1. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm Sandeep Bhowmik Archana Jha Sukriti Sinha Department of Computer Science & Engineering, Hooghly Engineering & Technology College, Hooghly, India ICII 2012, 01-02 December, Kolkata, India

2.  Introduction Genetic Algorithm is one important Artificial Intelligence procedure. Based on the theory of natural selection and evolution. Application of GA is being examined in different field of Science and Technology. Search for approximate solutions in optimization problems where solution space is huge. We investigate the Mutation process of GA. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

3.  Introduction Search is for a chromosome that will disturb the arrangement of the elements (genes) the most. A chromosome of size N has been considered. Each element of the chromosome is an integer indicating the new position of the current genes in the chromosome. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

4. The fitness function of the chromosomes is calculated on the basis of the sum of total variation (length of displacement) of each gene. The objective is to maximize the fitness value so that when the chromosome is applied it can shuffle the arrangement of elements.  Introduction Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

5. In the permutation encoding mutation two frame of genes (having one or more chromosomes) will swap their place. We consider a frame of length F (>1). So two randomly generated positions at least has to be at a distance of F. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

6.  Our Goal Search for a good pattern. To analyze the effect of the size of frame in mutation. Performance has been analyses statistically in terms of Fitness value of the chromosomes. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

7.  Fitness function The fitness function evaluates the quality of the solutions. A displacement of an element (gene) in a string (chromosome) is the length it has been shifted from its original position. The fitness is the sum of displacement of all the genes in a chromosome. Selection allows chromosome with higher fitness to appear with higher probability in the next generation. Displacement of ‘A’ is (14-2) or 12 New index of ‘A’ is 14 Initial index of ‘A’ is 2 Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

8.  Key Selection 1.Randomly generate initial population of 100 chromosomes among N! options 2. Repeat until increase in fitness value stops for a sufficient no of generations 3. Repeat for 100 times (to populate new generation of 100 offspring) o Randomly selected 10 individuals from the current population o Calculate the fitness of each selected individual o Select the chromosome with the best fitness value o Breed new generation through mutation and give birth to new offspring o Select the better one between these two for the next generation 4. Select the best chromosome in terms of fitness from the final population. This selected chromosome is the ‘key’ in our encryption process. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

9. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India Frame sizes used in test cases test cases for different chromosomes.

10. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India Minimum and maximum fitness values achieved using different sizes of frame in mutation process with chromosomes of size 16 bytes.

11.  Relationship between Fitness values and Frame Size of chromosome. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

12. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India Minimum and maximum fitness values achieved using different sizes of frame in mutation process with chromosomes of size 24 bytes.

13.  Relationship between Fitness values and Frame Size of chromosome. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

14. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India Minimum and maximum fitness values achieved using different sizes of frame in mutation process with chromosomes of size 32 bytes.

15.  Relationship between Fitness values and Frame Size of chromosome. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

16.  Conclusion There is not much deviation in the fitness values of the generated chromosomes for frames of length up to one third the length of the chromosome. There is a sharp decrease in fitness afterwards. Permutation encoding mutation when performed by swapping two individual genes (ie. single gene mutation), gives the optimum fitness of the chromosomes. Effect of Modified Permutation Encoding Mutation in Genetic Algorithm ICII 2012, 01-02 December, Kolkata, India

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