A Hybrid Tabu Search for the m-Peripatetic Vehicle Routing Problem

This article presents a hybridization of a perfect b-matching within a tabu search framework for the m-Peripatetic Vehicle Routing Problem (m-PVRP). The m-PVRP models for example money transports and cash machines supply where, for security reasons, no path can be used more than once during m periods and the amount of money allowed per vehicle is limited. It consists in finding a set of routes of minimum total cost over m periods from an undirected graph such that each customer is visited exactly once per period and each edge can be used at most once during the m periods. Each route starts and finishes at the depot with a total demand not greater than vehicle capacity. The aim is to minimize the total cost of the routes. The m-PVRP can be considered as a generalization of two well-known NP-hard problems: the vehicle routing problem (VRP or 1-PVRP) and the m-Peripatetic Salesman Problem (m-PSP). Computational results show that the hybrid algorithm obtained improves the tabu search, not only on the mPVRP in general, but also on the VRP and the m-PSP using classical VRP instances and TSPLIP instances.