COMPARATIVE STUDY OF SELECTION METHODS IN GENETIC ALGORITHM

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1 COMPARATIVE STUDY OF SELECTION METHODS IN GENETIC ALGORITHM 1 MANSI GANGWAR, 2 MAIYA DIN, 3 V. K. JHA 1 Information Security, 3 Associate Professor, 1,3 Dept of CSE, Birla Institute of Technology, Mesra Ranchi, Jharkhand, India 2 Scientific Analysis Group Lab, Defence Research Development Organization New Delhi India 1 mansigangwar18@gmail.com, 2 anuragimd@gmail.com, 3 vkjha@bitmesra.ac.in Abstract - Genetic algorithm is a directed random search technique, based on mechanics of natural selection and natural genetics. Genetic algorithm can find the global optimal solution in complex multi-dimensional search space. This paper mainly compares the various selection techniques, which is the most critical step in GA. Selection is based on fitness value; higher the fitness value more chance of selection for next Keywords - Genetic algorithm, Fitness proportionate Selection, Steady State Selection, Rank Selection, Truncation Selection, Tournament Selection, Hybrid Selection. I. INTRODUCTION Genetic Algorithm (GA) are optimization search algorithms proposed by John Holland in the early 1970s [1][2]. GA is used to solve problems for which there are no satisfactory solution exists. It is also described as a directed random search technique, based on mechanics of natural selection and natural genetics. Genetic algorithms are inspired by Survival of fittest theory which is Darwin's theory of evolution. Basically, GA begins with a set of solutions (represented by chromosomes) called Solutions are taken from the one population and used to form a new generation by keeping the fact, that new generation is better than older ones. The new solution is selected based upon the fitness value (higher the fitness value will have more chance of selection).this is repeated until some suitable condition is satisfied or termination condition occurred. The Basic Fundamental steps of GA are: 1. Define the problem variable domain as chromosome of a fixed size; choose the size of the chromosome population as N, set the crossover probability pc and the mutation probability pm. 2. For measuring the performance, or fitness of chromosome in problem domain set a fitness function f(x). The fitness function establishes the basis for selecting chromosomes that will be required during reproduction. 3. Randomly generate an initial population of chromosomes of size N: X 1, X 2 X 3 X n. 4. Calculated the fitness of each individual chromosome in every generation. 5. Select a pair of chromosomes for reproducing the new Parent chromosomes are chosen mainly with the probability related to their fitness value. High fitness valued chromosomes have a higher probability of being selected for reproduction than less fitness chromosomes. 6. New chromosomes are selected by applying the genetic operators: crossover and mutation, crossover takes the two parent value from crossover point and mutate (flip of one bit) in mutation. 7. Replace the newly generated chromosomes in the older 8. Repeat Step 5 until the size of the new chromosome population becomes equal to the size of the initial population, N. 9. Replace the initial chromosomes in the population with the newly generated 10. Go to Step 4, and repeat the process until some termination criterion is satisfied and returning the best solution to the Fig.1.Basic Flowchart of Genetic Algorithm So, with the three primary genetic operators: selection, crossover, mutation new population is 11

2 being generated from an older The GA uses a measure of fitness value of individual chromosomes to carry out reproduction. As reproduction takes place, the crossover operator exchanges parts of two single chromosomes to create new chromosomes, and the mutation randomly selects the location in a chromosome to flip the gene value in chromosomes [3]. This paper mainly forces on the various selection operators and based on these selection operators how the new population is generated. The selection criteria are fundamentally based on survival of fittest chromosomes. There are many methods how to select the best chromosomes. For example, Roulette wheel selection, Proportionate selection, Rank selection, Truncation Selection, Tournament selection, Steady state selection and some others. II. SELECTION METHODS In selection method, each chromosome for reproduction is chosen according to the fitness value. Each chromosome is selected depending on the own fitness value and the fitness value of all the other chromosomes fitness value of every chromosome and based on these fitness value they will have reproduction probability. Following terms are used to select the different selection techniques: 1. Selective pressure: Comparing the probability of best chromosome with the average probability of the entire chromosome in that 2. Selection intensity: On applying selection method on normalized Gaussian distribution we will get the expected average fitness value of the 3. Selection variance: On applying selection method on normalized Gaussian distribution we will get the expected variance fitness value of the 4. Loss of diversity: It provides the proportion of chromosomes that are not selected in the selection phase. 5. Bias: The essential absolute difference between normalized fitness value of chromosome and its expected probability of reproduction. 6. Spread: It provides the exact range of possible value for the number of offspring of a chromosome in that 7. Loss of diversity: Proportion of a chromosome of a population which are selected not during the selection phase. 2.1 FITNESS PROPORTIONATE SELECTION Fitness Proportionate Selection is the most prominent ways of selecting a parent. In this, every individual will get a chance to become a parent with a probability which is proportional to their fitness 12 value. Therefore, the higher fitness value is selected and will be propagated to the next generation. Such a selection method applies a selection pressure to the fitter chromosome in the population, evolving better chromosome over time [5]. Consider a circular wheel. The wheel is divided into n pieces, where n is the number of chromosomes in the Each chromosome gets a fragment of the circle which is proportional to its fitness value. Two implementations of fitness proportionate selection method are: ROULETTE-WHEEL SELECTION In a roulette wheel selection method, a circular wheel is there as described above. A fixed point is also there for selecting different chromosome which is on the circumference of the wheel. For selecting first parent, the region of the wheel which comes in front of fixed point is selected. For the second parent, the same process will be repeated. It is clear that a fitter individual which has a greater area on the wheel will have a greater chance of arriving in front of the fixed point when the wheel is rotated. Therefore, the probability of choosing an individual depends directly on its fitness value. So, by considering the below example as the fitness value of chromosome 4 is highest will have more chance of selection than the other chromosomes, and the chromosome 3 have very rare or no chance of selection. Fig.2. Roulette Wheel Approach Following algorithm perform the working of Roulette wheel: 1. Calculate the sum of all the chromosome fitness in population; sum S. 2. Generate random number in the interval (0, S) - r. 3. Going through the population and sum fitness from (0 - sum s). When the sum S is greater than r, stop and return the chromosome where you are.

3 4. Step 1 is performed for each population only once for selecting every new entire roulette wheel then the other chromosomes will have very rare chances of selection [1][3] STOCHASTIC UNIVERSAL SAMPLING Stochastic Universal Sampling is approximately same to the Roulette wheel selection. The only difference is that instead of having just one fixed point, we have multiple fixed points as shown in the following image. Therefore, all the parents are randomly chosen in just one spin of the wheel according to the fitness value. Also, such a setup encourages that the highly fittest chromosome is selected at least once in a spin [6][7]. The below figure, explains the stochastic universal sampling, portion of the wheel is divided according to the fitness value of each chromosome. Instead of one fixed point, there are two fixed point for selecting chromosome for the reproduction. Considering the example wheel is rotated once, Chromo A and chromo D is selected. In this case, there is more chance that higher fitness valued chromosome will likely to be selected among the two chromosomes in the one spin. Table 1: Fitness value of Different Chromosomes Fig.4. Ranking Selection Rank selection method firstly sorts the chromosomes according to their fitness Value and provide them ranking based on that. The worst chromosome in population will have fitness 1, second worst fitness 2 and so on and the best have fitness N. But this method can lead to slower convergence because the best chromosomes do not differ so much from other chromosomes because of their nearly approximate values. But it is more robust than any other methods because it provides uniform scaling across the whole population and it also overcomes the premature convergence [8]. Considering the following example: Fig.3. Stochastic Universal Sampling It is likely to be noted that fitness proportionate selection methods doesn t work for cases where the fitness is negative valued. 2.2 RANK SELECTION Roulette wheel selection method will not provide the significant result when the fitness values have the large difference in between them. For Example: If the best chromosome fitness acquires the 90% of the Table 2: Evaluation of Next Generation Based on Rank Selection Method 2.3 TRUNCATION SELECTION In truncation selection method chromosomes are sorted according to their fitness value. Only the best chromosomes are selected as parents for the new population [8][1]. Trunc (Truncation threshold) is the main parameter for truncation selection. It indicates 13

4 the specified proportion of the population to be selected as parents and takes values ranging from 50%-10%. Individuals below the Trunc do not produce new population and they are discarded. The term selection intensity is often used in truncation selection process. 2.4 TOURNAMENT SELECTION Tournament Selection is among the most widely used selection method in evolutionary algorithms. It works well for a wide range of problems, it can be implemented efficiently, and it is amenable to parallelization [2][5]. survive to next reproduction too. It works in the following way: In every new population few good chromosomes are selected to create new chromosomes, these good chromosomes are selected on the basis of their fitness value. So, higher fitness value chromosomes are selected and some of the bad chromosomes are removed these are ones who have less fitness value. So, these chromosomes are removed from the matting pool, and replaced by the new chromosome which has higher fitness value. Example: At its simplest form tournament selection involves randomly selecting the two individuals from the population and performing a tournament to determine which one will get selected. It just involves generating a random value between zero and one and comparing it to a pre-determined selection probability. If the random value is less than or equal to the selection probability, than the fitter candidate is selected, otherwise the weaker candidate is chosen. The probability parameter provides a convenient mechanism for adjusting the selection pressure, and it is always set to be greater than 0.5 in order to get fitter candidates. The tournament can be extended to involve more than two individuals if desired [8]. Below figure provides the working of tournament selection method, in which the tournament is held between the different chromosomes (competitors) as: V, W, X, Z. W wins the whole tournament (tournament winning is decided according to the fitness value) and therefore it is added to the reproduction. Fig.6. Steady State Selection 2.6 HYBRID SELECTION In order to make the selection more strong and to have stronger population for future generation we can hybrid two methods: Roulette wheel and Truncation method. According to this, we will perform the Trunc function before performing the roulette wheel. Firstly, we will Trunc population according to Truncation method by adding a threshold and on that limited population we will perform the roulette wheel selection. So, this will help us to completely remove the chromosomes in the population which will have less fitness value. ACKNOWLEGEMENTS This research was provisioned by Defence research and development organization and Birla institute of Technology. We are obliged to Sc. Tejpal for sharing her pearls of wisdom with us during the course of this research. CONCLUSION Fig.5. Tournament Selection 2.5 STEADY STATE SELECTION Steady state is not only a method for selecting parents for next generation [1][3]. Main idea of this selection is that higher fitness values chromosomes should In this paper, we have concluded various selection methods for Genetic Algorithms to find the fittest chromosome for the next generation rather selecting the weaker chromosome with the less fitness value. According to above discussed selection methods, Tournament selection is better because it gives the best chromosomes to fight in the tournament and every time the higher fitness valued chromosome is selected. So, it will provide the convergence rate compared to other selection methods and also have better time complexity. Below table gives the 14

5 complexity of selection method that we have discussed. Table 3: Complexity of Various Selection Techniques REFERENCES [1] Sivaraj, R., and T. Ravichandran, A Review of Selection Methods in Genetic Algorithm. International Journal of Engineering Science & Technology 3.5 (2011). [2] Anshul Sharma and Anuj Mehra, Review Paper of Various Selection Method. International Journal of Advanced Research in Computer Science and Software Engineering, vol 3, Issue 7, July [3] Anupriya Shukla, Hari Mohan Pandey and Deepti Mehrotra, Comparative Review of Selection Techniques In Genetic Algorithm. IEEE conference, [4] David E. Goldberg and Deb Kalyanmoy, A comparative analysis of Selection Schemes used in genetic algorithms. Urbana (1991): [5] Baker and James Edward, Adaptive selection methods for genetic algorithms. Proceedings of an International Conference on Genetic Algorithms and their applications(1985). [6] Ali, Elnims and Elgasim Elamin, A proposed genetic algorithm selection method. (2006). [7] David E. Goldberg, Genetic algorithm in search, optimization, and machine learning. (1989). [8] Melanie Mitchell, An introduction to genetic algorithm. prentice Hall of India, New Delhi, ISBN ,