Delivery options are at the heart of the generalized vehicle routing problem with time windows (GVRPTW) allowing that customer requests are shipped to alternative delivery locations which can also have different time windows. Recently, the vehicle routing problem with delivery options was introduced into the scientific literature. It extends the GVRPTW by capacities of shared locations and by specifying service-level constraints defined by the customers’ preferences for delivery options. The vehicle routing problem with delivery options also generalizes the vehicle routing problem with home roaming delivery locations and the vehicle routing problem with multiple time windows. For all these GVRPTW variants, we present a widely applicable matheuristic that relies on a large neighborhood search (LNS) employing several problem-tailored destruction operators. Most of the time, the LNS performs relatively small and fast moves, but when the solution has not been improved for many iterations, a larger destruction move is applied to arrive in a different region of the search space. Moreover, an adaptive layer of the LNS embeds two exact components: First, a set-partitioning formulation is used to combine previously found routes to new solutions. Second, the Balas-Simonetti neighborhood is adapted to further improve already good solutions. These new components are in the focus of our work and we perform an exhaustive computational study to evaluate four configurations of the new matheuristic on several benchmark instances of the above-mentioned variants. On all the benchmark sets, our matheuristic is competitive with the previous state-of-the-art methods. In summary, the four configurations provide 81 new best-known solutions.

交付选项是具有时间窗口 (GVRPTW) 的广义车辆路径问题的核心，允许将客户请求运送到也可以具有不同时间窗口的替代交付地点。最近，科学文献中引入了具有交付选项的车辆路径问题。它通过共享位置的容量和通过指定由客户对交付选项的偏好定义的服务级别约束来扩展 GVRPTW。具有交付选项的车辆路径问题还概括了具有家庭漫游交付位置的车辆路径问题和具有多个时间窗口的车辆路径问题。对于所有这些 GVRPTW 变体，我们提出了一种广泛适用的数学方法，它依赖于使用多个针对问题定制的破坏算子的大型邻域搜索 (LNS)。大多数情况下，LNS 执行相对较小且较快的移动，但是当解决方案经过多次迭代都没有改进时，会应用更大的破坏移动以到达搜索空间的不同区域。此外，LNS 的自适应层嵌入了两个精确的组件：首先，集合分区公式用于将先前找到的路径组合到新的解决方案中。其次，Balas-Simonetti 社区经过调整以进一步改进已经很好的解决方案。这些新组件是我们工作的重点，我们进行了详尽的计算研究，以在上述变体的几个基准实例上评估新数学的四种配置。在所有基准集上，我们的数学方法与之前最先进的方法具有竞争力。总之，这四种配置提供了 81 个新的最知名的解决方案。