This study addresses a many-to-many hub location-routing problem where the best-found locations of hubs and the bestfound tours for each hub are determined with simultaneous pickup and delivery within the hard time window. To find practical solutions, the hubs and transportation fleet have constrained capacity, in which every node can be serviced by multiple allocations with the hard time window and limited tour length. First, a bi-objective optimization model is proposed to balance travel costs among different routes and to minimize the total sum of fixed costs of locating hubs, the costs of handling, traveling, assigning, and transportation costs. The problem is then solved using an augmented e-constraint technique for small to medium size instances of the problem. Due to the NP-hardness nature of the problem, the proposed multi-objective optimization model is solved by a multi-objective imperialist competitive algorithm (MOICA). To show the superior performance of the MOICA, the solutions are compared with those obtained by the non-dominated sorting genetic algorithm (NSGA-II). For the large-scale problem instances, the comparative results indicate that the MOICA can indeed provide better Pareto optimal solutions compared to NSGA-II for the large-scale problem instances.

Marine spatial planning (MSP) has recently attracted more attention as an efficient decision support tool. MSP is a strategic and long-term process gathering multiple competing users of the ocean with the objective to simplify decisions regarding the sustainable use of marine resources. One of the challenges in MSP is to determine an optimal zone to locate a new activity while taking into account the locations of the other existing activities. Most approaches to spatial zoning are formulated as non-linear optimization models involving multiple objectives, which are usually solved using stochastic search algorithms, leading to sub-optimal solutions. In this paper, we propose to model the problem as a Multi-Objective Integer Linear Program. The model is developed for raster data and it aims at maximizing the interest of the area of the zone dedicated to the new activity while maximizing its spatial compactness. We study two resolution methods: first, a weighted-sum of the two objectives, and second, an interactive approach based on an improved augmented version of the ϵ-constraint method, AUGMECON2. To validate and study the model, we perform experiments on artificially generated data. Our experimental study shows that AUGMECON2 represents the most promising approach in terms of relevance and diversity of the solutions, compactness, and computation time.