Multiobjective Optimization for Multimode Transportation Problems

Abstract

We propose modelling for a facilities localization problem in the context of multimode transportation. The applicative goal is to locate service facilities such as schools or hospitals while optimizing the different transportation modes to these facilities. We formalize the School Problem and solve it first exactly using an adapted ϵ-constraint multiobjective method. Because of the size of the instances considered, we have also explored the use of heuristic methods based on evolutionary multiobjective frameworks, namely, NSGA2 and a modified version of PAES. Those methods are mixed with an original local search technique to provide better results. Numerical comparisons of solutions sets quality are made using the hypervolume metric. Based on the results for test-cases that can be solved exactly, efficient implementation for PAES and NSGA2 allows execution times comparison for large instances. Results show good performances for the heuristic approaches as compared to the exact algorithm for small test-cases. Approximate methods present a scalable behavior on largest problem instances. A master/slave parallelization scheme also helps to reduce execution times significantly for the modified PAES approach.