Abstract The location–routing problem (LRP) unites two important challenges in the design of distribution systems: planning the delivery of goods to customers (i.e., the routing of the delivery vehicles) and determining the locations of the depots from where these deliveries are executed. In this paper, we design an efficient and effective heuristic for the LRP based on an existing heuristic to solve the capacitated vehicle routing problem. Our heuristic reduces the solution space to a manageable size by the estimation of an upper bound for the number of open depots and then iteratively applies the routing heuristic on each remaining depot configuration. A progressive filtering framework, in which the vehicle routing problem is solved to a larger precision at each iteration, is employed to quickly detect unpromising configurations. Extensive experimentation reveals that the estimated upper bound effectively reduces the search space on different types of instances and that a good filtering design combines coarse and fine filters. Benchmarking shows that, despite its simple design, the final heuristic outperforms existing heuristics on the largest LRP benchmark set, on very-large-scale LRPs, and on 2-echelon LRPs.

中文翻译：

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位置路由问题及其变体的渐进式过滤启发式算法

摘要 位置路由问题 (LRP) 将配送系统设计中的两个重要挑战结合起来：规划向客户交付货物（即运输车辆的路线）和确定执行这些交付的仓库的位置。 . 在本文中，我们基于现有的启发式为 LRP 设计了一种高效且有效的启发式方法来解决有能力的车辆路径问题。我们的启发式通过估计开放仓库数量的上限将解决方案空间减小到可管理的大小，然后在每个剩余仓库配置上迭代应用路由启发式。采用渐进式过滤框架，在每次迭代中以更高的精度解决车辆路径问题，用于快速检测无希望的配置。大量实验表明，估计的上限有效地减少了不同类型实例的搜索空间，并且良好的过滤设计结合了粗细过滤器。基准测试表明，尽管设计简单，但最终启发式在最大 LRP 基准集、超大规模 LRP 和 2 级 LRP 上的性能优于现有启发式。