Hybridization of Metaheuristics with Methods Based on Linear Programming for the Traveling Car Renter Salesman Problem
Hybrid metaheuristics, linearprogramming, traveling car renter, scientific algorithms, evolutionary computation,variable neighborhood descent, adaptive local search.
The Traveling Car Renter Salesman Problem, or simply Traveling Car Renter Problem (CaRS), is a generalization of the Traveling Salesman Problem (TSP) where the tour can be decomposed into contiguous paths that are traveled by different rented cars. The objective is to construct a minimal cost Hamiltonian circuit, considering the penalty paid for changing cars in the tour. This penalty is the cost of returning a car to the city where it was rented. CaRS is classified as an NP-hard problem. This work studies the CaRS version classified as: complete, total, unrestricted, with no repetition, free and symmetric. This research is focused on hybrid procedures that combine metaheuristics and methods based on Linear Programming (LP). The following methods were investigated: scientific algorithms (ScA), evolutionary algorithms (EA), variable neighborhood descent (VND), adaptive local search (ASLP) and a new variant of ALSP called iterated adaptive local search (IALSP). The following techniques are proposed to deal with CaRS: ScA+ALSP, EA+IALSP, ScA+IALSP and ScA+VND+IALSP. A mixed integer programming model is proposed for CaRS which was used in the ALSP and IALSP. Non-parametric tests were used to compare the algorithms within a set of instances from the literature.