the product obtained from the mould-ing process is very dependent on the physical properties of the

0278-6125/$ – see front matter © 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.jmsy.2012.10.004


198 T. Ganesan et al. / Journal of Manufacturing Systems 32 (2013) 197– 205

moulding sand (such as hardness, permeability, green compressionstrength and bulk density). Incorrect proportions of the mentionedproperties may lead to casting defects such as poor surface finish,blowholes, scabs and pinhole porosity. Controllable variables suchas percentage of water, percentage of clay, grain fineness numberand number of strokes heavily influence the physical properties ofthe moulded sand. Hence, by characterizing these parameters as thedecision variables and the mould sand properties as the objectivefunction, the MO optimization problem was formulated in Surekhaet al. [14]. The purpose of this formulation is for the identifica-tion of best controllable parameters for optimal final-product ofthe moulding process. A more comprehensive study on the opti-mization and model formulation of mould systems can be seen in[15,16].

In this work, the green mould sand system is optimized furtherusing genetic algorithms (GA), Particle Swarm Optimization (PSO)and a hybrid GA-PSO in conjunction with the Normal BoundaryIntersection (NBI) method to generate a series of Pareto-optimalsolutions. Comparison studies were then performed on the optimalsolutions obtained in this work against those obtained in Surekhaet al. [14].

Genetic algorithms (GA) were introduced by Holland in thenineties [17]. GAs belong to the group of stochastic search meth-ods (such as simulated annealing [18] and some forms of branchand bound). While most stochastic search techniques operate on adistinct solution for a particular problem, GAs operates on a popu-lation of solutions. In recent times, GAs have been widely appliedin engineering scenario (see [19,20]). For a more comprehensivetext on GAs refer to [21]. Particle Swarm Optimization (PSO) is anoptimization method developed based on the movement and intel-ligence of swarms. PSO was developed by Kennedy and Eberhart[22] in 1995. Lately, PSO has been applied to a variety of areasincluding optimization problems in engineering [23] as well aseconomic dispatch problems. Many works have done on the appli-cation of meta-heuristic techniques for modelling and optimizationof manufacturing systems [24–26].

This paper is organized as follows. In Section 2 of this paper,the standard meta-heuristic techniques are presented, and this isfollowed by description on the Scalarisation Technique and Pro-posed Algorithms in Section 3. The real world application problemon green sand mould system is illustrated in Section 4. Section 5 dis-cusses computational results and finally, the concluding remarksare given in Section 6.

2. Standard meta-heuristic techniques

2.1. Genetic algorithm (GA)

A genetic algorithm (GA) was applied in conjunction to the NBIapproach for the MO optimization of the green sand mould system.GAs are categorized as a class of population-based search and opti-mization algorithms [27,28]. An N-point crossover operator wasused to create new offspring for each successive generation. Toavoid the solution from getting stagnant at the local minima, anN-bit flip mutation operator was used.

2.2. Particle Swarm Optimization (PSO)

The PSO algorithm introduced in 1995 (by Kennedy and Eberhart[22]) springs from two distinct frames of ideas. The first conceptwas based on the examination of swarming (or flocking) behavioursof certain species of organisms (such as birds, ants, bees and fire-flies). The second idea was sprung from the study of evolutionarycomputations. The PSO algorithm searches the search space forcandidate solutions and evaluates these solutions with respect to

some (user specified) fitness condition. The candidate optimal solu-tions obtained by this algorithm are achieved as a result of particleswhich are in motion (swarming) through the fitness landscape. Inthe beginning, some candidate solutions are selected by the PSOalgorithm. These solutions can be randomly selected or be estab-lished with the aid of some a priori facts. Next, the evaluation ofthe particles’ position and velocity (which are also the candidatesolutions) relative to the fitness function is carried out. Conse-quently, in conjunction with the fitness function a condition isintroduced; where if the fitness function is not fulfilled, then thealgorithm updates the individual and social terms by the aid of auser-specified update rule. Following this, the velocity and the posi-tion of the particles’ are updated. This recursive course of action isiterated until the fitness function is satisfied by all candidate solu-tions and solutions have thus converged into a fix position. It isessential to note that the velocity and position updating rule is crit-ical to the optimization capabilities of this method. The velocity ofeach particle in motion (swarming) is updated using the followingequation.

vi(t + 1) = wvi(t) + c1r1[x̂i(t) − xi(t)] + c2r2[g(t) − xi(t)] (1)

where each particle is identified by the index i, vi(t) is the particlevelocity and xi(t) is the particle position with respect to iteration(t). The parameters w, c1, c2, r1 and r2 are usually defined by theuser.

3. Scalarisation Technique and Proposed Algorithms

3.1. Scalarisation technique: Normal Boundary Intersection (NBI)method

The NBI method was first introduced by Das and Dennis [8].This method is a geometrically inspired scalarization approach forsolving MO problems. In contrast to the Weighted Sum method,the NBI approach has the ability to find a near-uniform spreadof Pareto-optimal solution options in the frontier. This makes theNBI approach a more interesting alternative as compared to theWeighted Sum method when solving non-convex MO problem.

The green mould system problem is presented as the following:

Min F(x) subject to

X = {x : g(x) = 0; h(x) ≤ 0, 1 ≤ x ≤ 4}F∗ = (f ∗

1 , f ∗2 , f ∗

3 , f ∗4 )T

(2)

where F* is the utopia point for this MO problem. Let the individualminimum be denoted as x∗

iand be obtained for i ∈ [1, 4]. The convex

hull of the individual minima is generated in this fashion. Thus, therepresentation of the simplex from the convex hull is as follows:

� = {� · Y : � = F(x∗i ); Y = ˇi : 1 ≤ x ≤ 4} (3)

where � forms a 4 by 4 matrix and∑4

i=1ˇi = 1. The formulation ofthe NBI �-sub problem is as the following:

Max(X,t)t subject to

� · Y + tn = F(x) and x ∈ X(4)

where t is some defined distance parameter, and n is the normalvector at the point towards the utopia point. The NBI scalarizationmethod finds the maximum distance, t in the direction of the nor-mal vector, n between a point on the simplex and the origin (orthe utopia point). Next, the scalarization is carried out. The scalars,Y are varied thoroughly to generate a near-uniform spread of thePareto frontier. The procedures of which this method is executedare as follows:


T. Ganesan et al. / Journal of Manufacturing Systems 32 (2013) 197– 205 199

Table 1Genetic algorithm (GA) settings.

Parameters Values

Length of individual string 6 bitNo. of individuals in the population 6Probability of mutation 0.3333Probability of recombination 0.5Initial string of individuals RandomBit type of individual’s string Real-codedCross-over type N-pointMutation type N-bit flipSelection type Tournament

• The MO maximization problem is reformulated as a minimizationproblem by inverting the objective functions.

• Obtain the local minima of individual objective functions.• The multi-objective (MO) problem is then reformulated as a

single-objective ˇ-sub problem by using the value of the localoptimums.

• The single-objective ˇ-sub problem is then solved.• The inverse transformation is then performed to re-obtain the

best maximal values of the objective functions.• The Pareto front for multiple scalarization values of ̌ is obtained.• The optimal value of the solutions is then selected from the

obtained Pareto front.

Thus, the single-objective ˇ-sub problem is solved using GA, PSOor the hybrid GA-PSO where these algorithms are termed as NBIPSO(NPSO), NBIGA (NGA) and NBI Hybrid GA-PSO (NHPSO).

Algorithm 1. Genetic algorithm (GA)

The GA scheme applied in this work is as the following. Theparameter settings initialized prior to the execution of the GA usedin this work are shown in Table 1. The flowchart of the GA algorithmis shown in Fig. 1.

Step 1: Initialize a random chromosome for n individuals in thepopulation.Step 2: Assign fitness conditions to each of the n individuals in thepopulation.

Step 3: By recombination from the current population, create off-spring for the next generation.Step 4: Mutate offspring for this generation.Step 5: The parent selection to create the next generation is doneby tournament selection.Step 6: The next population of n individuals is chosen.Step 7: Set new population to current population.Step 8: Assess the fitness of each offspring in the generation.Step 9: If the stopping criterion are satisfied halt program and printsolutions, else go to Step 3.

Algorithm 2. Particle Swarm Optimization (PSO)

These parameter settings for this algorithm are usually con-strained as the following:

0 ≤ w ≤ 1.2

0 ≤ c1 ≤ 2

0 ≤ c2 ≤ 2

0 ≤ r1 ≤ 1

0 ≤ r2 ≤ 1

(5)

The term wvi(t) in Eq. (1) (also referred to as the inertialterm) maintains the particle’s motion in the same direction asits original vector. The inertial coefficient w serves as a damp-ener or an accelerator during the movement of the particles’.The term c1r1[x̂i(t) − xi(t)] better known as the cognitive compo-nent functions serves as the memory. This component ensuresthat the particle tends to return to the position in the searchspace where the particle had a very high value of the fitnessfunction. The term c2r2[g(t) − xi(t)] (also known as the socialcomponent) function as mover of the particles to the positionwhere the swarm has visited in the previous iterations. Next,the particles’ position is then computed as is shown in thefollowing:

xi(t + 1) = xi(t) + vi(t + 1) (6)

Until all candidate solutions are at their highest fitness positionsand the termination criterion is satisfied, these iterations are then

Randomly initialize a populatio n of n

individuals.

Fitness criterions are assigned to each of the n individuals.

START

Offspring Mutation

Generate offspring by cross-

over/recombination

NO

STOP

Perform parent

selection

Set new population to current population

Evaluate offspring

fitness

Termination criterion satisfied?

YES

Fig. 1. Algorithm flow for GA.



sustained. The algorithm of the PSO method used in this work isshown as follows:

Step 1: Set number of particles, i and the initialize parameter sett-ings w, c1, c2, r1, r2, no

Step 2: Randomly initialize particles’ position xi(n) and velocityvi(n)Step 3: Calculate inertial and social components of the particlesStep 4: Compute position xi(n + 1) and velocity vi(n + 1) of the par-ticles at next iterationStep 5: If the swarm evolution time, n > no + T, update position xiand velocity vi and go to Step 3, else proceed to Step 6Step 6: Proceed with the evaluation of the fitness of each particlein the swarm.

Step 7: If the fitness conditions are satisfied, stop program andprint solutions, else go to Step 3.

where no is some constant, n is the swarm iteration and T is the over-all program iteration. However, in the event during this iterativeprocess the position of all the particles converges, the solutions arefeasible with respect to the specified ranges, no further optimiza-tion of the objective function occurs and all the decision variablesare non-negative (for the problem at hand) then it can be said thatthe fitness criterion are met. Hence the candidate solutions areat their fittest and the program is stopped and the solutions areprinted. The initialization parameters for this algorithm is shownin Table 2 and the workflow is provided in Fig. 2.

START

Initialize no of particles, i

YESEvaluate fitness of the

swarms

NO

T = T +1

NO

Is fitness criterion satisfied?

STOP

YES

Compute inertial and social influence

Randomly in itializeposition xi(n) and

velocity vi(n)

n = n +1

Is n > no+T ?

Compute position xi(n+1)and velocity vi(n+1) at

next iteration

Initialize algorithm

parameters

Fig. 2. Algorithm flow for PSO.



Table 2Particle Swarm Optimization (PSO) settings.

Parameters Values

Initial parameter (c1, c2, r1, r2, w) (1, 1.2, 0.5, 0.5, 0.8)Number of particles 6Initial social influence (s1, s2, s3, s4, s5, s6) (1.1, 1.05, 1.033,

1.025, 1.02, 1.017)Initial personal influence (p1, p2, p3, p4, p5, p6) (3, 4, 5, 6, 7, 8)

Algorithm 3. Hybrid GA-PSO

The hybrid GA-PSO in this work was developed by using bothtechniques at different sections of the NBI approach. As mentionedin the introduction section, meta-heuristic techniques (such as GAand PSO) can be incorporated into the NBI approach at two seg-ments. First being the use of these techniques as a tool to search forthe local minima of the individual objective functions. Secondly,using these techniques for solving the ˇ-sub problem by varyingthe weights. In contrast to the pure GA and PSO approach (whereboth segments in the NBI approach are embedded with the PSOor GA technique), the hybrid approach uses GA to find the localminima and PSO for solving the ˇ-sub problem. The parameter sett-ings in the hybrid method are identical to the settings employed inthe pure methods. The hybridization procedure in Fig. 3 shows themechanism of placement of the GA and PSO algorithms in the NBIsections.

The algorithm for the hybrid GA-PSO approach is as the follow-ing:

Step 1: Initialize a random chromosome for n individuals in thepopulation.Step 2: Assign fitness conditions to each of the n individuals in thepopulation.Step 3: By recombination from the current population, create off-spring for the next generation.Step 4: Mutate offspring for this generation.Step 5: The parent selection to create the next generation is doneby tournament selection.Step 6: The next population of n individuals is chosen.Step 7: Set new population = current population.Step 8: Assess the fitness of each offspring in the generation.Step 9: If the stopping criterion are satisfied halt program and printsolutions, else go to Step 3.Step 10: Set no of particles, i and the initialize parameter settingsw, c1, c2, r1, r2, no

Step 11: Randomly initialize particles’ position xi(n) and velocityvi(n)Step 12: Calculate inertial and social components of the particlesStep 13: Compute position xi(n + 1) and velocity vi(n + 1) at nextiteration

Fig. 3. Flow of the pure and hybrid GA and PSO techniques in the NBI method.

Step 14: If the swarm evolution time, n > no + T, update position xiand velocity vi and go to Step 12, else proceed to Step 6Step 15: Evaluate fitness swarm based on the objective functionof the ˇ-sub problem for each scalarization.Step 16: If fitness criterion satisfied, halt and print solutions, elsego to Step 12.

4. Application data

The responses of the mould heavily influence the quality of thefinal product of the green sand mould system. In Surekha et al. [14],these responses are represented mathematically as the objectivefunctions. The responses are; green compression strength (f1), per-meability (f2), hardness (f3) and bulk density (f4). These objectiveson the other hand are influenced by on the process (or decision)variables which are; the grain fineness number (A), percentage ofclay content (B), percentage of water content (C) and number ofstrokes (D). The objective functions and the range of the decisionvariables are shown as follows:

f1 = 17.2527 − 1.7384A − 2.7463B + 32.3203C + 6.575D

+ 0.014A2 + 0.0945B2 − 7.7857C2 − 1.2079D2 + 0.0468AB

− 0.1215AC − 0.0451AD + 0.5516BC + 0.6378BD + 2.689CD)

(7)

f2 = 1192.51 − 15.98A − 35.66B + 9.51C − 105.66D + 0.07A2

+ 0.45B2 − 4.13C2 + 4.22D2 + 0.11AB + 0.2AC + 0.52AD

+ 1.19BC + 1.99BD − 3.1CD (8)

f3 = 38.2843 − 0.0494A + 2.4746B + 7.8434C + 7.774D

+ 0.001A2 − 0.00389B2 − 1.6988C2 − 0.6556D2 − 0.0015AB

− 0.0151AC − 0.0006AD − 0.075BC − 0.1938BD + 0.65CD

(9)

f4 = 1.02616 + 0.01316A − 0.00052B − 0.06845C + 0.0083D

− 0.00008A2 + 0.0009B2 + 0.0239C2 − 0.00107D2

− 0.00004AB − 0.00018AC + 0.00029AD − 0.00302BC

− 0.00019BD − 0.00186CD (10)

52 ≤ A ≤ 94

8 ≤ B ≤ 12

1.5 ≤ C ≤ 3

3 ≤ D ≤ 5

(11)

To obtain the size distributions of the silica sand and thegrain fineness number, sieve analysis tests were carried out inParappagoudar et al. [29]. Similarly, the authors also conductedgelling index tests for the determination the strength of clay. Next,experiments were conducted by varying the combination of theparameters using the central composite design. The mathematicalmodel of the green mould system was developed where; the objec-tive functions as given in Eqs. (7)–(10) and the constraints as given



Table 3The comparison of the best solutions obtained by the algorithms.

Description Algorithms

GA [14] PSO [14] NGA NPSO NHPSO

Objective functionf1 54.9377 55.4112 61.5992 61.3174 58.2195f2 53.679 107.895 60.2611 120.022 135.478f3 89.4473 84.7936 89.0263 88.8441 88.3809f4 1.5888 1.5079 1.58366 1.51525 1.50958

Decision variableA 93.9998 52.0001 73.3421 54.5778 52.7462B 11.9999 11.9998 11.9024 11.574 11.9231C 2.6546 2.8452 2.05415 2.54539 2.1876D 4.9998 4.9999 4.00906 4.18636 3.80256

in Eq. (11). The MO optimization problem statement for the greenmould system problem is shown as follows:

Max(f1, f2, f3, f4) subject to

52 ≤ A ≤ 94

8 ≤ B ≤ 12

1.5 ≤ C ≤ 3

3 ≤ D ≤ 5

(12)

The algorithms used in this work were programmed using theC++ programming language on a personal computer (PC) with anIntel dual core processor running at 2 GHz.

5. Results and discussion

The comparison of the best candidate solutions obtained by theNBI-Genetic Algorithm (NGA), NBI-Particle Swarm Optimization(NPSO) and the NBI-hybrid GA and PSO (HNPSO) methods in thiswork and by the PSO and GA methods (Weighted-Sum) in Surekhaet al. [14] is shown in Table 3. The Pareto frontiers of the objectivesobtained by the NGA method are presented in Fig. 4.

The best solution candidate in Table 3 was obtained bythe NGA method at the weights (objective function trade-offs)

(ˇ1, ˇ2, ˇ3ˇ4) = (0.4, 0.1, 0.4, 0.1). The best solution candidateobtained by the NPSO method at the weights (objective functiontrade-offs) (ˇ1, ˇ2, ˇ3ˇ4) = (0.1, 0.4, 0.2, 0.3). In Table 3 the solu-tion was obtained by the NPSO method at the weights (objectivefunction trade-offs) (ˇ1, ˇ2, ˇ3ˇ4) = (0.1, 0.1, 0.5, 0.3). The Paretofrontiers of the objectives obtained by the NGA, NPSO and NHPSOmethods are presented in Figs. 4–6, respectively.

It can be observed in Table 3 that the NGA and NPSO meth-ods outperform the GA and PSO method from Surekha et al. [14].However, a new optima is achieved by the NPSO method (seeTable 3) since it outperforms the NGA method. The NHPSO methodcompromises on the objectives f1, f3 and f4 while maximizing theobjective f2 very effectively. Thus, it can be said that the NPSOmethod in this work outweighs the overall optimization capabil-ities of NHPSO and NGA. The computational time taken for thealgorithms in the previous work (see Surekha et al. [14]) for the GAand PSO are, respectively, 0.021 and 0.013 s. In this work, the com-putational time taken for the NGA, NSPO and the NHPSO algorithmsare 282.404, 21.683 and 31.48 s respectively.

In Surekha et al. [14], the GA and the PSO method was used inconjunction with the Weighted Sum method on an Intel PentiumIV processor (single core). As mentioned previously, the algorithmspresented in this work: NGA, NPSO, and NHPSO were executedon an Intel dual-core processor which is more superior than themachine used in Surekha et al. [14]. However, it can be seen that thecomputational time for NGA, NPSO and NHPSO algorithms are fargreater as compared to the GA and PSO in [14]. Although the algo-rithms NGA, NPSO and NHPSO are executed on a superior machine,these algorithms seem to be computationally inferior as comparedto the GA and PSO [14] algorithms. This can be mainly attributedto the complexity of the NBI scheme which is incorporated into thealgorithms presented in this work. The NBI scheme (see Method-ology – Section A) requires the application of the algorithms twice,first to obtain the individual optima then to solve the ˇ-sub prob-lems for each of the scalarization. Thus, although the NGA, NPSOand NHPSO may produce excellent results, it does compromise interms of computational due to the complexity of the algorithm. It isalso observed similar to the results in Surekha et al. [14], the NPSOperforms better and computationally more efficient as compared

Fig. 4. Pareto frontiers of the objectives obtained by the NGA method.



Fig. 5. Pareto frontiers of the objectives obtained by the NPSO method.

to the NGA algorithm. Due to the incorporation of the GA segmentin the NHPSO, thus it is computationally more expensive than theNPSO but more efficient than the NGA.

In Surekha et al. [14], the Weighted Sum method producesa progression of Pareto efficient solutions although the spreadof solutions are not well distributed. In this work, using the NBImethod, the spread of Pareto efficient solutions are near-uniformlyspaced. The spread of the Pareto efficient solutions are vital inMO scenarios. This is because a uniform solution spread gives amore gradual change in the relative significance of the objectives

in the alternative solutions. However, both methods (NBI andWeighted Sum) do not guarantee Pareto optimality (only in theweak sense [30]). The NGA, NPSO and NHPSO algorithms per-formed stable computations during the search of the individualminima as and while solving the ˇ-sub problems. The stoppingcriteria used in the algorithms used in this work was the max-imum number of function evaluations (which was pre-definedto 50). All Pareto-efficient solutions produced by the algorithmsdeveloped in this work were feasible and no constraints werecompromised.

Fig. 6. Pareto frontiers of the objectives obtained by the NHPSO method.



The advantages of using the NPSO algorithm as compared to theother algorithms used in this work is that it produces highly effec-tive results in terms of optimization of the parameters. Besides,among the algorithms used in this work it can be said that the NPSOhas the lowest execution time. However, although the NPSO per-forms well relative to algorithms used in this work, it can be clearlyseen that the execution time is much higher than the one obtainedby Surekha et al. [14] using the Weighted-Sum method.

The NGA method can be said to be the second best optimizeras compared to the NPSO method. Since the NGA method uses anevolutionary background the diversification of the search space ishigh and thus resulting in high computational time as comparedwith the NPSO and NHPSO. Besides, in comparison with the NHPSOalgorithm the NGA method produces much superior results.

As for the NHPSO, this hybrid is high in terms of algorithmiccomplexity and due to the GA component is performs inferior toNPSO method in terms of computational time. However, the effec-tiveness of the overall optimization of all the objectives is not assatisfactory as the NGA or the NPSO method. This method optimizesthe second objective to a very high degree while compromising onthe other objectives. Thus, it also performs poorly in terms of theoverall optimization as compared with the NGA and NPSO methods.

6. Conclusions

In this work, a new local maximum was achieved using the NPSOmethod. More Pareto-efficient solution options to the green mouldsystem MO optimization problem were obtained. Besides, usingthe NGA, NPSO and NHPSO algorithms, the solution spread of thefrontier was near-uniformly distributed. This work also producesresults of testing the green mould sand problem with a hybridalgorithm. In the future, other meta-heuristic algorithms such asGenetic Programming (GP) [31], Analytical Programming (AP) [32],Hybrid Neuro-GP [33], Hybrid Neuro-PSO [34], Hybrid Tabu [35],MO evolutionary algorithm [36,37] and Artificial Immune Systems(AIS) [38,39] should be applied in conjunction with the NBI method.During these numerical experiments, the spacing metric should bemeasured and compared for the observation the uniformity of thespreads with respect to the algorithms. Besides, convergence anddiversity metrics should also be utilized to compare the perfor-mance of the algorithms. More large-scale MO problems shouldbe studied using the NGA, NPSO and NHPSO method for a bet-ter understanding of the mentioned algorithm’s performance andefficiency.

Acknowledgements

This work was supported by STIRF Grant (STIRF CODE NO:90/10.11) of University Technology Petronas (UTP), Malaysia. Theauthors sincerely thank the anonymous reviewers for their valuableand constructive comments and suggestions for the improvementof this research paper.

References

[1] Eschenauer H, Koski J, Osyczka A. Multicriteria design optimization. Berlin:Springer-Verlag; 1990.

[2] Statnikov RB, Matusov JB. Multicriteria optimization and engineering. NewYork: Chapman and Hall; 1995.

[3] Zitzler E, Thiele L. Multiobjective optimization using evolutionaryalgorithms—a comparative case study. In: Eiben AE, Bäck T, SchoenauerM, Schwefel H-P, editors. Parallel problem solving from nature, V. Berlin,Germany: Springer; 1998. p. 292–301.

[4] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multi-objectivegenetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation2002;6(2):182–97.

[5] Fishburn PC. Additive utilities with incomplete product set: applications topriorities and assignments. Baltimore, MD, USA: Operations Research Societyof America (ORSA); 1967.

[6] Triantaphyllou E. Multi-criteria decision making: a comparative study. Dor-drecht, The Netherlands: Kluwer Academic Publishers (now Springer); 2000.p. 320.

[7] Luyben ML, Floudas CA. Analyzing the interaction of design and control. I.A multiobjective framework and application to binary distillation synthesis.Computational Chemical Engineering 1994;18(10):18–933.

[8] Das I, Dennis JE. Normal-boundary intersection: a new method for generat-ing the Pareto surface in nonlinear multicriteria optimization problems. SIAMJournal of Optimization 1998;8(3):631–57.

[9] Van Sickel JH, Venkatesh P, Lee KY. Analysis of the Pareto front of a multi-objective optimization problem for a fossil fuel power plant. In: IEEE PESgeneral meeting. 2008.

[10] Kim IY, de Weck OL. Adaptive weight-sum method for biobjective optimization:Pareto front generation. In: AIAA structures, structural, dynamics, and materialsconference. 2002.

[11] Sendín JOH, Alonso AA, Banga JR. Efficient and robust multi-objective opti-mization of food processing: a novel approach with application to thermalsterilization. Journal of Food Engineering 2010;98:317–24.

[12] Sandgren E. Multicriteria design optimization by goal programming. In: AdeliH, editor. Advances in design optimization. London: Chapman & Hall; 1994. p.225–65 [Chapter 23].

[13] Stanikov RB, Matusov JB. Multicriteria optimization and engineering. NewYork: Chapman and Hall; 1995.

[14] Surekha B, Kaushik LK, Panduy AK, Vundavilli PR, Parappagoudar MB.Multi-objective optimization of green sand mould system using evolution-ary algorithms. International Journal of Advance Manufacturing Technology2011;58(1–4):1–9.

[15] Kumar S, Satsangi PS, Prajapati DR. Optimization of green sand cast-ing process parameters of a foundry by using Taguchi method. Inter-national Journal of Advance Manufacturing Technology 2010;55(1–4):23–34.

[16] Rosenberg RS. Simulation of genetic populations with biochemical properties.Ph.D. thesis, University of Michigan; 1967.

[17] Holland JH. Adaptation in natural and artificial systems: an introductory analy-sis with applications to biology. In: Control and artificial intelligence. USA: MITPress; 1992.

[18] Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by simulated annealing. Sci-ence 1983;220:671–80.

[19] Li CL. A feature-based approach to injection mould cooling system design.Computer-Aided Design 2001;33(14):1073–90.

[20] Li CL. Automatic synthesis of cooling system design for plastic injection mould.In: ASME 2001 design engineering technical conferences and computers andinformation in engineering conference, 27th design automation conference.2001.

[21] Gen M, Cheng R. Genetic algorithms and engineering optimization. John Wiley& Sons; 1997, 432 pp.

[22] Kennedy J, Eberhart R. Particle swarm optimization. In: IEEE proceedings of theinternational conference on neural networks. 1995. p. 1942–8.

[23] Phuangpornpitak N, Prommee W, Tia S, Phuangpornpitak W. A study of par-ticle swarm technique for renewable energy power systems. In: PEA-AITinternational conference on energy and sustainable development: issues andstrategies, Thailand. 2010. p. 1–7.

[24] Chryssolouris G, Lee M, Domroese M. The use of neural networks in determin-ing operational policies for manufacturing systems. Journal of ManufacturingSystems 1991;10(2):166–75.

[25] Williams NR. Neural networks vs. regression in localized scan correc-tion for robotic drilling applications. Journal of Manufacturing Systems2005;24(1):21–34.

[26] El Maraghy H, Patel V, Abdallah IB. Scheduling of manufacturing systems underdual-resource constraints using genetic algorithms. Journal of ManufacturingSystems 1991;10(2):166–75.

[27] Lee TS, Ting TO, Lin YJ. An investigation of grinding process optimization viaevolutionary algorithms. In: Proceedings of the 2007 IEEE swarm intelligencesymposium. 2007.

[28] Sardinas RQ, Santana MR, Brindis EA. Genetic algorithm based multi-objectiveoptimization of cutting parameters in turning process. Engineering AppliedArtificial Intelligence 2006;19:127–33.

[29] Parappagoudar MB, Pratihar DK, Datta GL. Non-linear modeling using centralcomposite design to predict green sand mould properties. Proceedings IMechEB: Journal of Engineering Manufacture 2007;221:881–94.

[30] Shukla PK. On the normal boundary intersection method for generation of effi-cient front. In: Shi Y, et al., editors. ICCS 2007, Part I. LNCS, vol. 4487. BerlinHeidelberg: Springer-Verlag; 2007. p. 310–7.

[31] Koza JR. Genetic programming: on the programming of computers by meansof natural selection. USA: MIT Press; 1992.

[32] Zelinka I. Analytic programming by means of soma algorithm. Mendel’02.In: Proc 8th international conference on soft computing Mendel’02. 2002. p.93–101. ISBN 80-214-2135-5.

[33] Ganesan T, Vasant P, Elamvazuthi I. Optimization of nonlinear geologicalstructure mapping using hybrid neuro-genetic techniques. Mathematical andComputer Modelling 2011;54(11):2913–22.

[34] Ganesan T, Vasant P, Elamvazuthi I. Hybrid neuro-swarm optimizationapproach for design of distributed generation power systems. Neural Com-puting and Applications 2012, http://dx.doi.org/10.1007/s00521-012-0976-4.

[35] Vasant P, Ganesan T, Elamvazuthi I. Hybrid Tabu search hopfield recurrent ANNfuzzy technique to the production planning problems: a case study of crude



oil in refinery industry. International Journal of Manufacturing, Materials, andMechanical Engineering 2012;2(1):47–65.

[36] Qu BY, Suganthan PN. Multi-objective evolutionary algorithms based on thesummation of normalized objectives and diversified selection. InformationSciences 2010;180:3170–81.

[37] Li K, Kwong S, Cao J, Li M, Zheng J, Shen R. Achieving balance between proximityand diversity in multi-objective evolutionary algorithm. Information Sciences2011;182:220–42.

[38] De Castro LN, Timmis J. Artificial immune systems: a new computational intel-ligence approach. Springer; 2002, 380 pp.

[39] Yang D, Jiao L, Gong M, Liu F. Artificial immune multi-objective SAR imagesegmentation with fused complementary features. Information Sciences2011;181:2797–812.

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