A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem

Nowadays, offering fast and reliable delivery service has become a vital issue associated with all shipment delivery systems. Due to unpredictable variability in travel times, configuration of transportation systems plays a key role in ensuring of meeting the delivery service requirement. This paper tries to investigate the effect of delivery service requirement on the configuration of the transportation system through a hub-and-spoke network. The primary goal of this paper is to study a bi-objective single allocation p-hub center-median problem (BSpHCMP) by taking into account the uncertainty in flows, costs, times and hub operations. The proposed problem is modeled through a bi-objective mixed-integer non-linear programming (BMINLP) formulation that simultaneously locates p hubs, allocates spokes to the located hubs, and assigns different transportation mode to the hub-to-hub links. Then, a fuzzy-queuing approach is used to model the uncertainties in the network. Additionally, an efficient and powerful evolutionary algorithm based on game theory and invasive weed optimization algorithm was developed to solve the proposed BSpHCMP model and obtain near optimal Pareto solutions. Several experiments besides a real transportation case show the applicability of the proposed model as well as the superiority of the proposed solution approaches compared to NSGA-II and PAES algorithms.