Probabilistic and Experimental Analysis of Heuristic Algorithms for the Multiple-Depot Vehicle-Routing Problem

Licentiatavhandling, 2006

The aim of this thesis is to analyze different heuristic algorithms for solving the Multi-Depot Vehicle-Routing problem (MDVRP) with k depots and n points to be serviced (customers). The objective is to produce a set of service routes which minimizes the total distance traveled. Heuristic approaches are essential since the problem is NP-hard. The first part of the thesis deals with a simpler version of the optimization problem, which is to find a collection of disjoint TSP tours with minimum total length such that all points are covered and each tour contains exactly one depot (MDTSP). The analysis is done in a setting where depots as well as points are randomly, independently and uniformly distributed in the unit square [0,1]^2. The analysis shows that the asymptotic behavior of MDTSP depends on the ratio k/n. It is also proven that the heuristic which first clusters points around the nearest depot and then performs the TSP routing gives an asymptotic tour length of (1 + o(1))OPT almost surely. The second part of the thesis contains an empirical study of two new measures used in cluster-first-route-second heuristics for the MDVRP with Time-Windows (TW). In real problems more restrictions often appear, such as limited visiting hours either for the depots, customers or both, referred to as the TW. When TW are present and the problem is to be solved approximately it is necessary to find groups of customers that are close not only geographically but in the sense of TW. Two measures which take into account both distance and TW are introduced and analyzed. The experiments were carried out on test cases on the Atlanta City map. The results show average savings of 5-6% using these new measures.