The path cover problem: Formulation and a hybrid metaheuristic

Abstract This paper introduces the path cover problem (PCP) that is a variant of the capacitated vehicle routing problem (CVRP). In contrast to CVRP, a vehicle route in PCP involves a set of vertex-disjoint paths where a vehicle starts at a customer and finishes at another customer without traveling to the depot. PCP is defined to find a set of service paths to serve a set of customers that aiming to minimize the total traveling cost and hiring cost. This paper develops a hybrid approach that integrates variable neighborhood search (VNS) and tabu search (TS) to solve the problem. This algorithm presents an approach to explore the solution space by utilizing multi-set neighborhood and applying the systematic changing neighborhood of VNS. TS is incorporated into the algorithm to guide the search toward diverse regions. The computational results indicate that the proposed algorithm efficiently solves PCP.