The generalized vehicle routing problem with time windows (GVRPTW) is defined on a directed graph $\mathcal{G}=(\mathcal{V},\mathcal{A})$ where the vertex set $\mathcal{V}$ is partitioned into clusters. One cluster contains only the depot, where is located a homogeneous fleet of vehicles, each with a limited capacity. The other clusters represent customers. A demand is associated with each cluster. Inside a cluster, the vertices represent the possible locations of the customer. A time window is associated with each vertex, during which the visit must take place if the vertex is visited. The objective is to find a set of routes such that the total traveling cost is minimized, exactly one vertex per cluster is visited, and all the capacity and time constraints are respected. This paper presents a set covering formulation for the GVRPTW which is used to provide a column generation based heuristic to solve it. The proposed solving method combines several components including a construction heuristic, a route optimization procedure, local search operators and the generation of negative reduced cost routes. Experimental results on benchmark instances show that the proposed algorithm is efficient and high-quality solutions for instances with up to 120 clusters are obtained within short computation times.

具有时间窗的广义车辆路径问题 (GVRPTW) 在有向图上定义 $\mathcal{G}=(\mathcal{伏},\mathcal{一种})$ 顶点集在哪里 $\mathcal{伏}$被划分成簇。一个集群只包含一个仓库，那里有一个同质的车队，每个车队的容量有限。其他集群代表客户。一个需求与每个集群相关联。在集群内，顶点表示客户的可能位置。一个时间窗口与每个顶点相关联，在该时间窗口期间，如果访问了顶点，则必须进行访问。目标是找到一组路线，使得总旅行成本最小，每个集群只访问一个顶点，并且所有容量和时间限制都得到尊重。本文提出了 GVRPTW 的集合覆盖公式，用于提供基于列生成的启发式方法来解决它。所提出的求解方法结合了几个组件，包括构造启发式，路线优化程序、本地搜索运营商和负成本降低路线的生成。在基准实例上的实验结果表明，该算法是有效的，并且在较短的计算时间内获得了多达 120 个集群的实例的高质量解决方案。