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In the cargo transportation system, the hub-and-spoke transport network can make full use of the scale effect between logistics hubs and reduce logistics costs. Joint transportation of multiple modes of transportation can give full play to the advantages of different modes of transportation, which not only reduces logistics costs but also improves transportation efficiency. Therefore, this paper combines the advantages of multimodal transportation and hub-and-spoke network, and establishes an optimization model of multimodal hub-and-spoke transport network under demand uncertainty. The model takes into account hub capacity constraints and customer satisfaction with respect to transportation time, and to facilitate the model solution, we utilize the fuzzy expected value method and the fuzzy chance constraints based on credibility to clarify the uncertain variables in the model. We use mixed coding to describe the selection of hubs, assignment of nodes, and choice of transportation modes in this study and use the NSGA-II algorithm with local reinforcement to solve the problem. Finally, numerical experiments are designed to verify the validity of the model and algorithm through sensitivity analysis of relevant parameters, determine the reasonable number of hubs and confidence level, and obtain the influence of the change of hub capacity limit and the ratio of single and double hub transit on the research objectives. The results show that: the NSGA-II algorithm with local reinforcement can significantly improve the convergence speed of the algorithm; There is benefit inversion between economic cost and time cost, and the pursuit of economic cost minimization and time cost minimization, respectively, will lead to different choices of the number of hubs; Increasing the ratio of goods transfer between hubs is beneficial for fully utilizing the scale effect between hubs, achieving the goal of reducing economic costs, but at the same time, it will increase time costs.
Zhang et al. (Wed,) studied this question.