Improving variable neighborhood search to solve the traveling salesman problem

Abstract

The traveling salesman problem (TSP) is one of the classical combinatorial optimization problems and has wide application in various fields of science and technology. In the present paper, we propose a new algorithm for solving the TSP that uses the variable neighborhood search (VNS) algorithm coupled with a stochastic approach for finding the optimal solution. Such neighborhood search with various other local search algorithms, named as VNS-1 and VNS-2, has been reported in the literature. The proposed algorithm is compared in detail with these algorithms, in the light of two benchmark TSP problems (one being symmetric while the other is asymmetric) suggested in the TSPLIB dataset in programming language R, along with two asymmetric problems obtained through simulation experiment. The present algorithm has been found to perform better than the conventional algorithms implemented in R for solving TSP's, and also, on an average, found to be more effective than the VNS-1 and the VNS-2 algorithms. The performance of the proposed algorithm has also been tested on 60 benchmark symmetric TSPs from the TSPLIB dataset. Apart from solving the TSP, the flexibility of the proposed hybrid algorithm to solve some other optimization problems related to other disciplines has also been discussed.