A general variable neighborhood search algorithm for the k-traveling salesman problem

Abstract

This paper addresses a variant of the traveling salesman problem, i.e., k-traveling salesman problem (k-TSP). Given a set of n cities and a fixed value 1 < k ≤ n, the k-TSP is to find a minimum length tour by visiting exactly k of the n cities. The k-TSP is a combination of both subset selection and permutation characteristics. In this paper, we have proposed a general variable neighborhood search algorithm for the k-TSP. A variable neighborhood descent consisting of two neighborhood structures is used as local search in our approach. To the best of the authors knowledge, this is the first metaheuristic approach for the k-TSP. Moreover, to present the computational experiments, a set of benchmark instances is generated by using the standard TSPLIB.