The application of ant colony optimization in the solution of 3D traveling salesman problem on a sphere

Abstract

Traveling Salesman Problem (TSP) is a problem in combinatorial optimization that should be solved by a salesperson who has to travel all cities at the minimum cost (minimum route) and return to the starting city (node). Todays, to resolve the minimum cost of this problem, many optimization algorithms have been used. The major ones are these metaheuristic algorithms. In this study, one of the metaheuristic methods, Ant Colony Optimization (ACO) method (Max-Min Ant System – MMAS), was used to solve the Non-Euclidean TSP, which consisted of sets of different count points coincidentally located on the surface of a sphere. In this study seven point sets were used which have different point count. The performance of the MMAS method solving Non-Euclidean TSP problem was demonstrated by different experiments. Also, the results produced by ACO are compared with Discrete Cuckoo Search Algorithm (DCS) and Genetic Algorithm (GA) that are in the literature. The experiments for TSP on a sphere, show that ACO’s average results were better than the GA’s average results and also best results of ACO successful than the DCS.

Keywords

• Ant colony optimization
• Metaheuristic
• Spherical geometry
• Max-Min Ant System
• nonEuclidean TSP