Self-Crossover and Its Application to the Traveling Salesman Problem

Abstract

Crossover is an important genetic operation that helps in random recombination of structured information to locate new points in the search space, in order to achieve a good solution to an optimization problem. The conventional crossover operation when applied on a pair of binary strings will usually not retain the total number of 1’s in the offsprings to be the same as that of their parents. But there are many optimization problems which require such a constraint. In this article, we propose a new crossover technique called, “self-crossover”, which satisfies this constraint as well as retains the stochastic and evolutionary characteristics of genetic algorithms. We have also shown that this new operator serves the combined role of crossover and mutation. We have proved that self-crossover can generate any permutation of a given string. As an illustration, the effectiveness of this new operator has been demonstrated in solving the traveling salesman problem (TSP) using GA. This new technique is best suited for path representation of tours and performs better for TSP with large number of cities. Performance of the proposed scheme is compared with that of ordered crossover (OC) scheme.