Comparison of Different Genetic Crossover operators for travelling salesman problem

Abstract

The travelling salesman problem (TSP) is the most well-known combinatorial optimization problem. TSP is used to find a routing of a salesman who starts from a home location, visits a prescribed set of cities and returns to the original location in such a way that the total distance travelled is minimized and each city is visited exactly once . This problem is known to be NP-hard, and cannot be solved exactly in polynomial time. Many exact and heuristic algorithms have been developed in the field of operations research (OR) to solve this problem . TSP is solved very easily when there is less number of cities, but as the number of cities increases it is very hard to solve, as large amount of computation time is required. The numbers of fields where TSP can be used very effectively are military and traffic. Another approach is to use genetic algorithm to solve TSP because of its robustness and flexibility . Some typical applications of TSP include vehicle routing, computer wiring, cutting wallpaper and job sequencing In genetic algorithms, crossovers are used as a main search operator for TSP. There were a lot attempts to discover an appropriate crossover operator. This paper presents the strategy which used to find the nearly optimized solution to these type of problems. It is the order crossover operator (OX) which was proposed by Davis, which constructs an offspring by choosing a subsequence of one parent and preserving the relative order of cities of the other parent.