A parallel variable neighborhood search for solving covering salesman problem

Covering salesman problem (CSP) is to construct a minimum length Hamiltonian cycle over a subset of vertices, in which the vertices not visited on the cycle must be covered by at least one visited vertex. In this paper, the CSP is reformulated as a bilevel CSP (BCSP) with a leader and a follower sub-problem. Two parallel variable neighborhood search (PVNS) heuristics, namely, synchronous “master–slave” PVNS and asynchronous cooperative PVNS, are proposed to solve the BCSP. To test the proposed algorithms, extensive computational experiments on the benchmark instances are performed, and the results indicate the effectiveness of the proposed approaches.