Hybrid evolutionary algorithms and Lagrangian relaxation for multi-period star hub median problem considering financial and service quality issues

Abstract

Hub facilities are centralized locations that consolidate and distribute the commodities in transportation networks. In many real world applications, transport service providers may prefer to lease hub facilities for a time horizon rather than being owned or constructed. In this paper, a modeling framework is proposed for the multi-period hub location problem that arises in the design of the star–star network with two types of hubs and links. It includes a designated static central hub, some movable hub facilities and a set of nodes with pairwise demands. A periodic growth in the amount of budget is considered at each period to expand the transportation network and an interest rate is also applied to the unused budget available during each period. Since the overall quality of services in the hub and spoke systems rely on the length of the paths, upper bound constraints are considered for the paths between nodes. Numerical experiments are carried out to show the applicability of the proposed model. Due to the computational complexity of the model, an improved genetic algorithm (GA) and a hybrid particle swarm optimization (HPSO) are utilized to find near optimal solutions. Both algorithms employ caching strategy to improve the computation times. Moreover, the HPSO benefits from genetic operators and local search methods to update the particles. In order to assess the effectiveness of the proposed methods, the results are compared with a pure GA and a proper lower bound achieved by a Lagrangian relaxation method.