A highly effective hybrid evolutionary algorithm for the covering salesman problem

Abstract

Abstract Covering salesman problem (CSP) is an extension of the popular traveling salesman problem (TSP) arising from a number of real-life applications. Given a set of vertices and a predetermined coverage radius associated with each vertex, the goal of CSP is to find a minimum cost Hamiltonian cycle across a subset of vertices, such that each unvisited vertex must be within the coverage radius of at least one vertex included in the tour. For this NP-hard problem, we present a highly effective hybrid evolutionary algorithm (HEA) that integrates a crossover operator based on solution reconstruction, a destroy-and-repair mutation operator to generate multiple distinct offspring solutions, and a two-phase tabu search procedure to seek for high-quality local optima. Another distinguishing feature of HEA is the use of the Lin–Kernighan TSP heuristic to find an improved node sequence of a CSP tour during multiple stages of HEA. Extensive experiments on a large set of benchmark instances show that the proposed approach is able to surpass the current best-performing CSP heuristics. In particular, it reports new upper bound (improved best-known solution) for 21 out of the 27 large instances, while matching the best-known result for the remaining small and medium instances. In addition to CSP, the proposed HEA is adapted to solve the generalized covering traveling salesman problem (GCTSP). Extensive experimental results on the GCTSP benchmark disclose that the proposed adaptation of HEA outperforms all the existing GCTSP heuristics from the literature.