A Multi-Start Split based Path Relinking (MSSPR) approach for the vehicle routing problem with route balancing
This paper addresses the vehicle routing problem with route balancing (VRPRB), which aims at minimizing two criteria simultaneously: the total routing cost and the difference between the largest and smallest route cost. We propose a multi-start approach based on two search spaces each of them using a different solution presentation: a TSP tour that denotes an indirect solution based on a sequence of customers as in the Traveling Salesman Problem, and a VRPRB solution that denotes a complete solution containing a set of vehicle trips. Switching from an indirect to a complete solution is possible through an adaptation of a splitting algorithm considering both optimization criteria. More precisely, such an adaptation requires an acceptance criterion allowing the generation a set of non-dominated VRPRB solutions from a single TSP tour. A path relinking algorithm improves the set of obtained VRPRB solutions. The proposed method is evaluated on VRPRB instances derived from classical VRP instances and the results reveal the method as effective in comparison with the best published algorithms for the problem optimizing the total routing cost. Regarding both criteria, the method competes with a previous published method handling the VRPRB. In fact, it is able to provide similar results in shorter computational time and since no details are available on state-of-the-art fronts, no further conclusion can be made. A web page presents all the solutions on our fronts to favor future comparative studies. Furthermore, the proposed method allows tackling a variant of the problem ignored by the previous works on VRPRB, which integrates limitation on vehicle service time.
split path relinking route balancing capacitated vehicle routing problems