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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 and compare three metaheuristic approaches   for solving this problem: Particle Swarm Optimization (PSO), Simulated   Annealing (SA), and a combination of Reduced and Basic Variable Neighborhood   Search Method (VNS). We used the representation of solutions and objective   function calculation that are adequate for all three proposed methods.   Additional strategy is implemented in order to provide significant time   savings when evaluating small changes of solution's code in improvement   parts. Constructive elements of each of the proposed algorithms are adapted   to the problem under consideration. The results of broad computational tests   on modified problem instances from the literature show good performance of   all three proposed methods, even on large problem dimensions. However, the   obtained results indicate that the proposed VNS-based has significantly   better performance compared to SA and PSO approaches, especially when solving   large-scale problem instances. Computational experiments on large scale   benchmarks demonstrate that the VNS-based method is fast, competitive, and   able to find high-quality solutions, even for large-scale problem instances   with up to 2000 clients and 2000 potential facilities within reasonable CPU   times

Metaheuristic approaches to solving large-scale Bilevel Uncapacitated Facility Location Problem with clients' preferences