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Heuristic algorithms for the bi-objective hierarchical multimodal hub location problem in cargo delivery systems

机译：货物送货系统中双目标分层多模式集线器位置问题的启发式算法

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摘要

In this paper, we introduce an extended version of hub location problem, called bi-objective hierarchical multimodal hub location problem to simultaneously minimize the overall system-wide costs and the maximum delivery time. This problem is distinct from the classic hub location problem in designing a hierarchical multimodal hub-and-spoke network involving multiple transportation modes, multi-class hubs and corresponding layers. Combining cost and time dimensions, we first propose a bi-objective mixed-integer linear programming to model this problem formally with diverse flow balance constraints. We then show that the proposed model can be efficiently solved by a reformulation approach based on the e-constraint method for only small instances. Hence, we develop two heuristics, a variable neighborhood search algorithm and an improved non-dominated sorting genetic algorithm-Ⅱto obtain high-quality Pareto solutions for realistic-sized instances. We further illustrate the application of the proposed model to provide decision support for cargo delivery systems. Finally, we conduct extensive numerical experiments based on Turkish network to demonstrate the superiority of the proposed solution methods compared to the standard non-dominated sorting genetic algorithm-Ⅱ. The statistical results confirm the efficacy of the developed heuristic algorithms by adopting the Wilcoxon test.
机译：在本文中，我们介绍了集线器位置问题的扩展版本，称为双目标分层多模式集线器位置问题，同时最小化整体系统的成本和最大交付时间。该问题与设计涉及多个运输模式，多类集线器和对应层的分层多模式集线器和辐条网络中的经典集线器位置问题不同。结合成本和时间尺寸，我们首先提出了一种双目标混合整数线性编程，以便使用多样化的流量平衡约束正式模拟此问题。然后，我们表明，所提出的模型可以通过基于小型实例的电子约束方法进行重新约束方法有效地解决。因此，我们开发了两个启发式，可变邻域搜索算法和改进的非主导分类遗传算法-Ⅱ获得高质量的帕累托解决方案，用于现实大小的实例。我们进一步说明了所提出的模型的应用，为货运系统提供决策支持。最后，我们基于土耳其网络进行广泛的数值实验，以证明与标准的非主导分选遗传算法-Ⅱ相比提出的解决方案方法的优越性。统计结果通过采用Wilcoxon测试证实了发育的启发式算法的功效。

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