Two hybrid metaheuristic approaches for the covering salesman problem

Abstract

This paper addresses the covering salesman problem (CSP), which is an extension of the classical traveling salesman problem (TSP). Given a set of cities and a coverage radius associated with each one of them, the CSP seeks a Hamiltonian cycle over a subset of cities such that each city not in the subset is within the coverage radius of at least one city in the subset and that has minimum length among all Hamiltonian cycles over such subsets. To solve this problem, one has to deal with the aspects of subset selection and permutation. The CSP finds application in emergency and disaster management and rural healthcare. This paper presents two hybrid metaheuristic approaches for the CSP. The first approach is based on the artificial bee colony algorithm, whereas the latter approach is based on the genetic algorithm. Both the approaches make use of several new first improvement or best improvement based local search strategies defined over various neighborhood structures. Computational results on a wide range of benchmark instances demonstrate the effectiveness of the proposed approaches. We are able to improve the best known solution values on majority of the large instances.