This paper introduces a distributionally robust cluster-based hierarchical hub location problem for the integration of urban and rural public transport system at the strategic level. Lacking complete information on the true probability distributions of construction cost and travel time, a distributionally robust optimization (DRO) model is proposed to formulate this problem formally. The proposed DRO model is demonstrated to be semi-infinite and computationally hard but admits a safe approximation and an equivalent under two kinds of ambiguity sets: bounded perturbations with zero mean and Gaussian perturbations, respectively. Since the resulting formulations can be solved to optimality by the CPLEX software for only small instances, a variable neighborhood search algorithm and a population-and-searching based heuristic algorithm are designed to handle the realistic-sized instances. To validate the superiority of the DRO model and the efficiency of the proposed methods, two sets of numerical experiments are implemented on a case study of Guangrao in Shandong Province of PR China and a randomly generated example, respectively. Suggestions for possible extensions of the original problem are also discussed.

本文介绍了基于分布鲁棒集群的分层集线器选址问题，用于在战略层面整合城乡公共交通系统。缺乏关于建设成本和行程时间的真实概率分布的完整信息，提出了一种分布式鲁棒优化（DRO）模型来正式地表达此问题。所提出的DRO模型被证明是半无限的，并且计算上很困难，但是在两种歧义集下分别接受安全近似和等效：分别为零均值的有界扰动和高斯扰动。由于只能通过CPLEX软件在很小的情况下解决生成的配方的问题，因此，设计了可变邻域搜索算法和基于人口和搜索的启发式算法来处理实际大小的实例。为了验证DRO模型的优越性和所提方法的有效性，分别在山东省广饶市的一个案例研究和一个随机生成的实例上进行了两组数值实验。还讨论了可能扩展原始问题的建议。