A general variable neighborhood search for solving the uncapacitated r-allocation p-hub maximal covering problem

This paper deals with the uncapacitated r-allocation p-hub maximal covering problem (UrApHMCP) with binary coverage criterion. This problem consists of choosing p hub locations from a set of nodes so as to maximize the total demand covered while satisfying the r-allocation strategy. The applied binary coverage criterion ensures that the distance between any origin-destination pair through located hubs should be shorter than a predetermined distance. An integer linear programming model for the considered problem is introduced. As a solution method to UrApHMCP, a General Variable Neighborhood Search (GVNS) heuristic is proposed. A greedy procedure is used to construct an initial solution to GVNS. Neighborhood structures explored within the GVNS are defined by operators that change a set of chosen hubs and node to hub assignments. Variable Neighborhood Descent with sequential search strategy is used as an improvement procedure. The results of computational experiments on standard p-hub benchmark instances show the efficiency and effectiveness of the proposed GVNS when solving the considered problem.