Solving Travelling Salesman Problem Using Greedy Genetic Algorithm GGA

Abstract

Abstract-Travelling Salesman Problem represents a class of problems in computer science. This problem has many application areas in science and engineering. Genetic Algorithm is used to solve these problems and the performance of genetic algorithm depends on its operators. In this paper new greedy genetic algorithm has been proposed to solve TSP. The proposed greedy genetic algorithm is applied and tested on some standard TSP problems; the obtained results are compared with existing methods and found better in terms of path length. The proposed greedy genetic algorithm search deeper in the search space and find better solutions as compared to existing algorithms. The proposed algorithm finds solutions which are approximately 5% better than the existing algorithm.Keyword-Travelling Salesman Problem, Genetic Algorithms, Greedy Approach I. INTRODUCTION Travelling Salesman Problem (TSP) is a well-known problem in computer science. It has many application areas in science and engineering. In TSP a hypothetical salesman has to visit a set of cities. Salesman start the journey from a city and visit each and every city exactly once. As the number of cities increases the number of possible paths also increases and the complexity of algorithm becomes n! if there are n cities. Evolutionary techniques such as Genetic Algorithm, PSO are very popular methods for solving NP-Complete and NP-Hard problems. In literature work has been done in solving Travelling Salesman Problem using Genetic Algorithm. Mei Mi et.el.[1] Proposed Liuhai cross over which includes the best individual preservation policy. Author generates the initial population using greedy approach. To generate the initial population, any city is selected randomly and then the remaining cities are selected according to the nearest neighbor approach. Author also selects the excellent chromosome to participate in the cross over. Shakeel Arshad, and Shengxiang Yang [2] try to solve TSP. Author divided the procedure into two phases. In phase 1 author uses SBGA technique. SBGA generate the initial population first and then uses embedded sequence based ordered cross over (e-SBOX) to generate new children. E-SBOX further uses SBLS to perform cross over. Phase 2 perform the modified inner over cross over algorithm. This phase perform restricted inner over with partial random initialization to generate new children with better fitness. Oliviu Matei and Petrica Pop [3] proposed a solution using GA for generalized travelling salesman problem. The proposed GA uses steady state approach. The chromosomes enter into the population as soon as they are produced and inferior chromosomes are removed from the population. Equal number of chromosome leave the population and equal number of chromosome enter into the population and the count or size of the population remains the same. The algorithm will make cluster of chromosomes. Ren Shuai, Wang Jing, Xuejun Zhang [4] proposed a genetic algorithm based solution for travelling salesman problem. The author perform the genetic operations in ...

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