An evolutionary approach for the p-next center problem
Abstract
The p-next center problem is an extension of the classical p-center problem, in which a backup center must be assigned to welcome users from a suddenly unavailable center. Usually, users tend to seek help in the closest facility they can find. However, during a significant event or crisis, one only realizes that the closest facility has been disrupted upon his/her arrival. Therefore, the user seeks help in the next closest center from the one that has failed to provide service. Therefore, the objective of the p-next center problem is to minimize the path of any user, which is made by the distance from this origin to its closest installed facility, plus the distance from this facility to its backup. We propose an evolutionary approach for the p-next center problem and an extension for the current benchmark instances. The proposed methods are built on the Multi-Parent Biased Random-Key Genetic Algorithm with Implicit Path-Relinking. Computational experiments carried out on 416 test instances show, experimentally, the outstanding performance of the developed algorithms and their flexibility to reach a good quality-speed trade-off.