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

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.