Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator.

Abid Hussain,Alaa Mohamd Shoukry,Yousaf Shad Muhammad,Showkat Gani,M Nauman Sajid,Ijaz Hussain

doi:10.1155/2017/7430125

Abstract

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements.

Highlights

Genetic algorithms (GAs) are derivative-free stochastic approach based on biological evolutionary processes proposed by Holland [1]
We proposed a new crossover operator for traveling salesman problem (TSP) which is moved within two selected parents as previous cycle crossover operator
We perform the proposed crossover operator CX2 along two traditional crossover operators PMX and OX on twelve benchmark instances which are taken from the TSPLIB [28]

Summary

Introduction

Genetic algorithms (GAs) are derivative-free stochastic approach based on biological evolutionary processes proposed by Holland [1]. Over the last three decades, TSP received considerable attention and various approaches are proposed to solve the problem, such as branch and bound [6], cutting planes [7], 2-opt [8], particle swarm [9], simulated annealing [10], ant colony [11, 12], neural network [13], tabu search [14], and genetic algorithms [3, 15,16,17].

Crossover Operators for TSP

Proposed Crossover Operators

Computational Experiments and Discussion

Results

Conclusion