A Multiobjectivization Approach for Vehicle Routing Problems

In this chapter, we describe a new approach for vehicle routing problems (VRPs), which treats VRPs as multi-objective problems using the concept of multiobjectivization. The multiobjectivization approach has generated in the field of Evolutionary Multi-Criterion Optimization (EMO) (Knowles et al., 2001). This approach transforms a single-objective problem into a multi-objective problem. It is most important feature of this approach to provide more freedom to explore and to reduce the likelihood of becoming trapped in local optima by adding additional objectives. There have been many studies using EMO algorithm to optimize multi-objective VRPs, with objectives including the number of routes and total travel distance or number of routes and duration of routes, etc (Jozefowiez et al., 2002). In these studies, EMO treats the original objective of VRPs directly as multi-objective. On the other hand, our approach deals not only with the original objective of VRPs but also with newly defined objectives related to assignment of customers. Generally, VRPs seem to have two different determinations: the assignment of customers and the order of the route. The assignment of customers is known to have a stronger influence on the search than the order of the route in many studies (Doerner et al., 2005). Therefore, we expect that the proposed approach will get better solutions in minimization of the total travel distance than the approach using only the total travel distance as a single objective. In our approach, we add two new objective functions used by MOCK (Handl & Knowles, 2005) as the objective related to assignment of customers. Our multiobjectivization aims to accelerate the search for original objective by adding supplementary objective. We investigated the characteristics and effectiveness of the proposed approach by comparing the performance of the conventional approach and multiobjectivization approach. In numerical experiments, we used Taillard's test functions as a benchmark problem. In addition, we used NSGA-II (Deb et al., 2002) in implementing our approach. Through numerical examples, we showed that the proposed multiobjectivization approach can obtain the solution with good quality and little variation in VRPs.