Assessing Different Crossover Operators for Travelling Salesman Problem

Abstract

Many crossover operators have been proposed in literature on evolutionary algorithms, however, it is still unclear which crossover operator works best for a given optimization problem. In this study, eight different crossover operators specially designed for travelling salesman problem, namely, Two-Point Crossover, Partially Mapped Crossover, Cycle Crossover, Shuffle Crossover, Edge Recombination Crossover, Uniform Order-based Crossover, Sub-tour Exchange Crossover, and Sequential Constructive Crossover are evaluated empirically. The select crossover operators were implemented to build an experimental setup upon which simulations were run. Four benchmark instances of travelling salesman problem, two symmetric (ST70 and TSP225) and two asymmetric (FTV100 and FTV170), were used to thoroughly assess the select crossover operators. The performance of these operators was analyzed in terms of solution quality and computational cost. It was found that Sequential Constructive Crossover outperformed other operators in attaining 'good' quality solution, whereas Two-Point Crossover outperformed other operators in terms of computational cost. It was also observed that the performance of different crossover operators is much better for relatively small number of cities, both in terms of solution quality and computational cost, however, for relatively large number of cities their performance greatly degrades.