A matheuristic for locating obnoxious facilities

Abstract

Facilities such as waste plants or wind turbines are often referred to as obnoxious facilities because they negatively affect their nearby environment, for example, through noise or pollution. In the obnoxious p-median problem, a set of clients and a set of potential locations for obnoxious facilities are given. From the set of potential locations, p facilities must be opened. The goal is to place the facilities far away from the clients to avoid high negative effects. Existing approaches for this planning problem are either not scalable to large instances or not flexible in considering practical constraints that often arise in real-world settings. To address these limitations, we propose a matheuristic for the obnoxious p-median problem. First, the matheuristic generates diverse initial solutions, allowing an effective exploration of the solution space. Second, it iteratively improves these initial solutions using enhanced mathematical models. We additionally propose a clustering-based scaling technique to tackle large instances. Thus, our matheuristic is scalable to instances involving thousands of clients and potential locations and is flexible to incorporate practical constraints. Our computational results show that our matheuristic outperforms the leading metaheuristics from the literature on large instances and is competitive with the leading metaheuristics on small and medium instances. The features of our matheuristic can be generalized and applied to related planning problems.