This article reports on an approach for the VeRoLog Solver Challenge 2019: the fourth solver challenge facilitated by VeRoLog, the EURO Working Group on Vehicle Routing and Logistics Optimization. The authors were awarded third place in this challenge. The routing challenge involved solving two interlinked vehicle routing problems for equipment: one for distribution (using trucks) and one for installation (using technicians). We describe our solution method, based on a matheuristics approach in which the overall problem is heuristically decomposed into components that can then be solved by formulating them as set partitioning problems. To solve these set partitioning problems we introduce a novel method we call “columnwise neighborhood search,” which allows us to explore a large neighborhood of the current solution in an exact manner. By iteratively applying mixed‐integer programming methods, we obtain good quality solutions to our subproblems. We then use a simple local search “fusion” heuristic to further improve the solution to the overall problem. Besides introducing and discussing this solution method, we highlight the problem instances for which our approach was particularly successful in order to obtain general insights about our methodology.

中文翻译：

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列式邻域搜索：一种新颖的集合划分数学及其在 VeRoLog Solver Challenge 2019 中的应用

本文报告了 2019 年 VeRoLog 求解器挑战的方法：由欧洲车辆路线和物流优化工作组 VeRoLog 推动的第四个求解器挑战。作者在这项挑战中获得了第三名。路由挑战涉及解决设备的两个相互关联的车辆路由问题：一个用于配送（使用卡车），另一个用于安装（使用技术人员）。我们描述了我们的解决方法，基于一种数学方法，其中将整个问题启发式地分解为组件，然后可以通过将它们制定为集合分区问题来解决这些组件。为了解决这些集合划分问题，我们引入了一种称为“列邻域搜索”的新方法，它允许我们以精确的方式探索当前解决方案的大邻域。通过迭代地应用混合整数编程方法，我们获得了子问题的高质量解决方案。然后我们使用简单的局部搜索“融合”启发式来进一步改进整体问题的解决方案。除了介绍和讨论这种解决方法之外，我们还强调了我们的方法特别成功的问题实例，以便获得关于我们方法的一般见解。