(A) heuristic method for the multi-path orienteering problem

Abstract

Many research articles in the literature have dealt with the problem of finding an optimal tour such as the traveling salesman problem (TSP) and vehicle routing problem (VRP). They commonly assumed that "all" nodes on a given graph should be visited exactly once and only once. In this thesis, however, we deal with a multi-path orienteering problem (MPOP) that does not require visiting all the nodes. We want to find a set of paths for each vehicle that has to leave the distribution center and arrive at a specified destination. The objective is to maximize the total rewards collected by visiting as many customers as possible under a specified time limit. The manager of department store, and mineral water manufacturing and distribution company faces a similar problem during peak-sale periods. First, the problem is formulated in mathematical model. Then recognizing the difficulty in finding an optimal solution, a heuristic is developed that has three phases, i.e., construction phase, improvement phase, and balancing phase. To examine the validity of the algorithm, 450 problems are generated varying the numbers of nodes, the number of vehicles, and the time limit of each vehicle. Recognizing that some previous studies in the orienteering problem turn out to be a special case of MPOP, two heuristics, one for single path and the other for multiple paths, are adopted for the comparison purpose. The computational results show that the proposed heuristic tends to outperfonn the existing algorithms.