Fourier descriptors for 2-Opt and 3-Opt heuristics for traveling salesman problem

Abstract

This study provides speedup of the 2-Opt and 3-Opt processes by a new method based on Fourier descriptors (FDs) for the planar traveling salesman problem. By treating the planar tour as a closed contour, the proposed FD-based method, which is used as a potential swap identification function (PSIF), can limit the search space of 2-Opt/3-Opt by identifying the potential swap points/cities. In this article, approximate versions of the 2-Opt and 3-Opt procedures are adopted to investigate the performance of proposed PSIF. The experimental results using the proposed PSIF to reinforce the 3-Opt procedure show that the proposed method provides good quality solutions and faster computation.