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.

枢纽设施是集中的位置，用于合并和分配运输网络中的商品。在许多实际应用中，运输服务提供商可能更愿意在一定时间范围内租赁枢纽设施，而不是被拥有或建造。在本文中，提出了一个针对多周期集线器位置问题的建模框架，该问题是在具有两种类型的集线器和链接的星型网络设计中出现的。它包括一个指定的静态中央集线器，一些可移动集线器设施以及一组成对需求的节点。在每个时期都考虑周期性增加预算额，以扩大运输网络，并在每个时期内将可用利率应用于未使用的预算。由于集线器和分支系统的整体服务质量取决于路径的长度，对节点之间的路径考虑上限约束。数值实验表明了该模型的适用性。由于该模型的计算复杂性，因此使用了改进的遗传算法（GA）和混合粒子群优化（HPSO）来寻找接近最优的解决方案。两种算法均采用缓存策略以缩短计算时间。此外，HPSO得益于遗传算子和局部搜索方法来更新粒子。为了评估所提出方法的有效性，将结果与纯GA和通过拉格朗日松弛法获得的适当下限进行比较。由于该模型的计算复杂性，因此使用了改进的遗传算法（GA）和混合粒子群优化（HPSO）来寻找接近最优的解决方案。两种算法均采用缓存策略以缩短计算时间。此外，HPSO得益于遗传算子和局部搜索方法来更新粒子。为了评估所提出方法的有效性，将结果与纯GA和通过拉格朗日松弛法获得的适当下限进行比较。由于该模型的计算复杂性，因此使用了改进的遗传算法（GA）和混合粒子群优化（HPSO）来寻找接近最优的解决方案。两种算法均采用缓存策略以缩短计算时间。此外，HPSO得益于遗传算子和局部搜索方法来更新粒子。为了评估所提出方法的有效性，将结果与纯GA和通过拉格朗日松弛法获得的适当下限进行比较。