Solving the p-median bilevel problem with order through a hybrid heuristic

Display Omitted A variant of the p-median in which customer preferences are taken into account, named the p-median bilevel problem with order, is studied.A comparison among two single-level reformulations herein proposed and an adaptation of an existing reformulation for the SPLPO is made.A hybrid heuristic algorithm based on Scatter Search and GRASP that obtains high-quality solutions in reasonable time is proposed.A fair comparison with regards to other heuristic procedures (Scatter search, GRASP and Genetic algorithm) is performed.A large set of instances in which the proposed heuristic obtains the best results when solving large-size instances is tested. A variant of the p-median problem is considered and presented in this paper. This variant is based on the assumption that customers are free to choose the located facility that will serve them. The latter decision is made by considering the customers preferences towards the facilities. To study this problem, a mathematical bilevel programming formulation is proposed. Given the difficulty in solving such bilevel programs, two reformulations are used for solving the problem. The first reformulation adds constraints and variables to the mathematical model, while the second one adds only constraints. Yet, both reformulations avoid the need to solve an optimization problem parameterized by the upper level variables to find the value of the lower level variables. The results of numerical experiments show that the required time for both reformulations is significant increased as the size of the instance increases. Moreover, the reformulations are unable to solve the large-size instances. This led us to develop a hybrid heuristic algorithm based on scatter search, which obtains high-quality solutions for all tested instances in less time than is required by the abovementioned reformulations. Furthermore, the proposed heuristic was able to solve larger-size instances obtaining the optimal or currently best known solution. The registered results from the computational experimentation show that the proposed algorithm performs steadily. A comparison against a scatter search with random construction, a scatter search with greedy construction, a GRASP and a genetic algorithm shows that the proposed hybrid heuristic outperforms the other algorithms.