An overview of GA technique for Surface Roughness Optimization in Milling
Process
Azlan Mohd Zain
Faculty of Computer Science
& Information System
Universiti Teknologi
Malaysia, Skudai Johor,
Malaysia
azlanmz@utm.my
Habibollah Haron
Faculty of Computer Science
& Information System
Universiti Teknologi
Malaysia, Skudai Johor,
Malaysia
habib@utm.my
Abstract
Optimization of parameters in machining is a
nonlinear model with constraints, so it is difficult to be
conducted using conventional approaches. As
alternative, non conventional approaches become
useful approaches to conduct machining parameter
optimization problem. Genetic Algorithm (GA) is one
of the well known techniques classified as non
conventional approaches with intelligent in human
behavior that is mostly applied to ensure efficient and
fast selection of the optimum cutting conditions for
parameters in machining process. This paper outlines
an understanding of how GA system operates in order
to optimize the surface roughness performance
measure in milling process. Example of works that
applied GA technique for machining optimizing
problem for surface roughness is also given.
1. Introduction
In many real machining applications, three
conflicting objectives are often considered; these are
the minimum production rate, minimum operational
cost, and quality of machining. In term of quality of
machining, the criterion for the assessment is usually
referred to the surface quality of the machined part.
Improvement of the quality could be indicated by
referring to a performance measure known as surface
roughness.
Several optimization techniques that can be
classified as non conventional approaches could be
effectively applied to optimize the cutting parameters
that affecting the surface roughness (Ra) value. With
reference to the published literatures, technique
Safian Sharif
Faculty of Mechanical
Engineering
Universiti Teknologi
Malaysia, Skudai Johor,
Malaysia
safian@fkm.utm.my
classified as non conventional techniques include
Genetic Algorithm (GA), Simulated Annealing (SA),
Tabu Search (TS), Ant Colony Algorithm (ACO), and
Particle Swarm Optimization (PSO) [1, 2, 3]. Most of
these techniques are suitable and have the potential to
be applied for cutting parameters optimization
problems during machining. Among these techniques,
GA is widely used by most researchers for the
optimization objectives which include minimizing
production cost and maximizing material removal rate,
and improving product quality [4].
With consideration that GA is able to handle
machining optimization problem, this paper outlines an
understanding of how GA system operates in order to
optimize the surface roughness in milling operation.
Application example of GA technique for machining
optimizing problem for surface roughness is also given
with reference to previous works.
2. Optimization of cutting conditions for
surface roughness
This section discusses the basis measurement of
surface roughness performance with its mathematical
model. In machining, the surface roughness is generally
specified mathematically in terms of the arithmetic
average deviation from the mean line and which is also
known as Ra using the following equation:
1 L
Ra =
(1)
∫ Y ( x ) dx .
L 0
where L is the sampling length, and Y is the
ordinate of the profile curve. In other word, Ra is the
area between the roughness profile and its mean line in
µm, or the integral of the absolute profile height over
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the evaluation length that need to be optimized as
shown in Figure 1.
optimized) that will survive in the best possible manner
in the environment. The parameters of the search
identified as x1, x2, x3, x4, and x5 which are called the
phenotypes. In GA, the phenotypes (parameters) are
usually converted to genotypes (chromosome) by using
a coding procedure. Knowing the ranges of x1, x2, x3,
x4, and x5 each variable is to be presented using a
suitable binary string. The representation using binary
coding makes the parametric space independent of type
of variables used.
3. Relationship between modeling and
optimizing phase for Ra prediction
Figure 1. Surface roughness profile [5]
Generally, Ra value is influenced by many factors
such as tool geometry, cutting conditions and the
irregularities of machining operations namely tool
wear, chatter, tool deflections, cutting fluid, and
workpiece properties. The effect of cutting conditions
such as feed rate, cutting speed, axial-radial depth of
cut, and machining tolerance are parameters that mostly
influence the Ra value of surface quality in machining,
particularly in milling operation. The Ra value is
expected to be as low as possible and could be
achieved by adjusting these cutting conditions with the
assistance of an appropriate numerical optimization
method. Therefore, minimization of surface roughness
value must be formulated in the standard mathematical
model. For example, if the value of Ra that given in
equation (1) tries to be optimized, the function could be
written as [6,7]:
i.
Optimization function:
1L
min f ( x1 , x2 , x3 , x4 , x5 ) = ∫ Y ( x) dx.
L0
ii. Value of coefficients : Vc , ft , aa , ar , mt.
iii. Objective function : Ra-min (Vc , ft , aa , ar , mt).
iv. Limitation functions : Vc-min ≤ Vc≤ Vc-max , ftmin ≤ ft≤ ft-max , aa-min ≤ aa≤ aa-max , ar-max ≤ ar≤ armax , mt -max ≤ mt≤ mt -max.
where x1 = Vc , x2 = ft , x3 = aa , x4 = ar , x5 =mt.Vc is
cutting speed, ft is feed rate, aa is axial depth of cut, ar
is radial depth of cut, and mt is machining tolerance.
The value of coefficients (cutting conditions) is
statistically determined on the basis of the data
measured experimentally. The objective function to be
minimized is necessary in order to define the standard
optimization.
In GA application, the given problem is transformed
into a set of genetic characteristics (parameters to be
Generally, there are two phases needed in
optimizing the machining process parameters which are
modeling and optimizing [2]. The first phase involves
the development of models to predict the values of
response or performance measure such as Ra. value. It
also can be defined as modeling phase of machining
processes which is important to provide the basis
mathematical model for formulation of the objective
function. Second phase is the determination of
optimization conditions for the objective function. It is
also called optimizing phase which is important to
obtain the optimal solution of the predicted value
obtained from the modeling phase. Figure 2 illustrates
an example of the flow relation between modeling and
optimizing
phase
in
machining
parameters
optimization.
Based on Figure 2, surface roughness, labeled as Ra
is one of the important responses or performance
measure to be measured in machining to indicates the
surface quality of the machined workpiece. Normally,
the predicted model of surface roughness value for
milling process in relation to the independent variables
investigated can be expressed as:
^
R a = kv X 1 f
X2
a X3 .
^
(2)
From Equation (2), R a is the predictive surface
roughness in µm, v is the cutting speed, f is the feed
per tooth, a is the cutting depth and k, x1, x2, x3 are the
model parameters to be estimated using the
experimental data. Then, all the parameters that affect
^
the predicted R a value obtained from modeling phase
must be optimized by using conventional or non
conventional approaches. The standard mathematical
equation of surface roughness to be optimized in
milling is expressed in the Equation (1).
Recently, non conventional approaches are mostly
used by researchers to find the optimal value of the
predicted model obtained from the modeling phase. In
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the next section, the potential of GA technique to be
applied for optimizing cutting conditions for surface
roughness performance measures is highlighted.
Technological data
base
Ts ,Tc ,Ti ,Ct , Cl ,Co ,V
Calculation of
Tp , Cp , Ra
Random
generation of
cutting
conditions
(v, f, a)
Calculation of function
Y (v, f, a)
Limitation
equations
Preprocessing /
Normalization
Large-scale
optimization
algorithm max
(y)=?
Neural
network for
prediction
y
Training, Testing, Prediction
v, f, a
Optimization / prediction model
Optimum cutting
conditions
Vopt , fopt, aopt
Calculation
of
Tp min , Cp min , Ra min
Calculation of
statistic
Print-out graphs and
statistic
Figure 2. Flow of searching for optimum
cutting conditions [7]
4. GA for Optimization Problem
The machining optimization problem becomes
complicated when a large number of constraints are
involved. Conventional optimization approaches are
useful for specific problems and are inclined to provide
local optimal solution [1, 2]. Non conventional
approaches consist of a variety of methods including
optimization paradigms that are based on evolution
mechanisms such as biological genetics and natural
selection. These methods use the fitness information
instead of the functional derivatives making them more
robust and effective. Non conventional approach such
as GA is widely used for solving optimization
problems.
Generally, some steps are taken in order to apply
GA in optimizing problem, The performance measures
to be optimized is based on several variables, as given
in the following steps [8]:
[i] The variables should be coded. An appropriate
coding for the variables should be such that the
new variables appear as strings consisted of
integers. These strings will be used by the GA to
lead the optimization in areas that give a high
value to the quantity under optimization. A widely
applied coding is the transformation of the
variables into binary numbers. These binary
numbers may be seen as strings consisted of the
integers 0 and 1.
[ii] A set of randomly-selected strings is created. This
set of strings is called the initial population 1. The
size of the initial population varies from several
tens even to several thousands, depending on the
application. The size of the population is usually
set after testing, since there is not a criterion that
gives the best size of the population for a GA. An
average size for a population is usually 50 strings.
[iii] For each string of the population, the value of the
quantity to be optimized is calculated. Then, based
on this value, an objective function value (fitness)
is assigned to the string. This objective function
value is usually a multiple of the quantity value
divided by the average of the quantity values of the
strings of the population.
[iv] A set of GA operators is applied to the population.
This set of operators, based on the strings of the
existing population and their corresponding
objective function values, will hopefully provide a
new population whose strings will be better. The
new population replaces the old one. This
procedure, namely the creation of a new
population, based on the old one, and the
replacement of the old population, is called
generation.
[v] A predefined stopping criterion is checked. This
criterion is usually a pre-set maximum number of
generations that should be performed. If this
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criterion is not satisfied, then the GA continues
with step 3 (the application of the GA operators on
the new population), otherwise it terminates.
An example of pseudo code for the GA algorithm in
obtaining a global optimum solution is given as in
Figure 3. Based on the pseudo code given, there are
five main parameters affecting the performance of GA:
population size, number of generations, crossover rate,
offspring, and mutation rate. Example of flow for the
GA algorithm in obtaining optimal cutting conditions
in metal cutting problem is given in Figure 4.
An empirical input-output and in-process
parameter relationship(s) model(s) developed
and single objective function f(x) formulated.
Initializing search algorithm:
1. Choose for feasible operating region of
each input decision variable (vector x).
2. Select encoding of process decision
variables vector x, population size P,
length of the spring, selection criteria,
crossover and mutation probability, and
number of generation (say Genmax). Set
initial number of generation as Gen=0.
Begin;
Generate random population of P solutions
(chromosomes);
For each individual i∈P: calculate fitness
(i);
For i=1 to number of generations;
Randomly
select
an
(crossover or mutation);
operation
If crossover;
Select two parents at random ia and
i b;
Generate on offspring ic=crossover
(ia and ib);
Create as many feasible random encoded
decision vector strings (combination level of
decision variables, such as speed and feed
rate value) as the current population size.
Gen= Gen+1
Update current population (The best P
chromosomes from parent and
offspring population)
Perform mutation operation offspring
based on mutation probability.
Else If mutation;
Select one chromosome i at
random;
Generate an offspring ic=mutate (i);
Perform crossover of random pair of
string from mating pool, to form new
offspring,
based
on
crossover
probability.
End if;
Calculate the fitness of the offspring ic;
If ic is better than the worst
chromosome then replace the worst
chromosome by ic;
Select
populations
by
suitable
selection method, to form mating pool
of same population size.
Next i;
Check if termination=true;
End;
Figure 3. Pseudo code for the GA algorithm for
global optimum solution [9]
Assign fitness value of each string in
current population based on single
objective function f(x).
Is Gen >
Genmax
No
Yes
Decode current population of strings, which
are the near optimal cutting conditions.
Figure 4. GA-based optimization technique
for metal cutting process problems [2]
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No
1.
Table 1. Application of GA for Ra values
optimization in milling process
5. Example works of Application of GA for
Ra optimization
Author,
Year
H.
Oktem et
al, 2006
[6]
GA technique could be effectively applied for
different types of milling operations such as singlepass, two-pass, three-pass and multiple-pass [4]. For
surface roughness optimization in milling process, it
was found that usage of non conventional approaches
to model and optimize surface roughness was very
limited [10]. Examples of applications of GA-based
technique conducted by several researchers for Ra
values optimization problem in milling operation given
in Table 1.
There are various parameters that influence Ra value
such as cutting speed, feed rate, axial depth of cut,
radial depth of cut, machining tolerance, nose radius,
and vibrations. The table also shows the various
techniques such as Respond Surface Methodology
(RSM), ANN (Artificial Neural Network), DP
(Dynamic Programming) and GA could be used as the
effective approaches to model the predicted Ra value
that to be optimized by GA techniques in milling.
2.
P.V.S.
Suresh
et al,
2002
[10].
3.
O. Colak
et al,
2007 [11]
Modeling
technique
ANN
Remark
Feed, cutting speed,
axial depth of cut, radial
depth of cut, machining
tolerance. GA produces
the Ra value that is lower
than the values of
experimental results.
RSM
Speed, feed, depth of
cut, nose radius. Ra
decreases
with
an
increase
in
cutting
speed, and increases as
feed
increases.
Ra
increases
with
an
increase in depth of cut,
and nose radius.
GA
Spindle speed, feed rate,
depth of cut. High cutting
speed values is preferred
for low Ra value.
4.
H.
Oktem et
al,2005
[12]
RSM
Feed, cutting speed,
axial depth of cut, radial
depth of cut, machining
tolerance. GA reduces
the Ra value in the mold
cavity from 0.412μm to
0.375μm corresponding
about 10 percents (%)
improvement.
5.
M.
Brezocni
ck et al,
2004 [13]
GA
Spindle speed, feed rate,
depth of cut, vibrations.
Feed rate has the
greatest influence on Ra.
6.
I.N.
Tansel et
al, 2006
[14]
ANN
Cutting speed, feed rate,
radial depth of cut,
tolerance. Ra decreases
with high cutting speed
and very small feed rate.
7.
P.
Palanisa
my et al,
2007 [15]
DP
Cutting speed, feed rate,
depth of cut. GA reduces
the Ra value on the mild
steel from 2.60μm to
0.71μm.
6. Conclusion
This paper discussed on how GA system operates in
order to optimize the surface roughness performance
measure in milling process. The application of GA
technique for machining optimizing problem
specifically to optimize the Ra value is also given by
referring to the example of works. Based on the
discussion made in this paper, GA could be used to
obtain the optimal Ra values based on various cutting
conditions (parameters) in milling operation mainly
cutting speed, feed rate, tool geometry and depth of
cut.
The study shows that GA technique can be applied
for different predicted Ra values that are modeled by
using different conventional approaches (such as DP,
and RSM) and non conventional approaches (such as
ANN, and GA itself). In other word, GA technique
does not strictly state particular modeling approaches
in order to be coupled with it in finding the optimal Ra
value. It is important for researchers to provide many
alternatives by using various matching approaches
between modeling and optimizing approaches to give
the best result of Ra value in optimization problem.
GA also has its own genetic expression
programming which makes a global function search for
problem, developed as a resultant of GA and Genetic
Programming (GP). GP algorithms try to find a suitable
solution using parse tree which they created to define
relations between different non-linear models.
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Advantages of GA and GP algorithms are combined in
the GEP (Genetic Expression Programming). The
effectiveness of the GEP for optimization problem of
Ra value in milling process has been proven by the
works conducted by O. Colak et al. [11] and M.
Brezocnick et al. [13].
To conclude, the study has shown and has proven
the capability of GA in solving surface roughness
performance measure by providing the optimal
combination of cutting condition value compared to the
result estimated by intuitive method obtained in the
actual experiment. An issue also could be highlighted
from this study relates to the capability of one the
established non conventional techniques, ANN, as
modeling technique to be coupled with GA optimizing
technique. It is unexpected to find that there is little
published work relates on this issue yet. In future,
consideration should be taken to study the feasibility of
coupling the ANN and GA.
7. References
[1] R. Siva Sankar, P. Asokan, R. Saravanan, S. Kumanan,
and G. Prabhaharan, Selection of machining parameters for
constrained machining problem using evolutionary
computation, International Journal Advanced Manufacturing
Technology, 32 (2007) 892–901.
[2] I. Mukherjee, and P.K. Ray, A review of optimization
techniques in metal cutting processes. Computer & Industrial
Engineering, 50 (2006):15-34.
[3] Aman Aggarwal, and Hari Singh, Optimization of
machining techniques - a retrospective and literature review,
Sadhana Journal (India), 30: (2005) 699-711.
[4] Azlan Mohd Zain, Habibollah Haron, and Safian Sharif,
Non conventional approaches for optimizing of cutting
parameters in machining process: a review, The 4th
Postgraduate Annual Research Seminar 2008 (PARS’ 08)
Faculty of Computer Science, UTM., 2nd-3rd July 2008.
[8] Manolas D.A., Gialamas T.P., Frangopoulos C.Aft, and
Tsahalis D.T, A genetic algorithm for operation optimization
of an industrial cogeneration system, Computers Chem.
Engineering, 20 (1996) 1107-1112.
[9] Emad Elbeltagia, Tarek Hegazy, and Donald Grierson,
Comparison among five evolutionary-based optimization
algorithms, Advanced Engineering Informatics, 19 (2005)
43–53.
[10] P.V.S Suresh, P. Venkateswara, S.G Deshmukh, A
genetic algorithmic approach for optimization of surface
roughness prediction model, International Journal of machine
Tools & Manufacture, 42 (2007) 675-680.
[11] Oguz Colak, Cahit Kurbanoglu, M. Cengiz Kayacan,
Milling surface roughness prediction using evolutionary
prigramming methods, Journal of Material and Design, 28
(2007) 657-666.
[12] H. Oktem, T. Erzurumlu, H. Kurtaran, Application of
response surface methodology in the optimization of cutting
conditions for surface roughness, Journal of Material
Processing Technology 170 (2005) 11-16.
[13] M. Brezonick, M. Kovavic, M. Ficko, Prediction of
surface roughness with genetic programming, Journal of
Materials processing Technology 157-158 (2004) 28-36.
[14] I.N. Tansel, B. Ozcelik, W.Y. Bao, P. Chen, D.Rincon,
S.Y. Yang, A. Yenilmez, Selection of optimal cutting
conditions by using GONNS, International Journal of
Machine Tools & Manufacture 46 (2006) 26-35.
[15] P. Palanisamy, I. Rajendaran, S. Shanmugasundaram,
Optimization of machining parameters using genetic
algorithm and experimental validation for end-milling
operations, International Journal Advanced manufacturing
Technology (2007) 32: 644-655.
[5] Yang JL, and Chen JC, A systematic approach for
identifying optimum surface roughness performance in endmilling operation, Journal Industrial Technology (2001).
[6] H. Oktem, Tuncay Erzurumlu, and Fehmi Erzincanli,
Prediction of minimum surface roughness in end milling
mold using neutral network and genetic algorithm, Journal of
Material and Design, 27 (2006) 735-744.
[7] Uros Zuperl, and Franci Cus, Optimization of cutting
conditions during cutting by using neural networks, Journal
of Robotics and Computer Integrated Manufacturing 19
(2003) 189-199.
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