Improving variable neighborhood search to solve the traveling salesman problem

• Published in: Applied soft computing Vol. 68; pp. 83 - 91
• Main Authors: Hore, Samrat, Chatterjee, Aditya, Dewanji, Anup
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2018
• Subjects: Cost matrix; Hybrid VNS; Near-optimal solution; Neighborhood structure; Stopping rule; Hybrid VNS; Stopping rule; Cost matrix; Near-optimal solution; Neighborhood structure
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2018.03.048

•The ability to solve the traveling salesman problem (TSP), in a computationally efficient way, is often considered to be the benchmark of any optimization algorithm.•An improvement in the variable neighborhood search (VNS) algorithm with a stochastic approach has been suggested. This algorithm is named as hybrid VNS algorithm.•The proposed algorithm can deal both the symmetric and asymmetric TSPs with equal efficiencies.•At some instances the proposed algorithm shows better solution than what is available in the TSPLIB data set.•The algorithm can solve various other problems in statistics, computer science and telecommunications. 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.