Enhancing Solution Similarity in Multi-Objective Vehicle Routing Problems with Different Demand Periods

Abstract

In this chapter, we consider vehicle routing problems (VRPs) where the demand of customers varies. We have proposed a problem with two periods of different demand (Murata & Itai, 2005). In each period, we treat the VRPs as multi-objective optimization problems (MOPs). In MOPs, we can handle several objectives such as minimizing total cost for delivery, minimizing maximum cost, minimizing the number of vehicles, minimizing total delay to the date of delivery and so on. Although a set of non-dominated solutions can be searched independently in each period, NDP or HDP, drivers of vehicles prefer to have similar routes in the both periods in order to reduce their fatigue to drive on a different route. We propose a local search that enhances the similarity of routes in NDP and HDP. Simulation results show that the proposed local search can find a similar set of nondominated solutions in HDP to the one in NDP. As for the algorithm to find a set of solutions for MOPs, we have various approaches in Evolutionary Multi-criterion Optimization (EMO) community community (Zitzler et al., 2001; Fonseca et al., 2003; Coello Coello et al., 2005; Obayashi et al, 2007). However, there are few research works that investigate the similarity among obtained sets of non-dominated solutions. Deb (2001) considered topologies of several non-dominated solutions in Chapter 9 of his book. He examined the topologies or structures of three-bar and ten-bar truss. He showed that neighboring non-dominated solutions on the obtained front were under the same topology, and NSGA-II could find the gap between the different topologies. While he considered the similarity of solutions in a single set of non-dominated solutions from a topological point of view, there is no research work relating to EMO that considers the similarity of solutions in different sets of non-dominated solutions. In this chapter, we propose a local search in an EMO algorithm that enhances the similarity of solutions in different sets of non-dominated solutions. O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m