Bi-objective optimization approaches to many-to-many hub location routing with distance balancing and hard time window

This study addresses a many-to-many hub location-routing problem where the best-found locations of hubs and the best-found 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 ε-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.