A memetic algorithm for the prize-collecting Traveling Car Renter Problem

This paper introduces a new variant of the Traveling Car Renter Problem, named Prize-collecting Traveling Car Renter Problem. In this problem, a set of vertices, each associated with a bonus, and a set of vehicles are given. The bonus represents a degree of satisfaction to visit the vertex. The objective is to determine a cycle that visits some vertices collecting, at least, a pre-defined bonus, i.e. reaching a pre-specified satisfaction, and minimizing the cost of the tour that can be traveled with different vehicles. A mathematical formulation is presented and implemented in a solver to produce results for sixty-four instances. A memetic algorithm is proposed and its performance is evaluated in comparison to the results obtained with the solver.