The Complete Subtour Order Crossover in Genetic Algorithms for Traveling Salesman Problem Solving

Abstract

The traveling salesman problem (TSP) is one of many well-known combinatorial problems. TSP could be ex-plained as difficulty of finding the shortest distance to travel from the first city, via all cities, and then return to the starting point. Among the standard problems, TSP is often used for de-termining the efficiency of new algorithms. One of the successful algorithms for TSP solving is the genetic algorithm (GA). The key mechanism for GA efficiency for solution finding is the crossover operator. Many studies have suggested new crossover or even improved previous methods to solve TSP including other related problems. Nevertheless, the solution quality is the foremost factor. This paper proposes Complete Subtour Order Crossover (CSOX) for GA to search the solution for TSP. CSOX employs the Order crossover (OX) principle and expands the crossover to mainly cover the parts of the quality solution. Notably, one operation can generate six new solutions. This outcome increases the variety of solutions to the problem and the quality while lowering computing times. From three studies, five types of crossover operators are compared with CSOX. The summarized results from the experiments revealed that CSOX outperforms all in terms of solution quality and good computing times quality.