Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

Abstract

The problem addressed here is a combinatorial bilevel programming problem called the uncapacitated facility location problem with customer’s preferences. A hybrid algorithm is developed for solving a battery of benchmark instances. The algorithm hybridizes an evolutionary algorithm with path relinking; the latter procedure is added into the crossover phase for exploring the trajectory between both parents. The proposed algorithm outperforms the evolutionary algorithm already existing in the literature. Results show that including a more sophisticated procedure for improving the population through the generations accelerates the convergence of the algorithm. In order to support the latter statement, a reduction of around the half of the computational time is obtained by using the hybrid algorithm. Moreover, due to the nature of bilevel problems, if feasible solutions are desired, then the lower level must be solved for each change in the upper level’s current solution. A study for illustrating the impact in the algorithm’s performance when solving the lower level through three different exact or heuristic approaches is made.

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

“…Another study considers location of logistics distribution centers by minimizing the planners' cost at the upper level and customers' cost at the lower level [158]. Other applications of bilevel optimization to facility location problem may be found in [88], [164], [159], [7], [36], [38], [128], [38], [118], [41], [114]. 7) Inverse Optimal control: Inverse optimal control problems are essentially bilevel in nature [123], [6], [89], [160] with wide applications in robotics, computer vision, communication theory and remote sensing to name a few.…”

A facility location problem for extracurricular workshop planning: bi‐level model and metaheuristics

“…Therefore, we introduce two metaheuristics to solve realistic‐size instances of the workshop location problem. Contrary to other methods commonly used for the solution of bi‐level FLPs that rely on population metaheuristics like (hybrid) genetic algorithms (Maldonado‐Pinto et al., 2016; Calvete et al., 2020), scatter search (Pérez Posada et al., 2017), and the cross‐entropy method (Casas‐Ramírez et al., 2018), our two proposed metaheuristics are trajectory‐based methods based on PR and ILS.…”

“…To the best of our knowledge, there is only one paper using PR in the solution of a bi‐level FLP, and this is the paper by Maldonado‐Pinto et al. (2016). In their work, the authors hybridized an evolutionary algorithm with PR.…”

“…The method proposed by Maldonado‐Pinto et al. (2016) differs from the one we are proposing here in several aspects: (i) we propose a trajectory‐based metaheuristic, while theirs is a population‐based evolutionary algorithm that relies on random solution generation, solution recombination, and mutation as main search components; (ii) by contrast, we are proposing PR as the main solution method not only as a component of the algorithm; (iii) the solution representation is very different as we do not use a binary vector to represent the solutions; and the differences in (iv) the manner that initial and guide solutions are selected; (v) the selection of final solutions to continue the algorithm; and (vi) the number of iterations performed, that is, in their evolutionary algorithm only one PR iteration is performed for each pair of solutions.…”