Metaheuristic methods for solving the Bilevel Uncapacitated Facility Location Problem with Clients' Preferences

In this study, we consider a variant of the Bilevel Uncapacitated Facility Location Problem (BLUFLP) in which the clients choose suppliers based on their own preferences. We propose three metaheuristic methods for solving this problem: Particle Swarm Optimization (PSO), Simulated Annealing (SA) and a combination of Reduced and Basic Variable Neighborhood Search Method (RVNS-VNS). The solution encoding and constructive elements of all three proposed algorithms are adapted to the problem under consideration. The results of computational tests on problem instances with up to 2000 clients and 2000 potential facility locations show good performance of all three proposed methods, even on large problem dimensions. Finally, the obtained results indicate that the proposed RVNS-VNS method outperforms the PSO and SA methods in the sense of solutions' quality and running times.