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 DOI: 10.1177/0954405414523593

March 2014 published online 20Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture

Abolfazl Golshan, Danial Ghodsiyeh and Sudin Izmancomputation method: Effect of cutting variation

Multi-objective optimization of wire electrical discharge machining process using evolutionary  

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Original Article

Proc IMechE Part B:J Engineering Manufacture1–11� IMechE 2014Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0954405414523593pib.sagepub.com

Multi-objective optimization of wireelectrical discharge machining processusing evolutionary computationmethod: Effect of cutting variation

Abolfazl Golshan1, Danial Ghodsiyeh2 and Sudin Izman3

AbstractThis article focuses on comparing the performance of brass wire and zinc-coated brass wire that are widely used as thewire electrode in wire electrical discharge machining. To this end, an evolutionary computation method is presentedbased on non-dominated sorting genetic algorithm in order to find an optimization of rough cutting of the Ti-6Al-4V tita-nium alloy with the aid of response surface methodology modeling. This research examines the effects of three processparameters, namely, pulse on-time, pulse off-time, and peak current on the process outputs, that is, material removalrate, sparking gap, and white layer thickness. The obtained results indicated that zinc-coated wire was more predictableand it showed more reliable response in the experimental and modeling results. Additionally, the optimization results forboth wires demonstrated the high performance of non-dominated sorting genetic algorithm approach to obtain thePareto optimal set of solutions.

KeywordsWire electrical discharge machining, brass wire, zinc-coated brass wire, response surface methodology, non-dominatedsorting genetic algorithm

Date received: 2 June 2013; accepted: 13 January 2014

Introduction

Wire electrical discharge machining (WEDM) is athermo-electrical process in which material is eroded bya series of sparks between the workpiece and the wireelectrode (tool).1 In this process, there is no contactbetween the workpiece and electrode; therefore, materi-als of any hardness can be cut as long as they can con-duct electricity.2 The movement of wire is controllednumerically to achieve the desired three-dimensionalshape and accuracy of the workpiece. That can makeWEDM one of the best choices for precision machiningas well as for machining supper hard materials andcomplex shapes.3

Since the early 1970s, brass has become the mostcommonly used electrode material for WEDM. It wasdue to two properties: good dimensional accuracy andhigh electrical conductivity.4 Brass electrical dischargemachining (EDM) wire is a combination of copper andzinc, typically alloyed in the range of 63–65% Cu and35–37% Zn. The addition of zinc provides significantlyhigher tensile strength, a lower melting point and higher

vapor pressure rating. Since brass wires cannot be effi-ciently fabricated with any higher concentration of zinc,the logical next step was the development of coatedwires, sometimes called plated or ‘‘stratified’’ wire.They typically have a core of brass or copper, for con-ductivity and tensile strength, and are electroplatedwith a coating of pure or diffused zinc for enhancedspark formation and flush characteristics but coatedwires are costly almost twice of brass.5 As a result, uti-lizing brass wire is more economically acceptable unlessthe advantages of coated wire are really irresistible.

1Department of Mechanical Engineering, Faculty of Engineering, Universiti

Putra Malaysia, Serdang, Malaysia2Department of Mechanics and Aerospace, Politecnico di Torino, Torino,

Italy3Department of Materials, Manufacturing & Industrial Engineering, Faculty

of Mechanical Engineering, Universiti Teknologi Malaysia, Skudai, Malaysia

Corresponding author:

Danial Ghodsiyeh, Department of Mechanics and Aerospace, Politecnico

di Torino, 10129 Torino, Italy.

Email: danial.ghodsiyeh@gmail.com

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Among different factors that play an important role inimprovement of the overall performance of WEDM,the evolution of materials for the wire that is employedin WEDM is the most important one. In addition, thecost of the wire is only about 10% of the total operatingcost of the WEDM process; therefore, it can be consid-ered as completely cost-effective to evaluate the proper-ties of the wire used for optimization of the overallperformance of the process. The literature contains justa few studies that have been focused on comparing thewires in different aspects.4,6–8 As a result, there is a needfor specifically evaluating and comparing the character-istics of the wires performance in the WEDM process.

Antar et al.6 presented the study on workpiece pro-ductivity and integrity when WEDMing nickel-basedsuperalloy and titanium alloy, and it was found that anincrease in productivity of about 40% for nickel-basedsuperalloy and about 70% for titanium alloy was possi-ble when replacing standard uncoated brass wire withusing Cu core coated wires diffusion annealed underthe same operating parameters. In terms of recast layerthickness, better results were achieved using the coatedwire for both roughing and trim operation haveobtained. Actually with machining with coated wire,about 25% thinner recast for nickel-based superalloyand about 40% thinner for titanium alloy have pro-duced. Poros and Zaborski7 found that increase of dis-charge time can affect cutting speed and materialremoval rate (MRR) significantly by 62% for brasswire electrode and 138% for zinc-coated brass wire.Therefore, according to different researches, the cuttingspeed of the zinc-coated wire is almost twice of thebrass wire because the exterior zinc coating of the elec-trode has a lower melting temperature than the corematerial (brass). Hence, the zinc is overheated and eva-porated in the presence of a pulse. The evaporation actsas a heat sink, which helps to reduce the wire tempera-ture and improve the effectiveness of the WEDM pro-cess. Consequently, the cutting speed can increase upto 50% for zinc-coated brass wires.4

The most important performance measures inWEDM are MRR, workpiece surface quality, and kerfwidth (cutting width). The kerf width can be used todetermine the dimensional accuracy of the finishedpart; additionally, it puts a limitation on the internalcorner radius to be produced in WEDM operations.9 InWEDM operations, using MRR, the rate of productionand the economics of machining can be determined.When the machining parameters are being set, the desir-able condition is the minimum kerf width with the max-imum MRR. In addition, a technological challenge inWEDM is controlling the surface quality. In WEDM—at the machined surface of the workpiece—a multi-layered heat-affected zone is created whose upper recastlayer is known as the ‘‘white layer,’’ which crystallizesfrom the un-expelled molten metal at high speed. Thislayer is directly in contact with the environment, andthe micro cracks (if any) are typically restricted only tothis layer. It is undesirable to have a white layer on the

surface of the workpiece that is machined by WEDM;it is because this layer makes the surface completely sus-ceptible to fatigue failure. Several studies have been car-ried out to find thoroughly the properties and theformation mechanism of the white layer; although littleresearch10 has been focused on modeling the process asa problem of correlating the dominant input parametersof the WEDM process with the white layer depth as themachining performance or criterion. As a result, thisarticle attempts to develop a mathematical model ofwhite layer depth, kerf width, and MRR and analyzeextensively the impacts of the dominant input processparameters on the same responses in the process ofWEDM.

Evidently, in the context of WEDM, it is extremelydifficult even for a skilled operator to achieve an opti-mal performance criterion. This is due to existence ofmany variables in the WEDM process and its multifa-ceted and stochastic nature.11 The problem will be evenmore complicated in the case of multi-objective optimi-zation, that is, more than one objective must be opti-mized simultaneously. Multi-objective optimizationproblems can be solved using evolutionary computa-tional algorithms such as genetic algorithms (GAs) andparticle swarm optimization.12 According to the litera-ture,13,14 several studies have been conducted to find anoptimized condition for the machining parametersusing evolutionary computational algorithms such asGAs and particle swarm optimization (PSO).

One of the most widely employed algorithms formulti-objective optimization is non-dominating sortinggenetic algorithm-II (NSGA-II). Many researchershave employed NSGA-II to optimize machining para-meters in WEDM process.15–19 Kondayya and GopalaKrishna15 discussed a simultaneous optimization of theMRR and the surface roughness using the NSGA-II.Debabrata et al.16 carried out the multi-objective opti-mization of WEDM to maximize the MRR and mini-mize tool wear using NSGA-II. Prasad and GopalaKrishna17 developed a response surface model to corre-late EDM process parameters with MRR and surfaceroughness. And finally, non-dominated solutions wereobtained by response surface model–based NSGA-IItechnique. Baraskar et al.18 adopted NSGA-II to opti-mize machining parameters in EDM considering sur-face roughness and MRR as the output parameters.Moreover, there are some methods, which successfullymodeled WEDM-like feed-forward back-propagationneural network (BPNN)20 and normalized radial basisfunction network (NRBFN) with enhanced and tradi-tional k-means clustering techniques.21 Saha et al.19

proposed a multi-objective optimization using a neuro-genetic technique to optimize the cutting speed and kerfwidth in WEDM processing of TiC-reinforced compo-site. The technique was developed through hybridiza-tion of a radial basis function network (RBFN) andnon-dominated sorting genetic algorithm (NSGA-II).

However, to the best of our knowledge, in the litera-ture, there is not any research attempting to optimize

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machining parameters in WEDM of Ti-6Al-4V withrespect to the MRR, kerf width, and white layer thick-ness (WLT) objectives. Therefore, this article aims toobtain the optimum machining conditions for WEDMof Ti-6Al-4V for maximum MRR and minimum kerfwidth and WLT based on NSGA-II approach for bothwires. Experiments, based on central composite design(CCD), were carried out to study the effect of variousparameters, namely, pulse-on time, pulse-off time, andpeak current on response parameters for both wires.Using response surface methodology (RSM), mathe-matical models for the objectives are obtained from theexperimental data. Finally, a NSGA-II is used to obtainthe Pareto optimal set of solutions for both wires.

Experimental work

In this research, a series of experiments on titaniumalloy Ti-6AL-4V with the nominal chemical composi-tion of 6.3 Al, 4.1 V, 0.18 Fe, 0.182 O, and 0.03 Si inmass percent and balance titanium were conductedusing a Sodick series AQ 537L CNC WEDM machine.The yield strength of Ti-6Al-4V is 840 MPa, its ulti-mate tensile strength is 910 MPa, and its hardness is 45HRC. A brass wire and a zinc-coated brass wire wereused as tools and compared to each other. Some char-acteristics of brass wire and zinc-coated brass wire arepresented in Table 1. Servo voltage, wire speed, wiretension, and flushing pressure were kept as 40 V, 15 m/min, 600 g, and 55 bar, respectively. The machiningvoltage was set as 120 V. Deionized water was used asdielectric fluid. Figure 1 presents the basic features ofthe WEDM setup. Furthermore, the kerf width and thesparking gap (SG) were investigated using the setup, asshown in Figure 1.

The input parameters and their initial settings areselected based on the existing literature and some initialinvestigations. Three significant factors in the roughmachining process are considered in this study: thepulse on-time, the pulse off-time, and the peak current.The low, middle, and high levels of these three para-meters are presented in Table 2.

Design Expert 7.0.0 software was employed for thestatistical design of the experiments and the data analy-sis. The WEDM process was investigated using thestandard RSM design known as CCD. Generally, foreach factor, the central point is assumed 0, and thedesign is considered symmetric around this point. The

star points are located at the face of the cube portionon the design that corresponds to an a-value of 1. Thisis usually referred to as a face centered, CCD. In thecases in which there are three variables (n = 3), pointson a cube represent the CCD. The points (runs) areincluding 2n (2 3 3 = 6) star points, 2n (23 = 8) fac-torial points, and 3 center points (three replications).Table 3 presents the experimental plan and results withthree factors and three levels.

In each experimental run, the MRR, SG, and WLTwere measured. In each trial, a 10 mm length of cuttingwas made on 10 mm thickness of the workpieces. Thefollowing equation has been used to compute the MRRvalue

MRR (mm3=s)=Wi �Wj

T3pð1Þ

where Wi and Wj signify weights of workpiece materialbefore and after machining (g), respectively. T denotesmachining time (s) and p represents the density of Ti-6Al-4V (0.00442 g/mm3). A precise balance Mettler(92SM-202A DR) with high accuracy of 1023 g wasused to measure the weight of the workpiece required.The kerf width was measured using a Mitutoyo ProfileProjector PJ-3000 to compute the SG, and the follow-ing equation is used to determine the SG value

SG (mm)=average of kerf width� diameter ofwire

2

ð2Þ

Table 1. General characteristics of brass wire and zinc-coatedbrass wire.

Characteristics Brass Zinc-coated brass

Wire diameter 0.25 0.25Type symbol P (hard) ZWire diameter tolerance (mm) 60.001 60.001Minimum tensile strength (MPa) 980 883Minimum fracture load (N) 48.2 43.3Minimum conductivity (%) 22 20

Figure 1. Basic features of WEDM setup.

Table 2. Rough cutting parameters and their levels.

Parameters Symbol Levels

Low(21)

Center(0)

High(1)

Pulse on-time (ms) Ton 8 9 10Pulse off-time (ms) Toff 6.5 7.5 8.5Peak current (A) Ip 32 36 40

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A field emission scanning electron microscope(FESEM) (Philips XL40) was used to analyze and mea-sure the thickness of the altered surface (recast layer).Samples were thoroughly cleaned with acetone andthen mounted exposing an area of approximately 2 3

25 mm with resin and hardener in a mold. The mountedspecimens were then ground and polished. Polishing isperformed to have mirror finish on the transverse sec-tion, and subsequently, these faces are etched withKroll’s reagent (2% hydrofluoric acid + 10% nitricacid + 88% water) for 10–15 s. Henceforth, thesesamples were seen with the help of a field emissionscanning electron microscope. The white layers fromthe photographs are easily identified. The depths ofwhite layers were measured carefully from the micro-graph, and averages of readings were taken for eachexperimental run.

Experimental results

In these experiments, it was observed that due to lowthermal conductivity in titanium alloy material, highflushing pressure is absolutely necessary for roughmachining; otherwise, the short-circuit phenomenonwill cause to wire breakage. Figure 2 shows the cuttingline while machining titanium alloy Ti-6Al-4V in nor-mal flushing pressure. This figure shows that in theabsence of high flashing pressure, cutting line cannotcontinue more than 1 mm.

Figure 3 presents the interval plot of each responsefrom brass wire to zinc-coated brass wire based on theexperimental results (Table 3) using Minitab 16 soft-ware. Figure 3 demonstrates that the mean MRRsusing brass wire and zinc-coated brass wire were 0.29

and 0.38 mm3/s, respectively. Thus, the percentageincrease of the mean MRR from brass wire to zinc-coated brass wire was +31.03. Likewise, the percent-age increase of the SG and WLT from brass wire tozinc-coated brass wire were 224.49 and 217.13, respec-tively. The MRR of the zinc-coated wire is more thanthat of the brass wire because the exterior zinc coat-ing of the electrode has a lower melting temperaturethan the core material (brass). Therefore, the zinc isoverheated and evaporated in the presence of a pulse.The evaporation acts as a heat sink; it reduces thewire temperature and improves the effectiveness ofthe WEDM process. Consequently, the cutting speedincreases by up to 50% as more intense thermal flowsare enabled.4

Table 3. Experimental plan and results.

Std. Type of points in CCD design Rough machining parameters Response factors

MRR (mm3/s) SG (mm) WLT (mm)

Ton (ms) Toff (ms) IP (A) BW ZCBW BW ZCBW BW ZCBW

1 Factorial point 8 6.5 32 0.2451 0.3382 0.044 0.030 6.138 5.1882 Factorial point 10 6.5 32 0.2863 0.3934 0.050 0.040 7.015 6.3843 Factorial point 8 8.5 32 0.2386 0.3167 0.040 0.028 5.835 4.7554 Factorial point 10 8.5 32 0.2651 0.3606 0.045 0.038 6.925 6.1475 Factorial point 8 6.5 40 0.2927 0.4010 0.051 0.042 8.473 6.7146 Factorial point 10 6.5 40 0.3487 0.4468 0.058 0.050 10.328 7.8757 Factorial point 8 8.5 40 0.2729 0.3882 0.048 0.041 7.978 6.4788 Factorial point 10 8.5 40 0.3322 0.4225 0.052 0.048 9.538 7.3789 Center point 9 7.5 36 0.3030 0.3645 0.047 0.035 6.802 6.12510 Center point 9 7.5 36 0.2949 0.3670 0.045 0.037 7.185 6.23511 Center point 9 7.5 36 0.2973 0.3762 0.046 0.038 7.554 5.78612 Star point 8 7.5 36 0.2708 0.3492 0.046 0.033 6.642 5.46313 Star point 10 7.5 36 0.3094 0.3912 0.051 0.044 8.746 6.98314 Star point 9 6.5 36 0.2956 0.3906 0.050 0.035 7.337 6.58215 Star point 9 8.5 36 0.2979 0.3605 0.047 0.033 6.951 6.01116 Star point 9 7.5 32 0.2688 0.3394 0.046 0.032 6.479 5.23217 Star point 9 7.5 40 0.3175 0.3894 0.053 0.046 9.085 7.636

CCD: central composite design; MRR: material removal rate; SG: sparking gap; WLT: white layer thickness; BW: brass wire; ZCBW: zinc-coated

brass wire.

Figure 2. Wire broken and small cutting line in titaniummachining due to low flushing pressure.

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In addition, the coating evaporation increases thegap size, which results in better debris removal that canreduce the surface roughness and the SG.22 The coatedwire thus produces a better surface in terms of theWLT and homogeneity. This result is parallel to thoseobtained by Kuriakose and Shunmugam,8 which indi-cated that in order to obtain uniform surface character-istics, the coated wires are preferred over the uncoatedwires in WEDM process, and also with those of Antaret al.,6 which showed that thinner recast layer could beproduced in WEDM process using coated wire about25% and 40% for nickel-based superalloy and titaniumalloy, respectively. Figures 4 and 5 present cross-sectional FESEM images of the surface layer of theproduct at different levels of rough cutting parametersusing the brass wire and zinc-coated brass wire,respectively.

From Figures 4 and 5, it can be observed that oncesurface layers are generated, the WLT becomes

irregular. These variations not only demonstrate thatWEDM is a complex process, but also indicate that thedata should be analyzed and some models and methodsshould be found so that we can choose the best condi-tions and predict the results.

The main effects of the machine parameters on theMRR, SG, and WLT for both wires are presented inFigure 6. Figure 6(a) demonstrates that the MRRincreases as the Ton and Ip increase. Likewise, the Ip isthe most significant factor for both wires. With longerTon, the power available between the anode and cath-ode becomes greater, hence strengthening dischargeenergy, which facilitates the melting and evaporating ofmaterials.23–25 In addition, increasing the Ip causedmore electrical discharge energy to be conducted intothe machining gap and increasing the MRR.26 Thismeans that the machining condition was stable, andeffective material removal was achieved at high cuttingcurrents.

Figure 3. Interval plot of response factors from brass wire to zinc-coated brass wire.MRR: material removal rate; CI: confidence interval.

Figure 4. Cross-sectional views showing white layer using brass wire: (a) Std. 3, (b) Std. 6, and (c) Std. 9.

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Figure 6(b) shows that the Ton and Ip have more sig-nificant effects on the SG compared to the Toff. This out-come agrees with the results obtained by Tosun et al.9 andKanlayasiri and Boonmung.27 In addition, the Ton and Ipare in direct relationship to the SG, that is, increasing theTon and Ip significantly increases the SG. The reason isthat with the increase of discharge duration, the overcutduring discharge is also increased.28 Increasing the peakcurrent also increases the energy of each discharge, whichleads to producing wider and deeper craters.

From Figure 6(c), it can be concluded that the maineffect of Ip is being labeled as number one in rankingamong all the three factors on the WLT for both wires.It can be seen that Toff has little effect on the WLT forboth wires. These results are similar to those obtainedby Newton et al.29 and Ghodsiyeh et al.,30 whichdemonstrated the Ip and Ton as the driving factors indetermining average recast layer thickness and alsoindicated that Toff did not display a significant effecton the average recast layer thickness.

Figure 5. Cross-sectional views showing white layer using zinc-coated brass wire: (a) Std. 3, (b) Std. 6, and (c) Std. 9.

Figure 6. Main effects plot for the mean responses for brass wire and zinc-coated brass wire: (a) MRR, (b) SG, and (c) WLT.MRR: material removal rate; SG: sparking gap; WLT: white layer thickness.

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Experimental modeling

RSM includes useful mathematical and statistical tech-niques for modeling and analysis of engineering prob-lems in which the response under study is influenced byseveral variables. Owing to the form of the relationshipbetween the response and the independent variables isoften unknown, the first step in RSM is to find a suit-able approximation to the true functional relationshipbetween the response Y and a set of independent vari-ables {x1, x2, . xn}.

31 A second-order model isemployed when the response function is nonlinear orunknown

T=b0 +Xk

i=1

biXi +Xk

i=1

biiX2i

Xk

ii41

Xk

j

bij �Xi �Xj + � � � + e ð3Þ

where i signifies the linear coefficients, j denotes thequadratic coefficients, the b stands for the regressioncoefficients, k is the number of experimental factors,and e represents the random error. The aim of the RSMmodel is to obtain a significant model. To test the sig-nificance of the individual model coefficients, the modelcan be optimized by adding or deleting coefficientsthrough backward elimination.32

Based on the experimental results shown in Table 3,obtained from both wires, second-order RSM modelswere formulated for the responses. The models werereduced using the backward elimination procedure toautomatically remove the insignificant terms using anal-ysis of variance (ANOVA). The results of statisticalanalysis carried out on the estimated experimental modelparameters are presented in Table 4. The coefficient ofR2 and adjusted R2 were determined to show the ade-quacy of the models. The models are fitted well to thereal data due to their desirable high value of R2.

Predicted values for confirmation tests were sug-gested by the Design Expert software. For each wire, ineach model, six experiments have been done. Theaverage of mean error for each model is presented inTable 4. The marginal errors obtained from allresponses are lower than the allowable set of marginerror (i.e. 10%). It shows that all the empirical modelsare reasonably accurate due to the actual responses inthe range of prediction intervals. Furthermore, thezinc-coated wire was found more predictable, and itgave more reliable response because of lower averagemean errors compared to the brass wire.

NSGA-II

GA is widely used as a solution to the multi-objectiveoptimization problems in mathematics and engineeringresearch, and a rapid and an improved GA known asNSGA-II has been developed by Deb et al.33 In a GA,a population of candidate solutions (individuals) to anoptimization problem is evolved toward better solu-tions. Each candidate solution has a set of properties(its chromosomes or genotype), which can be mutatedand altered. Mutation is a genetic operator that altersone or more gene values in a chromosome from its ini-tial state. This can result in entirely new gene valuesbeing added to the gene pool. With these new gene val-ues, the genetic algorithm may be able to arrive at bet-ter solution than was previously possible.

Likewise, crossover is a genetic operator that com-bines (mates) two chromosomes (parents) to produce anew chromosome (offspring). The idea behind cross-over is that the new chromosome may be better thanboth of the parents if it takes the best characteristicsfrom each of the parents. Crossover occurs during evo-lution according to a user-definable crossover probabil-ity. It is worth tuning parameters such as the mutationprobability, crossover probability, and population size

Table 4. Model parameters for the response in WEDM of Ti-6Al-4V.

Coefficient Brass wire Zinc-coated brass wire

MRR (mm3/s) SG (mm) WLT (mm) MRR (mm3/s) SG (mm) WLT (mm)

Constant 20.42157 + 0.16187 + 31.64816 + 0.66239 + 0.24227 + 15.80133Ton + 0.14920 + 0.00270 + 0.74860 + 0.022120 20.037150 + 0.61690Toff 20.006170 20.00210 20.20640 20.19122 + 0.031808 20.19740Ip 20.0068850 20.00776466 21.96579 + 0.007490 20.011212 20.97125T2

on 20.010033 – – – + 0.00231944 –T2

off – – – + 0.011938 20.00218056 –I2p – + 0.000120690 + 0.031820 – + 0.000176215 + 0.016398Ton3Toff – – – – – –Ton3IP + 0.00148750 – – – – –Toff3IP – – – – – –R2 0.9745 0.9823 0.9500 0.9771 0.9790 0.9505Adjusted R2 0.9617 0.9706 0.9318 0.9688 0.9650 0.9325Average mean error (%) 9.166 7.866 9.966 4.111 3.1 6.22

MRR: material removal rate; SG: sparking gap; WLT: white layer thickness.

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to find reasonable settings for the problem class beingworked on.

The mutation and crossover operators of NSGA-IIhave remained unchanged, but the working process ofthe selection operator differs from the simple GA. Theselection operator is aided in the act of selection bycrowded-comparison operator based on ranking that isdone, in turn, according to non-domination level andcrowding distance.33 The algorithm flowchart ofNSGA-II is illustrated in Figure 7.

Optimization results

To optimize the process parameters and obtain thedesired outputs (maximum MRR, minimum SG, andminimum WLT), a multi-objective optimization wasperformed. The three-objective optimization functionsare formulated as follows

Maximize f(x)f g and minimize g(x), h(x)f g s:t x X

ð4Þ

where x represents the WEDM process parameters; x= x1, x2, x3 (x1 = Ton, x2 = Toff, and x3 = Ip); X sig-nifies all feasible values of the WEDM process para-meters; and the functions f(x), g(x), and h(x) stand forthe formulated RSM models (Table 4) for the MRR,SG, and WLT, respectively.

The NSGA-II was applied in MATLAB 7.12.0, andthe control factors of the NSGA-II were modified toimprove the performance. These control parametersproduced the optimal solutions and a satisfactory levelof convergence. As the NSGA-II parameters, inter-mediate crossover with crossover probability of 0.9 and

Gaussian mutation with mutation probability of 0.1were used. Intermediate crossover is a method onlyapplicable to real variables (and not binary variables).The Gaussian mutation operator is advantageous sinceit is very flexible and supports both fine tuning of solu-tions and searching the domain. A total of 250 genera-tions were generated to obtain the true optimalsolution. All the parameters for NSGA-II were sum-marized in Table 5. The Pareto frontiers of the 100non-dominated solutions for the three responses andboth the brass wire and zinc-coated brass wire are pre-sented in Figure 8.

As can be seen from the graphs, no solution in thePareto optimal front is better than any other as they arenon-dominated solutions. For better understanding, thethree-dimensional Pareto optimal front is plotted in atwo-dimensional objective space for viewing, as shownin Figure 8(b) and (c).

Figure 8(b) shows that the minimum SG is close to0.04 mm for brass wire and close to 0.028 mm for zinc-coated brass wire, with a corresponding MRR of0.2379 mm3/s for brass wire and MRR of 0.3162 mm3/sfor zinc-coated brass wire. The other combinations ofparameters will result in better MRR but higher SG forboth wires. It can be derived from Figure 8(c) that ahigher MRR will result in a higher WLT for both wires.The lowest WLT is close to 5.56 mmm with MRR of0.2379 mm3/s for brass wire and is close to 4.77 mmmwith MRR of 0.3162 mm3/s for zinc-coated brass wire.If a higher MRR is desired, some higher value for WLTshould be accepted.

Compared to other multi-objective algorithms,Nawaz Ripon et al.34 made a comparison betweenNSGA-II and Pareto archived evolution strategy(PAES), niched Pareto genetic algorithm (NPGA), vec-tor evaluated genetic algorithm (VEGA), and strengthPareto evolutionary algorithm (SPEA). This compari-son was made based on five benchmark test prob-lems,35 in which NSGA-II found better non-dominatedsolutions with a greater convergence and diversity inmost cases. Moreover, NSGA-II was compared to dif-ferential evolution (DE) by Kukkonen and Lampinen36

based on five multi-objective benchmark functions thathad been presented by Zitzler et al.35 The obtained

Figure 7. Flowchart for the NSGA-II algorithm.

Table 5. Control parameters of the NSGA-II.

Parameters Value/type

Population size 100Maximum generation number 250Crossover type IntermediateCrossover probability 0.9Mutation type GaussianMutation probability 0.1

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results indicated that on four out of the five benchmarkfunctions, NSGA-II performed better than the DE, interms of diversity and extent of the solutions.Additionally, Saha et al.21 made a comparison betweenNSGA-II and weighted sum method in WEDM pro-cessing of TiC-reinforced composite. The resultsobtained from weighted sum method were inferior toNSGA-II. In this study, we focused on comparing the

performance of brass wire and zinc-coated brass wireto optimize machining parameters in WEDM process-ing of Ti-6Al-4V using NSGA-II. As can be seen in allcurves in Figure 8, non-dominated solutions have agood convergence and diversity, which tends to demon-strate the suitability of the NSGA-II method in solvingthis multi-objective optimization problem. Moreover,the Pareto optimal front of zinc-coated brass wire wasmore uniform than that of brass wire, which tends toconfirm that the zinc-coated brass wire was more pre-dictable in WEDM process.

Furthermore, non-dominated optimal solutions thatform the Pareto front in objective function space canbe analyzed in decision variable space.37 The particlesrepresenting optimal set of decision variables given inFigure 8 are mapped into the decision variable space(i.e. Ton, Toff, and Ip), as shown in Figure 9. It can beseen from Figure 9 that the optimal machining para-meters occur along the boundary of the decision vari-able space for brass wire, that is, for all Ton between 8and 10 ms, for Toff between 6.5 and 8.5 ms, and for Ipbetween 32 and 40 A. Likewise, in the case of zinc-coated brass wire, the optimal machining parameters ofTon and Ip occur along the boundary of the decisionvariable space but the optimal values of Toff occur

Figure 8. Pareto frontier of optimal MRR, SG, and WLT in WEDM process: (a) Three-dimensional Pareto optimal front, (b) MRRand SG, and (c) MRR and WLT.MRR: material removal rate; SG: sparking gap; WLT: white layer thickness.

Figure 9. Decision variable space for optimal machiningparameters in WEDM.

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around 6.5 or 8.5 ms. This tends to confirm that therange levels of the Toff selected could be wider for zinc-coated wire.

Conclusion

This study focuses on comparing the performance ofbrass wire and zinc-coated brass wire in WEDM processof Ti-6Al-4V titanium alloy using experimental, statisti-cal modeling and multi-objective optimization results.The following conclusions were drawn from this study:

1. The percentage increase of the mean MRR, SG,and WLT from brass wire to zinc-coated brass wirewere +31.03, 224.49, and 217.13, respectively.

2. The WLTs of the workpieces cut with brass wireare much thicker than those cut with the zinc-coated wire because the zinc-coated brass wireimproves debris removal.

3. The Ton, Toff, and Ip are the most important para-meters that influence the response variables. TheMRR is most significantly affected by the Ton andIp for both wires. Also, the Ton and Ip have moresignificant effects than the Toff on the SG andWLT when either wire is used.

4. Empirical equations to predict the MRR, SG, andWLT are obtained for both wires using RSM.Confirmation runs verify that the developed math-ematical models are accurate, and the predictedvalues agree closely with the experimental values.Zinc-coated wire was found more predictable withmore reliable response.

5. NSGA-II was used to obtain the Pareto optimalset of solutions for both wires. The observedresults with both wire types demonstrate the suit-ability of the NSGA-II method in solving thismulti-objective optimization problem. The Paretooptimal front of zinc-coated brass wire was moreuniform, which confirmed that the zinc-coatedbrass wire was more predictable compared to brasswire in WEDM process.

6. This study can be extended in the future by chang-ing the work materials or applying different opti-mization methods.

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

This research received no specific grant from any fund-ing agency in the public, commercial, or not-for-profitsectors.

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