Comparison of Intelligent Optimization Algorithms for

2011 Third International Conference on Computational Intelligence, Modelling & Simulation

Comparison of Intelligent Optimization algorithms for Wire Electrical Discharge Machining Parameters Abolfazl Golshan

Soheil Gohari

Amran Ayob

Faculty of Mechanical Engineering

Faculty of Mechanical Engineering

Faculty of Mechanical Engineering

Isfahan University of Technology

Universiti Teknologi Malaysia 81310

Universiti Teknologi Malaysia 81310

Skudai, Johor, Malaysia

Skudai, Johor, Malaysia

Email: [email protected]

Email: [email protected]

Isfahan, Iran Email: [email protected]

Choosing the appropriate parameters in order to achieve the corresponding surface roughness and maximum material removal rate will be possible with having the knowledge of the way these parameters influence on mentioned factors which is also prioritized by this study. In the recent years, diverse theorical and experimental methods have been used in order to model and optimize wire electrical discharge machining (WEDM) process. Scott and his associations formulized and solved a multifunctional optimization problem aimed at choosing the best adjustment of wire electrical discharge machining (WEDM) machining parameters [1]. Their corresponding performance was material removal rate and surfacefinished quality. Spedding and Wang optimized this process with use of nerves network. They considered surface roughness, value of being wavy in a surface and material removal speed as outputs [2]. Rozenek and his associations used a piecework made of composite material with metal matrix composite and investigated the variation in feed rate and surface roughness led by changing the corresponding parameters [3]. Tosun and his associations used a statistical model for determining optimal parameters in order to minimize the holes led on the wire during the process [4]. Tosun and Cogun conducted a research regarding the effect of machining parameters on the rate of wire corrosion considering lessened weight from wire while being machined [5]. In the researchers conducted, the optimal conditions are led by piecework property and machining conditions and they cannot be used for other materials or different manufacturing conditions. In this study, for the first time, optimal machining conditions of wire electrical discharge machining (WEDM) are introduced in one sort of applicable coldwork steal 2601 using comparison of non-dominated sorting genetic algorithm (NSGA-II) and Tabu search algorithm both aimed at achieving the appropriate

Abstract-In this research the influence of wire electrical discharge machining on surface roughness and volumetric material removal rate is conducted. With use of experimental result analysis, design of experiments method and mathematical modeling, the correlation between corresponding parameters and process output characterization are studied. The investigated input parameters include electrical current, pulse-off time, opencircuit voltage and gap voltage. With use of experimental results and, subsequently, with exploitation of variance analysis, importance and effective percentages of each parameter are studied. In order to find optimal conditions, outputs extracted from Non-dominated Sorting Genetic and Tabu search algorithms compared with each other led in achieving appropriate models. Tabu search algorithm and Non-dominated Sorting Genetic Algorithm were compared with each other proving the superiority of Non-dominated Sorting Genetic Algorithm over Tabu search algorithm in optimizing machining parameters. Keywords: Wire Electrical Discharge Machining; Surface roughness; volumetric material removal rate; optimization; Tabu search algorithm; Non-dominated Sorting Genetic Algorithm.

I. INTRODUCTION These days, with advent of new material exploitation and era of technological advancement, particularly in manufacturing industries, the use of machining and methods of shaping the components has necessarily been increasing. Meanwhile, methods of machining concerning wire electrical discharge machining (WEDM) have high importance and increasingly high applications in industries. WEDM process is one of EDM machining in which by creation of alternative spark between tool (wire) and piece work, machining process of piece work is implemented. In WEDM process, it is vital to choose best machining parameters to economize choosing process whereas WEDM is a nonconventional, applicable and required machining process with high initial investment.

978-0-7695-4562-2/11 $26.00 © 2011 IEEE DOI 10.1109/CIMSim.2011.32

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conditions of surface roughness (Ra) and volumetric material removal rate (VMRR).

Where F is the average feed rate [mm/min], l is the value of length which is cut in t second and VMRR is volumetric material removal rate [mm3 / min] , Dw is wire diameter [mm] and H is piecework thickness [mm]. After obtaining the experimental samples, surface roughness was measured using a mobile roughness measurement (Mahr Perthometer M2) on each piece work 3 times and subsequently, the average of it was selected.

II. EXPERIMENTAL SETUP AND EQUIPMENT In this study, the experiments are done using ONA R250 Series 5-axis CNC Wire EDM on a piecework ,made of cold-work steel 2601 with thickness of 30 mm. Chemical synthesis of this steel is X165CrMoV12. For machining, brass wire (Cu Zn37) without cover with diameter of 0.25 [mm] and yield strength of 900 [MPA] is used. In this experimental analysis, sections with the length of 20 [mm] (to depth of piecework thickness) are made. Since the exact amount of machining period was recorded using chronometer, therefore, this value of time is used for assessing average feed rate and subsequently, for volumetric material removal rate according to Eq.1 and Eq. 2, respectively. F=

60 × l t

III. EXPERIMENTAL DESIGN The experiments were planed based on Taguchi’s orthogonal array for the design of experiments (DOE). It can help to reduce the number of experiments. In addition, four cutting parameters were chosen including electrical current, pulse-off time, open-circuit voltage and gap voltage. The three level tests for each factor was used whereas the considered factors are multi-level variables whose outcome effects are nonlinear related rather than linearly. The machining parameters which were used and their levels are presented in Table 1 and the experimental results are presented in Table 2.

(1)

VMRR = F × Dw × H

(2) TABLE 1. MACHINING PARAMETERS AND THEIR LEVELS Levels

Control Parameters

Unit

Symbol

Current

[A]

I

Pulse-Off Time

[µS]

Toff

14

10

8

22

Volt Servo

[volt] [volt]

V S

140 28

130 32

110 30

120 26

1 11

2 10

3 9

4 12

TABLE 2. EXPERIMENTAL RESULTS S.No.

I [A]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

11 11 11 11 10 10 10 10 9 9 9 9 12 12 12 12

Toff [µS] 14 10 8 22 14 10 8 22 14 10 8 22 14 10 8 22

VMRR

V [volt]

S [volt]

Ra [µS]

[mm3 / min]

140 130 110 120 130 140 120 110 110 120 140 130 120 110 130 140

28 32 30 26 30 26 28 32 26 30 32 28 32 28 26 30

3.169 3.410 3.229 2.707 3.018 3.035 3.046 2.754 2.421 2.845 3.270 2.575 3.462 3.293 3.528 3.408

12.555 13.785 12.645 7.995 11.108 12.255 10.913 6.698 7.725 8.205 9.593 6.000 11.033 12.435 14.288 8.250

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for surface smoothness are taken into account. For both of them, the correlation coefficients became 99.99% representing appropriate fitting between these models and experimental data. The results are shown in Table.3. The normal probability plots for surface roughness and volumetric material removal rate are illustrated in fig.1. It is noticeable that residuals fall on a straight line. It basically shows that the errors are dispersed and the regression model completely matches the observed values. Table.4 and Table.5 show that test results are valid. Predicted machining factors performance was compared with the actual machining performance and, subsequently, a good agreement was made. Since the amount of errors was proved to be acceptable, so these models can be selected as the best ones and use them in optimization level.

IV.PROCESS MODELLING AND ANALYSIS OF VARIANCE In this study, regression method was used to determine the relationship between input and output variables of cold-work steel 2601 using WEDM. For modeling the process, different types of exponential and second-order mathematical functions over 14 sets of outputs acquired from experimental results were fitted. Subsequently, these models were modified using statistical method of stepwise elimination in the Minitab environment and with confidence level of 95%. Eventually, equations coefficients for volumetric material removal rate and surface roughness were measured. Correlation coefficients calculated for each of the equations are used to choose the model. Meanwhile, model of second-order polynomial equations for volumetric material removal rate and exponential model

TABLE 3. FITTING EQUATIONS WITH THEIR CORRELATION PERCENTAGE Respond Value

Model Type

Volumetric

Second-order

Material Removal

polynomial

Rate

equation

Surface Roughness

Correlation

Fitting Equation

VMRR=15.8 + 22.9 I - 9.19 S - 0.742

(%)

0.0319

Toff2

+ 0.19

V + 0.00188

Toff

S - 0.00220VS

I2-

S2-

0.1I

Toff

99.99

0.00599 I V - 0.143 I S + 0.0132 Ra=exp (2.22-0.120

Toff

Toff

2

2

+ 0.523 I- 0.259S- 0.00519 I + 0.00602 S - 0.000677 I 99.99

Exponential V-0.00949 I S + 0.000606 Toff V + 0.00125 Toff S + 0.000078 V S )

TABLE 4. RESULTS OF CONFORMATION TEST FOR Ra I [A]

Toff

1

10

2

12

Run

V [volt]

S [volt]

Results of Model

Results of Experiments

Error (%)

8

120

28

2.98

3.05

-2.3

14

120

32

3.33

3.46

-3.76

[µS]

TABLE 5. RESULTS OF CONFORMATION TEST FOR VMRR I [A]

Toff

1

10

2

12

Run

V [volt]

S [volt]

Results of Model

Results of Experiments

Error (%)

8

120

28

10.67

10.91

-2.2

14

120

32

12.21

11.03

9.66

[µS]

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(a)

(b)

Fig.1. Normal plot of residuals: (a). Normal plot of residuals for average surface roughness (b). Normal plot of residuals for volumetric material removal rate

After choosing the appropriate models for investigation of each input parameter effect on outputs using variance analysis method, distribution percentage for each of parameters was calculated considering Table.6 and Table.7. According to these calculations, the most effective parameters concerning surface roughness (Ra) and volumetric material removal rate (VMRR) are demonstrated to be electrical current and pulse-off time, respectively. Moreover, gap voltage doesn’t have any influence on volumetric material removal rate (VMRR) statistically.

V. MULTI-OBJECTIVE OPTIMIZATION In this study, two objectives are put into consideration, volumetric material removal rate (VMRR) and surface roughness (Ra). It is noticed that if VMRR rises, Ra also increases. But our objective is aimed at maximizing VMRR and minimizing surface roughness. A single optimal solution does not help to achieve our goals as our purpose, since these objectives are opposing in nature. Choice of VMRR and surface roughness is also dependent on user and environment of the problem. Optimizing both of the output parameters requires multi-objective optimization [6].

TABLE 6. RESULTS OF VARIANCE ANALYSIS ON VOLUMETRIC MATERIAL REMOVAL RATE Factors

d.f.

Sum of Squares

Variance

F

Distribution Percentage

I

3

37.52164687

12.50721562

149.92

37.13

Toff

3

55.13897813

18.37965938

220.31

54.56

V

3

7.51227188

2.50409062

31.01

7.43

S

3

0.62510625

0.20836875

2.5

0.08

Error

3

0.2502844

0.0834281

-

0.8

Total

15

101.0482875

-

-

100

TABLE 7. RESULTS OF VARIANCE ANALYSIS ON SURFACE ROUGHNESS Factors

d.f.

sum of squares

Variance

F

Distribution percentage

I

3

0.89816618

0.29938873

23538.8

53.79

Toff

3

0.36541701

0.12180507

9576.7

21.88

V

3

0.20304333

0.06768111

5321.28

12.16

S

3

0.20300948

0.06766983

5320.39

12.15

Error

3

0.00003816

0.00001272

-

0.02

Total

15

1.66967416

-

-

100

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VI. NONE-DOMINATED SORTING GENETIC ALGORITHM One of the powerful and comprehensive algorithms is what was introduced by Srinivas and Deb [7] named as the non-dominated sorting genetic algorithm. It deals with a possible solution regarding a population and, therefore, it can have some applications in problems of multiobjective optimizations. It leads to have a number of simultaneous solutions. Despite, this algorithm is fast, but it has been either a controversial method or opposed due to have some difficulties and complexities when it comes to computational approach. The elitism is also disregarded in this method. The selection operator differs from simple genetic algorithm (SGA). Crowded comparison is the operator in which selections can be achieved considering ranking and crowding distance. The solution of initially parent population is checked with other solutions and eventually, put into consideration to make aware of solutions validation. They must satisfy rules given below [8]:

Obj.1[i] f Obj.1[ j ] and Obj.2[i ] ≥ Obj.2[ j ] ,Or

(3)

Obj.1[i] ≥ Obj.1[ j ] and Obj.2[i] f Obj.2[ j], i ≠ j (4) Where, chromosome numbers can be shown as i and j, respectively. Subsequently, it can be noticeable that the selected solution is validated by rules introduced in Role.3 and Role.4 and makes it be marked as dominated. If the rule doesn’t satisfy the corresponding equations above, it will be marked as non-dominated. The corresponding process must continues until all solution selected are ranked. Fitness which is as equal as its non-dominated level assigns to each solution. There is no result to demonstrate none of the solutions is better compared with other solutions. They are considered as part of a special rank or the non-dominated level. The crowding distance is considered to be as an average distance between two points on both sides of selected solution point along each objectives function. Subsequently, each objective function’s boundary solution with the largest and smallest values is assigned as an infinity value in this step. The algorithm flowchart is illustrated in Fig.2. For solving optimization problem using GA, fitness value is required. It connects the objective with decision variable. MATLAB codes have been developed in order to obtain the optimal output results based on none-dominated sorting genetic algorithm (NSGA-II).

Fig.2. Flow chart for the NSGA-II algorithm [8]

small possible changes in current solution’s values. In each iteration, after creation of each neighborhood, the values of purpose functions are calculated and, subsequently, compared with each other. In this step, the movement to the best solution in Tabu search is

VII.TABU SEARCH ALGORITHM Tabu search algorithm (Ts) was first proposed by Glover in the end of 80th decade [9]. The definition of neighborhood here is the entire solutions obtained via the

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implemented among current neighborhood solutions. This process continues until some stopping criterion has been satisfied. After each movement, the previous solution lies on Tabu list. Tabu list is apparently characteristics of Tabu search containing number of previous accepted solutions. Movement to those solutions is not possible in current iteration. Tabu search highly avoids creation of close loop and convergence of algorithm to local optimizations and, subsequently, provides possibilities of searching in more space. Size of Tabu search algorithm depends on properties and dimensions of problem and is usually determined experimentally [10-12]. In this study, suggested algorithm is coded using MATLAB scripts and uses this software for corresponding problem optimization. The propose function for optimizing two output factors of surface roughness and volumetric material removal rate can be stated using Eq.5 and Eq.6, respectively. In this process, the aim is to maximize Eq.5 and in contrast, minimize Eq.6. These equations represent the absolute difference between expected values and approximated ones (using proposed models in section IV).

machining (W1=1, W2=0), semi polishing (W1=W2=0.5) and finish polishing (W1=0, W2=1) is illustrated in the Table.8. In the next step, a non-dominated sorting genetic algorithm (NSGA-II) can be exploited for optimization issues including multi performance of non-linear models. The individuals are ranked by the use of NSGA-II concerning dominance. In order to achieve the high performance, the controlled factors in NSGA-II are adjusted. These factors are: crossover probability= 0.8, mutation probability 0.2 and population size 100. It was shown that for better convergence and optimal solution distribution, above controlled factor must be produced. The 100 generations were generated to acquire the true optimal solution. The none-dominated set obtained over the entire optimization is shown in Fig.3. For comparison of two mentioned algorithms used for surface roughness optimization and volumetric material removal rate for three levels of rough machining, semipolishing and finish polishing are shown in Table.8. Considering the experimental results shown in the Table 2, the parameters of trial number 11 resulted to surface roughness of 3.27 [µm] and VMRR of 9.593 [ mm 3 / min ]. After optimizing machining parameters through NSGA-II and Tabu search algorithm, considering NSGAII the value of surface roughness fell to 3.22 [µm] and volumetric material removal rate , in contrast, soared to 14.21 [ mm 3 / min ]. However, regarding Tabu search algorithm these mentioned values fell to 3.22 [µm] and increased to 14.19 [ mm 3 / min ], respectively (Refer to Table.8, Section semi polishing). Thus, considering the data given, as open-circuit voltage setting is kept constant, by changing pulse-off time, electrical current and gap voltage, it can be observed that higher VMRR and lower Ra can be achieved which both are more desirable. It is noticed that results in two mentioned algorithms both concerning optimization in the level of finish polishing were exactly same. However, in the level of semi polishing and rough machining, better results were achieved with use of NSGA-II. According to the level of semi polishing, the reason why use of NSGA-II is better is that despite both algorithms lead in same values for surface roughness, but values of 14.21[ mm 3 / min ] and 14.19 [ mm 3 / min ] were attributed to NSGA-II and Tabu search algorithms , respectively, demonstrating superiority of NSGA-II over Tabu search algorithm. Moreover, according to level of rough machining, results for both algorithms were same concerning VMRR. However, surface roughness achieved by use of NSGA-II and Tabu search algorithm resluts in 3.60 [µm] and 3.62 [µm] which again show superiority of NSGA-II algorithm over Tabu search algorithm.

*

F

F

SC

SC

1

2

=

=

F1 − F1 ( x )

(5)

F1 ( x )

F2 ( x) − F

*

2

F2 ( x )

(6)

Where,
  is output variable values (calculated by models),
 is expected value of output variable (chosen by operator). In this process of optimization, in order to indicate the importance of every output parameter in different levels of machining process, Eq.7 can be applicable.

Z = w1 F1SC + w2 F2SC

(7)

According to Eq.7, with changing the weighting coefficients including w1 (coefficient of volumetric material removal rate) and w2 (coefficient of surface roughness), the appropriate conditions for outputs can be achieved. VIII. DISCUSSION Machining processes are often followed in two or three levels of rough machining, finish polishing and semi polishing. Level of rough machining is usually aimed at rising machining speed in which surface roughness is not necessary. On the other hand, in level of semi polishing and finish polishing, the aim is raising the surface roughness. According to the forgoing analysis, the Tabu search algorithm used for three conditions of rough 139

TABLE 8. OPTIMUM MASHINING PARAMETERS ACQUIRED USING NSGA-II AND TABU SEARCH ALGORITHM Level of Machining

Rough Machining

Semi-Polishing

Finish Polishing

Algorithm Type

Current (A)

Pulse-Off Time (µS)

Volt (v)

Servo (v)

Ra(µm)

VMRR (mm3/min)

NSGA-II

11.94

8

110

26

3.60

14.80

Tabu Search

12

8

110

26

3.62

14.80

NSGA-II

10.97

13.22

140

26

3.22

14.21

Tabu Search

11

14

140

26

3.22

14.19

NSGA-II

9

22

110

26

2.05

3.39

Tabu Search

9

22

110

26

2.05

3.39

In conclusion, by comparison of Tabu search algorithm and NSGA-II it was noticed that in spite of the fact both algorithms have good results in optimization issues, but it was shown that NSGA-II had slightly superiority over Tabu search algorithm whereas NAGA-II results were more satisfactory than Tabu search algorithm in terms of optimizing machining parameters. REFERENCES [1] D.Scott , S.Boyna , K.P.Rajurkar ., "Analysis and optimization of parameter combinations in WEDM", Int. J. Prod. Res., Vol. 29, pp. 2189–2207, 1991. [2] T.A.Spedding, Z.O.Wang , "Parametric optimization and surface characterization of wire electrical discharge machining process", Int. J. Precision Eng., Vol.20, pp. 5–15, 1997. [3]M.Rozenek.M,J.Kozak,L.Dabrovwki,K.Lubkovwki, Electrical discharge machining characteristics of metal matrix composites,J.Mater.Process.Technol.109, pp.367-370, 2001. [4] N.Tosun, C.Cogun , H.Pihtili , "The effect of cutting parameters on wire crater sizes in WEDM", int. J . Adv. Manuf. Techonl., Vol. 21, pp. 857-865, 2003. [5] N.Tosun,C.Cogun, An investigation on wire wear in WEDM, j.Mater.Process.Technol.1349 (3) , pp. 273-278, 2003. [6] J.Y. Kao, Y.S. Tarng, A neutral-network approach for the on-line monitoring of the electrical discharge machining process, J. Mater. Process. Technol. 69, pp.112–119, 1997. [7] K. Deb, P. Amrit, A. Samir, and Meyarivan, IEEE Trans. Evol. Comput. 6, 182 , 2002. [8] M.Debabrata, K. Pa.Surjya, S.Partha, Modeling of electrical discharge machining process using back propagation neural network and multi-objective optimization using non-dominating sorting genetic algorithm-II, J. Mater. Process. Technol. 186, pp.154–162, 2007. [9] F.Glover, Tabu search: Part I, ORSA J Comp, 1989. [10] A.Hertz A., D. De Werra, "The tabu search metaheurestic: how we used it", Annual Mathematics in Artificial Intelligence, Vol. 1, pp. 111– 121, 1991. [11] F.Kolahan, M.Liang, "Optimization of hole-making operations: a tabu-search approach", Euro. J. Operational Res., Vol. 109, pp. 142- I59, 1998. [12] F.Kolahan, M.Liang, "An adaptive TS approach to JIT sequencing with variable processing times and sequence-dependent setups", Int. J. Machine Tools Manuf., Vol. 40, pp. 1735–1753, 2000. [13] K. Palanikumar, B. Latha , V.S.Senthilkumar ,R.Karthikeyan, Multiple Performance Optimization in Machining of GFRP Composites by a PCD Tool using Non-dominated Sorting Genetic Algorithm (NSGA-II),Met. Mater. Int.,Vol.15, No. 2, pp. 249-258, 2009.

Fig 3. Pareto optimal set with use of NSGA-II

IX.CONCLUSION As follows from forgoing analysis, the study based on the influence of WEDM on surface roughness and volumetric material removal rate was carried out. The nonlinear polynomial models were developed for volumetric material removal rate and average surface roughness were used for optimization. In this study, two multi-objective evolutionary algorithms concerning efficient methodology including NSGA-II and Tabu search algorithm were used to optimize machining parameters in cold-work steel 2601. The emphasis must be put on providing a preferred solution for the process engineer in the short period of the time. The choice of one solution over other ones is dependent on the requirements of process engineer [13].

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