Research Article Multiobjective Optimization for Multimode Transportation Problems Laurent Lemarchand , 1 Damien Massé , 1 Pascal Rebreyend , 2 and Johan Håkansson 2 1 Lab-STICC UMR CNRS 6285, University of Brest, Brest, France 2 Dalarna University, Falun, Sweden Correspondence should be addressed to Pascal Rebreyend; prb@du.se Received 5 December 2017; Accepted 15 April 2018; Published 7 June 2018 Academic Editor: Alessandra Oppio Copyright © 2018 Laurent Lemarchand et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We propose modelling for a facilities localization problem in the context of multimode transportation. Te applicative goal is to locate service facilities such as schools or hospitals while optimizing the diferent transportation modes to these facilities. We formalize the School Problem and solve it frst exactly using an adapted -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 modifed version of PAES. Tose 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, efcient 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 signifcantly for the modifed PAES approach. 1. Introduction Localization of facilities such as public services (schools, hos- pitals, etc.) is an important problem for social planners and policymakers. Most of the time, this problem is formulated as the (single objective) -median problem which is a central problem in Operations Research (see, for example, [1, 2] for surveys). Te -median was introduced by Hakimi [3] who describes its basic properties. Its basic variant can be defned as follows: given a set of  demand nodes, distance values for each pair of nodes, and a fxed number  of facilities, locating each facility at one of the nodes, while minimizing the sum of distances from each node to its closest facility. Recent developed algorithms solve the single objective version exactly for instances of thousands of nodes (e.g., 25.000nodesin[4]).However,forapolicymaker,considering additional objectives would be useful when solving -median problems on real cases, leading to diferent variants; e.g., (i) dispersion problem:the -dispersion problem consists of spanning the  facilities by maximizing the min- imal distance between two of them. Tis objective function is suitable to locate business franchises and also when locating obnoxious facilities [5]. (ii) -center problem: the -center problem [6] aims at minimizing the maximal distance of demand nodes from their facility, or the average distance of a fraction of those that are the farthest from their closest facility, e.g., 5% farthest of them. Tis problem formulation can be applied to locate emergency services such as fre stations. (iii) multimode transportation location (MTL) problem: in many real cases, transportation can be done by difer- entmeans(byfoot,bike,car,buses,etc.)dependingon criteria like a threshold on the distance to the nearest facility. As an example, pupils are going to school by Hindawi Advances in Operations Research Volume 2018, Article ID 8720643, 13 pages https://doi.org/10.1155/2018/8720643