A Heuristic Algorithm Based on Tour Rebuilding Operator for the Traveling Salesman Problem

TL;DR

This paper introduces a heuristic algorithm with a novel tour rebuilding operator for the Traveling Salesman Problem, achieving faster convergence and better solutions than existing methods on standard benchmarks.

Contribution

The paper presents a new tour rebuilding operator that enhances heuristic algorithms, leading to improved solution quality and convergence speed for TSP.

Findings

Best known solutions refreshed for 22 instances

Best solutions obtained for 18 instances

Algorithm demonstrates rapid convergence and strong global search ability

Abstract

TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate algorithms become the research focus and can be further divided into two types, tour construction algorithms and tour improvement algorithms. Researches show that the latter type of algorithms can obtain better solutions than the former one. However, traditional tour improvement algorithms have shortcomings. They converge very slowly and tend to be trapped in local optima. In practice, tour construction algorithms are often used in initialization of tour improvement algorithms to speed up convergence. Nevertheless, such a combination leads to no improvement on quality of solutions. In this paper, a heuristic algorithm based on the new tour rebuilding operator is proposed. The algorithm features rapid convergence and powerful global search. In the experiments based on 40 instances in TSPLIB, the best known solutions of 22 instances are refreshed by the proposed method. Meanwhile, the best known solutions of the other 18 instances are obtained.