Havrda and Charvat Entropy Based Genetic Algorithm for Traveling Salesman Problem

The application of evolutionary computation techniques for the solution of combinatorial optimization problems is now the major area of research. Genetic algorithm (GA) is an evolutionary technique that uses crossover and mutation operators to solve such problems using a survival of fittest idea. The traveling salesman problem (TSP) is used as a paradigm for a wide class of problem having complexity due to the combinatorial explosion. TSP has become a target for the GA community, because it is probably the central problem in combinatorial optimization and many new ideas in combinatorial optimization have been tested on the TSP. When GA is applied to TSP, frequently encounter a trap of falling into a local optimal solution rather than a best approximate solution. This paper proposes Havrda and Charvat entropy based genetic algorithm for TSP to obtain a best approximate solution in reasonable time. Havrda and Charvat entropy is a measure of diversity of each population into the process of GA to solve the above-mentioned problem of falling into a local optimal solution. The TSP with 10 nodes is used to evaluate the performance of the proposed algorithm. In order to validate the results, TSPs with 20 and 30 nodes are considered to examine the versatility of the proposed algorithm. It has been observed that the proposed algorithm works effectively for different TSPs as compare to general GA. The results of this study are quite promising.