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 -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.

中文翻译：

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多模式运输问题的多目标优化

我们建议在多式联运的背景下对设施本地化问题进行建模。该应用程序的目标是找到服务设施，例如学校或医院，同时优化针对这些设施的不同运输方式。我们对学校问题进行形式化，并首先使用适应性约束多目标方法精确地解决它。由于所考虑实例的大小，我们还探索了基于进化多目标框架（即NSGA2和PAES的修改版本）的启发式方法的使用。这些方法与原始的本地搜索技术混合在一起可以提供更好的结果。使用超量度度量对解决方案集质量进行数值比较。根据可以准确解决的测试用例的结果，PAES和NSGA2的高效实现允许比较大型实例的执行时间。结果表明，与针对小型测试用例的精确算法相比，启发式方法具有良好的性能。近似方法在最大的问题实例上表现出可伸缩的行为。主/从并行化方案还有助于大大减少修改后的PAES方法的执行时间。