Two-echelon vehicle routing problem (2E-VRP) is a challenging problem that involves both the strategic and tactical planning decisions on both echelons. The satellite locations and the customer distribution affect the cost of different components on the second echelon, thus the possibilities of satellite-to-customer assignment complicates the problem. In this paper, we propose a graph-based fuzzy evolutionary algorithm for solving 2E-VRP. The proposed method integrates a graph-based fuzzy assignment scheme into an iteratively evolutionary learning process to minimize the total cost. To resolve the possibilities of the satellite-to-customer assignment, graph-based fuzzy operator is used to take advantage of population evolution and avoid excessive fitness evaluations of unpromising moves in different satellites. Each offspring is produced via graph-based fuzzy assignment procedure out of an assignment graph from parent individuals, and fuzzy local search procedure is used to further improve the offspring. The experimental results on the public test sets demonstrate the competitiveness of the proposed method.

中文翻译：

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一种求解两梯队车辆路径问题的基于图的模糊进化算法

双梯队车辆路径问题 (2E-VRP) 是一个具有挑战性的问题，涉及两个梯队的战略和战术规划决策。卫星位置和客户分布影响第二梯队不同组件的成本，因此卫星到客户分配的可能性使问题复杂化。在本文中，我们提出了一种基于图的模糊进化算法来解决 2E-VRP。所提出的方法将基于图的模糊分配方案集成到迭代进化学习过程中以最小化总成本。为了解决卫星到客户分配的可能性，使用基于图的模糊算子来利用种群进化并避免对不同卫星中无希望移动的过度适应度评估。每个后代都是通过基于图的模糊分配程序从父个体的分配图中产生的，并且使用模糊局部搜索程序来进一步改进后代。在公共测试集上的实验结果证明了所提出方法的竞争力。