Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 931-937
Published Online October 2012 (http://www.SciRP.org/journal/jmmce)
Optimization of ECM Process Parameters Using NSGA-II
Chinnamuthu Senthilkumar1*, Gowrishankar Ganesan1, Ramanujam Karthikeyan2
1Department of Manufacturing Engineering, Annamalai University, Annamalai Nagar, Tamilnadu, India
2Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani, Dubai
Received July 1, 2012; revised August 5, 2012; accepted August 15, 2012
ABSTRACT
Electrochemical machining (ECM) could be used as one of the best non-traditional machining technique for machining
electrically conducting, tough and difficult to machine material with appropriate machining parameters combination.
This paper attempts to establish a comprehensive mathematical model for correlating the interactive and higher-order
influences of various machining parameters on the predominant machining criteria, i.e. metal removal rate and surface
roughness through response surface methodology (RSM). The adequacy of the developed mathematical models has also
been tested by the analysis of variance (ANOVA) test. The process parameters are optimized through Nondominated
Sorting Genetic Algorithm-II (NSGA-II) approach to maximize metal removal rate and minimize surface roughness. A
non-dominated solution set has been obtained and reported.
Keywords: Electro Chemical Machining; Metal Removal Rate; Response Surface Methodology; Surface Roughness;
NSGA-II
1. Introduction
Electrochemical machining (ECM) is one of the non-
traditional machining techniques; it can achieve a wanted
shape of a surface using metal dissolution by electro-
chemical reaction and can be applied to metals such as
high-strength, heat-resistant and hardened steel. ECM
has been used in industry for cutting, deburring, drilling
and shaping [1]. In ECM electrical current passes be-
tween the cathode tool and the anode workpiece through
an electrolyte solution. The workpiece is eroded in a way
that can be described by Faraday’s law of electrolysis.
ECM is suitable for the machining of components of
complex shape and high strength alloys, as typically
found in the semiconductors industries [2]. Metal Matrix
Composites (MMC’s) are relatively new class of materi-
als characterized by lighter weight and greater wear re-
sistance than those of conventional materials. These ma-
terials have been considered for use in automobile brake
rotors and various components in internal combustion
engines. The machining of MMCs is very difficult due to
the highly abrasive nature of the reinforcement [3]. Tra-
ditional edged cutting tool machining processes are un-
economical for such materials as the attainable degree of
accuracy and surface finish are quite poor. Machining of
complex shapes in such materials by traditional processes
is still more difficult. To meet these demands, ECM pro-
cesses has now emerged [4]. The present paper, therefore,
emphasizes features of the development of comprehend-
sive mathematical models for correlating the interactive
and higher-order influences of the various machining
parameters on the most dominant machining criteria, i.e.
the metal removal rate and surface roughness phenomena,
for achieving controlled ECM. The investigation into
controlled ECM has been carried out through response
surface methodology (RSM), utilizing the relevant ex-
perimental data as obtained through experimentation.
The adequacy of thedeveloped mathematical models has
also been tested by the analysis of variance test. The
process parameters were optimized using Non-Domi-
nated Sorting Genetic Algorithm-II (NSGA-II) to maxi-
mize MRR and minimize Ra.
2. Experimental Planning
Experiments were conducted on METATECH ECM
equipment. The dimensions of the specimens were 30
mm in diameter and 6 mm in height. The tool was made
up of copper with a square cross section. Electrolyte was
axially fed to the cutting zone through a central hole of
the tool. The electrolyte used for experiment was fresh
NaCl solution, because of the fact that NaCl electrolyte
has no passivation effect on the surface of the job. The
test specimens of LM25 Al/10%SiCp composites were
produced through stir casting. The machining has been
carried out for fixed time interval. The observations were
made by varying predominant process parameters such as
*Corresponding author.

C. SENTHILKUMAR ET AL. 932
applied voltage, electrolyte concentration, electrolyte flow
rate, and tool feed rate. MRR was measured from the
weight loss. The surface roughness of the machined test
specimens was measured using a Talysurf tester with a
sampling length of 10 mm.
3. Response Surface Methodology
Response surface methodology (RSM) is the procedure
for determining the relationship various between process
parameters with the various machining criteria and ex-
ploring the effect of these process parameters on the
coupled responses [5], i.e. the material removal rate and
surface roughness phenomena. In order to study the ef-
fects of the ECM parameters on the above-mentioned
two most important machining criteria, the metal re-
moval rate (MRR) and surface roughness phenomenon
(Ra), a second-order polynomial response surface mathe-
matical model can be developed as follows to evaluate
the parametric effects on the various machining criteria
2
11
nn n
uo ii iiiijij
ii ij
Yaax axaxx


 
 

(1)
where Yu is the corresponding response, e.g. the MRR
and Ra created by the various process variables of ECM
parameters. ai represents the linear effect of xi, aii repre-
sents the quadratic effect of xi and aij reveals the lin-
ear-by-linear interaction between xi and xj. The second
term under the summation sign of the polynomial equa-
tion i.e. Equation (1) attributes to linear effects, where as
the third term of the above equation represents the higher
order effects and lastly the fourth term of the above equ-
ation includes the interactive effects of the process pa-
rameters. In the response surface methodology each vari-
able is coded in a manner so that the upper level is taken
as +2 and lower level as −2 for designing the experiment
and the test observations in an optimized way. The actual
and coded parametric values for each parameter are listed
in Table 1.
A well-designed experimental plan can substantially
reduce the number of experiments. For determining the
Table 1. Actual and corresponding coded values for each
parameter.
Levels
Parameters
−2 −1 0 1 2
Electrolyte concentration,
X1 (g/lit) 10 15 20 25 30
Electrolyte flow rate,
X2 (lit/min) 5 6 7 8 9
Applied voltage,
X3 (Volts) 12 13 14 15 16
Tool feed rate,
X4 (mm/min) 0.2 0.4 0.6 0.8 1
equation of the surface integrity, experimental designs
have been developed with an attempt to formulate the
mathematical relations using the smallest number of ex-
periments possible. Keeping in view of the present re-
search objectives, response surface methodology has
been utilized in order to develop the mathematical rela-
tionship between the response, Yu i.e. MRR and surface
roughness and the predominant machining parameters
are electrolyte flow rate, electrolyte concentration, ap-
plied voltage and tool feed rate according to the experi-
mental plan based on central composite rotatable second
order design as shown in Table 2.
Table 2. Different controlling parametric combinations and
test results.
Ex.No. X1 X
2 X 3 X 4 MRR
(g/min)
Ra
(µm)
1 −1−1 −1−1 0.124 10.274
2 1 −1 −1−1 0.098 9.952
3 −11 −1−1 0.245 8.752
4 1 1 −1−1 0.278 8.196
5 −1−1 1 −1 0.197 8.851
6 1 −1 1 −1 0.219 8.248
7 −11 1 −1 0.197 9.324
8 1 1 1 –1 0.342 7.724
9 −1−1 −11 0.194 9.247
10 1 −1 −11 0.299 9.987
11 −11 −11 0.249 7.972
12 1 1 −11 0.389 8.131
13 −1−1 1 1 0.482 6.386
14 1 −1 1 1 0.472 6.265
15 −11 1 1 0.529 6.729
16 1 1 1 1 0.656 6.583
17 −20 0 0 0.173 10.925
18 2 0 0 0 0.324 9.647
19 0 −2 0 0 0.214 8.689
20 0 2 0 0 0.299 7.854
21 0 0 −20 0.099 9.548
22 0 0 2 0 0.286 7.136
23 0 0 0 −2 0.299 9.597
24 0 0 0 2 0.721 6.845
25 0 0 0 0 0.227 6.389
26 0 0 0 0 0.287 6.253
27 0 0 0 0 0.295 6.054
28 0 0 0 0 0.245 6.921
29 0 0 0 0 0.268 6.824
30 0 0 0 0 0.226 6.354
31 0 0 0 0 0.289 6.542

C. SENTHILKUMAR ET AL. 933
4. Development of Empirical Models Based
on RSM
After knowing the values of the observed response, the
values of the different regression coefficients of second
order polynomial mathematical equation i.e. Equation (1)
have been evaluated and the mathematical models based
on the response surface methodology have been deve-
loped by utilizing test results of different responses ob-
tained through the entire set of experiments by using a
computer software, MINITAB.14.
On Equation (1), the effects of various machining
process variables on MRR and Ra has been evaluated by
computing the values of different constants of Equation
(1) utilising the relevant experimental data from Table 2.
The mathematical relationship for correlating the MRR
and Ra the considered machining process parameters is
obtained as follows:

 





  
12
2
34 1
222
234
12 1314
23 2434
2
MRR
1.65380.0334 X0.0417X
0.3976X 5.0188X0.00008X
0.00002X0.01602X 1.5837X
0.00442 XX0.0004 XX0.01175 XX
–0.00575 XX0.015 XX0.2493 XX,
R 95.77 %
 






(2)

 





  
12
2
341
222
244
12 1314
2324 34
2
Ra 150.2250.977X11.29X
12.74X 7.388X0.035X
0.367X0.384X 8.855X
0.0023X X0.031XX0.232X X
0.439X X0.268X X1.983XX
R= 96.05%
 
 




(3)
5. Optimization
To optimize cutting parameters in the machining of
Al/SiCp composites, a non-dominated sorting genetic
algorithm was used. The objectives set for the present
study were as follows:
1. Maximization of the metal removal rate (MRR)
2. Minimization of average surface roughness (Ra)
The two-objective genetic algorithm optimization me-
thod used is a fast, elitist non-dominated sorting genetic
algorithm (NSGA-II) developed by Deb [6]. This algo-
rithm uses the elite-preserving operator, which favors the
elites of a population by giving them an opportunity to be
directly carried over to the next generation [7]. The
NSGA-II is a modified version, which has a better sort-
ing algorithm, incorporates elitism and does not require
the choosing of a sharing parameter a priority. The flow
chart of the NSGA-II is shown in Figure 1.
5.1. Description of NSGA-II Algorithm
The steps involved in the solution of optimization prob-
lem using NSGA-II are as follows.
5.1.1. Population Initialization
The population is initialized based on the problem range
and constraints if any.
5.1.2. Non-Dominated Sort
The initialized population is sorted based on non-domi-
nation. The fast sort algorithm is described as below
- For each individual p in main population P
- Initialize Sp = 0. This set would contain all the indi-
viduals that is being dominated by p.
- Initialize np = 0. This would be the number of indi-
viduals that dominate p.
- For each individual q in P
- If p dominates q then. add q to the set Sp i.e.


U
pP
SS q
- Else if q dominates p then increment the domination
counter for p i.e. np = np + 1
- If np = 0 i.e. no individuals dominate p then p belongs
to the first front; Set rank of individual p to one i.e
Prank = 1. Update the first front set by adding p to
front one, i.e.,


11
U
F
Fq
- This is carried out for all the individuals in main
population P.
- Initialize the front counter to one, i = 1
- The following is carried out while the ith front is non-
empty i.e. 0
i
F

- Q = 0. The set for storing the individuals for (i + 1)th
front.
- For each individual p in front Fi
- For each individual q in Sp (Sp is the set of individuals
dominated by p)
- If nq = nq − 1, decrement the domination count for
individual q.
- If nq = 0 then none of the individuals in the subse-
quent fronts would dominate q.
- Hence set qrank = i + 1. Update the set Q with individ-
ual q i.e. UQQq

.
- Increment the front counter by one.
- Now the set Q is the next front and hence Fi = Q.
This algorithm is better than the original NSGA [8]
since it utilize the information about the set that an indi-
vidual dominate (Sp) and number of individuals that
dominate the individual (np).
5.1.3. Crowding D i s tance
Once the non-dominated sort is complete the crowding
distance is assigned. Since the individuals are selected
based on rank and crowding distance all the individuals

C. SENTHILKUMAR ET AL. 934
Figure 1. Flow chart of NSGA-II program.
in the population are assigned a crowding distance value.
Crowding distance is assigned front wise and comparing
the crowding distance between two individuals in diffe-
rent front is meaningless (Raghuwanshi et al., 2004). The
crowing distance is calculated as below
- For each front Fi, n is the number of individuals.
- Initialize the distance to be zero for all the individuals
i.e. Fi(dj) = 0,where j corresponds to the jth individual
in front Fi.
- For each objective function m
- Sort the individuals in front Fi based on objective m
i.e. I = sort(Fi,m).
- Assign infinite distance to boundary values for each
individual in Fi i.e.

1
Id

 and

n
Id


- For k = 2 to (n – 1)
 
 
max min
11
kk
mm
I
kmIk
Id Idff
m

 
 
- I(k)·m is the value of the mth objective function of the
kth individual in I
- The basic idea behind the crowing distance is finding
the Euclidian distance between each individual in a
front based on their m objectives in the m dimen-
sional hyper space. The individuals in the boundary
are always selected since they have infinite distance
assignment.
5.1.4. Selection
Once the individuals are sorted based on non-domination
and with crowding distance assigned, the selection is
carried out using a crowded-comparison-operator (αn).
(1) Non-domination rank prank i.e. individuals
The comparison is carried out as below based on
in front
Fi
- rank
belong to the same front Fi then Fi(dp) >
urna-
m
5.1.5. Genetic Operators.
ed Binary Crossover (SBX)
lates the binary cross-
ov
will have their rank as prank = i.
(2) Crowding distance Fi(dj)
p < nq if
prank < q
- Or if p and q
Fi(dq) i.e. the crowing distance should be more.
The individuals are selected by using a binary to
ent selection with crowed- comparison-operator.
Real-coded GA’s use Simulat
operator for crossover and polynomial mutation [8].
1) Simulated Binary Crossover.
Simulated binary crossover simu
er observed in nature and is given as below.

1,1, 2,
111
2
kkkkk
cpp 

  


2,1, 2,
111
2
kkkk
cp 
k
p


 


th th
where ci,k is the i child with k component, pi,k is the
t
selected parent and 
k (0) is a sample from a random
number generated havinghe density
 
1

1, if0 1
2
c
c
p   

 
2
11
1,if
2c
c
p

 

1


This distribution can be obtained from a uniformly
sampled random number u between (0,1). 
c is the dis-
tribution index for crossover. That is
 

1
1  
2uu  
 

1
1
1
21
u
u






2) Polynomial Mutation:
is performed by The polynomial mutation


δ
ul
cp pp 
kk kkk
where ck is the child and pk is the parent with pu being
k
the upper bound on the parent component, l
k
p is the
lower bound and k is small variation which is calculated
from a polynomial distribution by using

1
1
δ21,if0.5 m
kk k
rr
 


1
1
δ121,if 0.5
m
kkk
rr
 
  

rk is an uniformly sampled random number beteen (0,1) w
and m

is mutation distribution index.

C. SENTHILKUMAR ET AL. 935
5.1.6. Recombin ation and Selection
The offspring population is combined with the current
erformed to set
est performance. The parameters are: Prob-
ab
ariance (ANOVA) and the F-ratio test
ed to justify the goodness of fit of the
aining an optimal solution.
H
points in the pareto solution set. The non-
do
rresponding objective
fu
generation population and selection is p
the individuals of the next generation. Since all the pre-
vious and current best individuals are added in the popu-
lation, elitism is ensured. Population is now sorted based
on non-domination. The new generation is filled by each
front subsequently until the population size exceeds the
current population size. If by adding all the individuals in
front Fj the population exceeds N then individuals in
front Fj are selected based on their crowding distance in
the descending order until the population size is N. And
hence the process repeats to generate the subsequent
generations.
The control parameters of NSGA–II must be adjusted
to give the b
ility of gross over Pc = 0.9 with distribution index ηc =
20, mutation probability Pm = 0.25 and population size Pz
= 100. It was found that the NSGA-II with those control
parameters produces better convergence and distribution
of optimal solutions located along the Pareto optimal
solutions. The 1000 generations are quite enough to find
the true optimal solutions.
6. Discussion
The analysis of v
have been perform
developed mathematical models. The results of the
analysis of variance are presented in Tabl e 3. The calcu-
lated values of F-ratio for the lack of fit are found to be
lesser than the standard percentage point of F distribution
for 99% confidence limit is 7.87 for MRR and Ra. Also,
values of R2 of regression analysis have been calculated
to test whether data is fitted in the developed model and
these values show that data for each response are fitted in
the developed models. The P-value for the model MRR
and surface roughness is lower than 0.05 (i.e. p= 0.05, or
95% confidence) indicates that the model is considered
to be statistically significant.
A single objective optimization algorithm will nor-
mally be terminated upon obt
owever, for most of the multi-objective problems, there
could be a number of optimal solutions .Suitability of
one solution depends on a number of factors including
user’s choice and problem environment, and hence find-
ing the entire set of optimal solutions may be desired.
Among the Pareto optimal solutions, none of the solu-
tions is absolutely better than any other solution and
hence this solution is called as non-dominated solution
[9]. GAs can find good solutions to linear and nonlinear
problems by simultaneously exploring multiple regions
of the solution space and exponentially exploiting prom-
ising areas through mutation, crossover and selection
operations. In general, the fittest individuals of any po-
pulation are more likely to reproduce and survive to the
next generation, therefore improving successive genera-
tions. Non dominating Sorting GA (NSGA-II) by Deb
and Goel (2002) is of the best methods for generating the
Pareto frontier and is used in this study. The NSGA-II
algorithm ranks the individuals based on dominance. The
fast non dominated sorting procedure allows us to find
the non domination frontiers where individuals of the
frontier set are not dominated by any solution. The crow-
ding distance is calculated for each individual of the new
population. Crowding factor gives the GA the ability to
distinguish individuals that have the same rank. This
forces the GA to uniformly cover the frontier rather than
bunching up at several good points by trying to keep
population diversity. The comparison operator (<n) is
used by the GA to sort the population for selection pur-
poses [10].
The procedure was repeated ten times to get greater
number of
minated solution set obtained over the entire optimiza-
tion process is shown in Figure 2.
This shows the formation of the pareto front leading to
the final set of solutions. The co
nction values and decision variables of this non-domi-
nated solution set are given in Table 4. The 31 out of 100
sets were presented since none of the solutions in the
non-dominated set is absolutely better than any other;
any one of them is an acceptable solution. The choice of
one solution over the other depends on the requirement
of the process engineer. If a better surface finish or a
higher production rate is required, a suitable combination
of variables can be selected from Table 4. From the ex-
perimental results presented in Table 2, the parameters
listed in the experiment number 25 leads to minimum Ra
of 5.021 µm and the corresponding MRR of 0.358
gm/min, where the electrolyte concentration, electrolyte
Figure 2. Optimal chart obtained through NSGA-II for com-
posite Al/10%SiCp composite using NaCl.

C. SENTHILKUMAR ET AL. 936
t results for the developed models.
p-value
Table 3. Analysis of variance tes
Sum of squares Mean sum of squares F-value
Source D.f MRR Ra MRR Ra MRR Ra MRR Ra
Linear 4 0.473 10.668 0.000000 168 25.70.0175 2.4213 15. 0.
Square 4 7. 6 4 0
In
Lt
0.1314 1034 0.0328 .804819.88 4.070.000 .000
teraction6 0.0505 2.4704 0.0084 1.1839 5.10 7.67 0.004 0.001
ack of fi10 0.0211 1.8967 0.0021 0.1896 2.4 1.98
Error 6 0.0052 0.5737 0.0008 0.0956
Total 30 0.6253 62.566
Tableptiminatioarameters for ECM Al/10%Si composite using NaCl.
Sl No. m)
4. Oal combns of pofCp
X1 X
2 X 3 X 4 MRR (g/min) Ra (µ
1 10 6.589 5 16 1.0 0.248
2 10 5 16 1.0 0.240 6.624
3 21 5 16 1.0 1.178 4.733
4 18 5 15 0.9 0.312 6.333
5 13 5 15 1.0 0.517 5.670
6 18 5 15 1.0 1.041 4.805
7 16 5 15 1.0 0.831 5.020
8 15 5 15 1.0 0.764 5.131
9 14 5 15 0.9 0.592 5.478
10 15 5 15 1.0 0.751 5.152
11 11 5 15 0.9 0.391 6.052
12 19 5 15 1.0 1.070 4.785
13 17 5 15 1.0 0.916 4.918
14 16 5 15 1.0 0.786 5.093
15 12 5 15 1.0 0.439 5.897
16 16 5 15 1.0 0.822 5.047
17 13 5 15 1.0 0.553 5.576
18 16 5 15 1.0 0.865 4.979
19 10 5 16 1.0 0.270 6.498
20 15 5 15 1.0 0.732 5.187
21 10 5 16 1.0 0.290 6.420
22 13 5 16 1.0 0.568 5.537
23 14 5 15 0.9 0.618 5.418
24 11 5 16 0.9 0.379 6.092
25 13 5 15 1.0 0.578 5.512
26 12 5 15 1.0 0.421 5.955
27 14 5 15 1.0 0.678 5.292
28 15 5 15 0.9 0.578 5.512
29 19 5 15 1.0 1.143 4.749
30 11 5 15 1.0 0.719 5.152
31 18 5 16 1.0 0.998 4.838

C. SENTHILKUMAR ET AL. 937
Table 5.lidation tesults for Al/1SiCp compositeNaCl.
R (gm/min) Ra (µm
Vat res0% using
MR)
#
yte
concentration,
gm/lit
ectrolyte
flow rate,
Lit/
plied Tool feed
rate, ed Actual %Error
Electrol El
min voltage, Volts mm/min PredictedActual %ErrorPredict
Ap
1 16 15 0.831 0.810 2 5.020 5.131 3 5 1.0
flow rate, d volt ta/li
7 lit/min, 1lts and 0minpectively. By op-
mizing using NSGA-II, the Ra value is very close to the
etween these performances. From
th
imized by
ted sorting genetic algorithm (NSGA
inated solution set is obtained. The
RR ha usul-
ve oation thod,ominsortinge-
netic algorithm-II. A pareto-optimal set of 100 solutions
in an Air-Lubricated Hydrodynamic Bearing,”
International Journal of Advanced Manufacturing Tech-
nology, Vol. 2726.
doi:10.1007/s0
applieage andool feed rate re 20 gmt, M
4 vo.6 mm/ res
ti
experimental value has been selected from the Table 4,
trail no: 7. The Ra value is 5.020 µm and the corre-
sponding MRR is 0.831 gm/min and the pertinent pa-
rameters are electrolyte concentration, electrolyte flow
rate, applied voltage and tool feed rate are MRR is 0.831
gm/min and the pertinent parameters are electrolyte con-
centration, electrolyte flow rate, applied voltage and tool
feed rate are 16 gm/lit, 5 lit/min, 15 volts and 1.0
mm/min respectively. This indicates that values obtained
from the NSGA-II optimization technique are in close
agreement with the experimental values and more or less
the same parameter settings. In this study, after deter-
mining the optimum conditions and predicting the re-
sponse under these conditions, a new experiment was
designed and conducted with the optimum values of the
machining parameters. Verification of the test results at
the selected optimum conditions for MRR and Ra are
shown in Table 5.
The predicted machining performance was compared
with the actual machining performance and a good agree-
ment was obtained b
e analysis of Table 5, it can be observed that the cal-
culated error is small. The error between experimental
and predicted values for MRR and Ra lie within 2% and
3%, respectively. Obviously, this confirms excellent re-
producibility of the experimental conclusions.
7. Conclusion
The ECM process parameters have been opt
using non domina
II), and a non dom
second order polynomial models developed for MRR and
Ra have been used for optimization. The choice of one
solution over the other depends on the process the engi-
neer. If the requirement is a better Ra or higher MRR, a
suitable combination of variables can be selected. Opti-
mized value obtained through NSGA-II, is 5.020 µm and
the corresponding MRR is 0.831 gm/min and the perti-
nent parameters are electrolyte concentration, electrolyte
flow rate, applied voltage and tool feed rate are 16 gm/lit,
5 lit/min, 15 volts and 1.0 mm/min respectively. Optimi-
zation will help to increase production rate considerably
by reducing machining time. The objectives such as
is obtained.
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