A Hybrid Solution Method for the Multi-Service Location Set Covering Problem

The Multi-Service Location Set Covering Problem is an extension of the well-known Set Covering Problem. It arises in practical applications where a set of physical locations need to be equipped with services to satisfy demand within a certain area, while minimizing costs. In this paper we formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, apply the hybrid framework of the D-Wave quantum annealer to solve it, and investigate the feasibility of this approach. To improve the often suboptimal initial solutions found on the D-Wave system, we develop a hybrid quantum/classical optimization algorithm that starts from the seed solution and iteratively creates small subproblems that are more efficiently solved on the D-Wave but often still converge to feasible and improved solutions of the original problem. Finally we suggest some opportunities for increasing the accuracy and performance of our algorithm.