Evolutionary computation plus Mathematical Programming for the Traveling Car Renter Salesman Problem

The Traveling Car Renter Salesman Problem (CaRS) is a generalization of the Traveling Salesman Problem. A new variant of the Adaptive Local Search Procedure (ALSP) algorithm called Iterated Adaptive Local Search Procedure (IALSP) is presented in this work. Two mathematical formulations are presented to model the CaRS problem. These formulations are compared using a MIP solver. The formulation with the best result is used in the IALSP algorithm. To deal with the CaRS problem, we propose a hybrid algorithm composed of an evolutionary algorithm called Scientific Algorithm (ScA) and the IALSP algorithm. We call the proposed hybrid algorithm ScA + IALSP. We have carried out computational experiments on a set of 15 instances extracted from the literature. We have compared the proposed algorithm with the best-known algorithm in the literature. The results show that the IALSP algorithm is competitive. Six new best results are reported.