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Among various machining process, Wire Electrical Discharge Machining is an important one, which have many features. The cutting parameters Gap Voltage, Wire feed, Pulse on time and Pulse off time are taken as input parameters. Rest of the parameters like Dielectric fluid pressure, wire speed, wire tension, resistance and cutting length are fixed. The surface roughness and kerf width are simultaneously optimized. This study presents a multi-objective optimization technique, based on genetic algorithms. The experiments were performed based on Taguchi's L-16 Orthogonal array.Full experiments were conducted with various combinations of Gap Voltage, Wire feed, Pulse on time and Pulse off time. Surface roughness and Kerf width for different conditions were obtained. The relation between the input and output parameters has been found by non-linear regression analysis using SPSS Software. An optimal parameter combination was obtained by using genetic algorithm based on multi objective function optimization.
Wire EDM is an electro-erosion machining process. The materials are removed by using repetitive spark cycle between the tool and workpiece. In Wire EDM machining,a high electric discharge is created in the tool wire. When the voltage across the gap becomes sufficiently large, the high power spark is produced. So the dielectric breakdown occurs. Thousands of sparks produced per seconds across the gap. Which causes increase in temperature about 10,000 degree Celsius. At high temperature and pressure, the work piece metal is melted, eroded and vaporised. In this way the material is removed from workpiece. A non-conductive dielectric fluid is supplied continuously to prevent the shorting out of created electric discharge. The dielectric fluid supplied is utilised for flushing out of removed material from the workpiece table. To conduct the sixteen experiments, brass wire of 0.25mm diameter is used as the tool-electrode and Stainless Steel is used as the work material for the present experiment. The composition of the working material has been tested and listed in the Table 1.
Table 1, Chemical Compositionof Titanium
Chemical Composition Wt%
Up to 0.08
Up to 2.00
Up to 0.75
Up to 0.030
Up to 0.045
8.00 - 10.50
18.00 - 20.00
Design of experiments based on Taguchi L-16 Orthogonal Array:
The process parameters and the selection of level for the process parameters were determined based on the machine tool, cutting tool and work piece capabilityand are listed in Table 2. There are 256 combinations of process parameter in four levels. Taguchi L-16 Orthogonal Array is used as aDesign of experiments which is used to reduce the number of experiments needed to be performed.
Table 2, Machining parameters and their levels
Pulse ON time (Ton)
Pulse OFF time (Toff)
In this study, Taguchi method, a powerful tool in parameter design of performance characteristics, was used to determine optimal machining parameters for minimum Surface Roughness in Wire EDM. Taguchi proposed to acquire the characteristic data by using orthogonal arrays, and to analyse the performance measure from the data to decide the optimal process parameters. This method uses a special design of orthogonal arrays to study the entire parameter space with small number of experiments only. In this study, four machining parameters were used as control factors and each parameter was designed to have four levels (Table 2).
Genetic Algorithm Optimization:
Genetic Algorithms are a part of evolutionary computing, inspired by Darwin's theory about evolution. Genetic Algorithms was introduced by John Holland at University of Michigan in the United States in the 1970's. Genetic Algorithms only suitable for mixed (continuous and discrete), combinatorial problems.
Genetic Algorithm needs solution to the problem as a genome (chromosome). Genetic Algorithm is beginning with a set of solutions (chromosomes) called population. New population is formed by using result of previous population to the fitness which are used to form new solution. These solutions are applied to genetic operators such as mutation and crossover to evolve the solutions in order to find the best result. The flow process of Genetic Algorithm is shown in Fig 1.
The three important facts to use genetic algorithms are:
Definition of the objective function
Definition and implementation of the genetic representation
Definition and implementation of the genetic operators
Fig 1, Genetic Algorithm Flow Chart
AÂ fitness functionÂ is a particular type ofÂ objective functionÂ that is used to summarize, as a single figure, how close a given design solution is to achieving the set aims. In this present research, two fitness functions are used in order to get the optimum results in both surface roughness and kerf width.
f1 = 2.057*(TON-0.046)*( TOFF0.020)*(WF-0.038)*(GV0.062) 
f2 = 0.397*(TON-0.011)*( TOFF-0.019)*(WF-0.013)*(GV-0.052) 
Generation of the initial populations:
The first step in genetic algorithms is generation of individual for initial population. There are two population must be created (i.e. static and dynamic). The values of decision variable for each individual in both populations are selected from given valid range. The restriction is given by equation.
x1 = rand(TON) : TON MIN â‰¤ TON â‰¤ TON MAX 
x2 = rand(TOFF) : TOFF MIN â‰¤ TOFF â‰¤ TOFF MAX 
x3 = rand(WF) : WFMIN â‰¤ WF â‰¤ WFMAX 
x4 = rand(GV) : GVMIN â‰¤ GV â‰¤ GVMAX 
The code string is formed by encoding the values of each three individuals. The code strings are called chromosome, it composed of binary digits (0 or 1) and 96 characters (32 foreach decision variable).
Chromosome contains information about solution. So chromosome should be in proper manner. In encoding method chromosome can changed into different form (i.e. corresponding to that method). In this present research, Binary encoding has been chosen because it gives many possible chromoses even with a small number of alleles than others.
Chromosomes are selected from population. Best chromosome should be selected. Tournament selection is chosen as a selection Method.
Randomly select 2 individuals from the population with equal probabilities (p=1/N).
Place a copy of the fittest individual in themating pool
After the selection of encoding method, we can make a step to a crossover. In crossover Genes are selected from the parents and creates new off springs. Crossover is done by choosing some random points in parent chromosome than interchange everything after the random point between parents.
Example of crossover (| - Random point)
Chromosome 1 - 10001|00100110110
Chromosome 2 - 11011|11000011110
Offspring 1 - 10001|11000011110
Offspring 2 - 11011|00100110110
Mutation take place only after crossover is finished. Mutation randomly changes the new offspring which is formed in crossover stage. Mutation is done by inverting the selected digit (i.e.0 into 1 & 1into 0) because binary encoding is selected. Mutation is mainly depends on crossover and encoding because if we choose permutation encoding, the mutation could be changed two genes.
Example for Mutation:
Original offspring 1 - 1101111000011110
Original offspring 2 - 1101100100110110
Mutated offspring 1 - 1100111000011110
Mutated offspring 2 - 1101101100110100
Creation of new population:
New population will be created at the end of evolutionary period based on result of current evolution process. The evolutionary process is repeated until maximum number of evolution process is achieved.
Population size = 10
Number of generations = 1000
Crossover probability = 80%
Mutation probability = 0.5%
Result and discussion:
In this research, an multi objective function is used in the genetic algorithm to optimize the process parameters in order to obtain the optimum results for both the surface roughness and the kerf width. The coding written to solve the problem in Matlab is given below.
TOFF = x(2);
WF = x(3);
GV = x(4);
f(1) = 0.397*(TON-0.011)*( TOFF-0.019)*(WF-0.013)*(GV-0.052)
f(2) = 0.397*(TON-0.011)*( TOFF-0.019)*(WF-0.013)*(GV-0.052)
By using GAMulti Objective tool, the above problem has been solved. From the 3 set of best results, the optimum results has been considered as desired value. The results obtained from the GA are tabulated in table 5.
Experimental investigation on wire electrical discharge machining of SS304 has been done. The process parameters has been optimized using Multi Objective function based Genetic Algorithm as an optimization technique. The optimum input parameter combinations to get the minimum Surface Roughness and Kerf Width are 53.691V Gap Voltage, 7.982mm/min Wire Feed, 9.864Âµs Pulse ON Time, 9.346Âµs Pulse OFF Time.