Solving Symmetric and Asymmetric Traveling Salesman Problems Through Probe Machine with Local Search

Abstract

Combinatorial optimization problems emerge extensively in the different fields and traveling salesman problem (TSP) is certainly one of the most representative and hardest (i.e., NPC) combinatorial optimization problems. In this paper, we propose a dynamical route construction algorithm to solve both symmetric and asymmetric TSP’s, which uses probe concept to generate the better routes step by step. Specifically, a reasonable value of filtering proportion is set in each step such that the worst routes are filtered out. On the other hand, a set of local search operators are further implemented on the retained routes for their variations and improvements. Actually, our proposed algorithm is tested on various TSP instances taken from TSPLIB and compared with the best-known results reported by the data library as well as the other four recent state-of-the-art algorithms. It is demonstrated by the experimental results that our proposed algorithm can achieve the best results in certain cases and generally get the results close to the best-known results within a reasonable period of time. In addition, the proposed algorithm outperforms in some cases and obtains superior results than the best-known results, and even performs better than the recent state-of-the-art algorithms.