Abstract In this paper, we extend, analyze and evaluate the exponential multi-insertion neighborhood for the vehicle routing problem with unit demands, originally proposed by Angel et al. (2008). In this neighborhood, a neighbor solution is obtained by the removal of a set of mobile nodes from a solution and a subsequent best reinsertion. At first, we examine theoretical properties of the neighborhood, such as its connectivity and the question how many nodes may be chosen as mobile. Furthermore, we prove that finding a best set of mobile nodes is NP-hard. Then, we present a two-stage approach in which first mobile nodes are selected heuristically and reinserted in an optimal way afterwards. Finally, this approach is embedded into a simulated annealing procedure and compared to other heuristics known for the more general vehicle routing problem with arbitrary demands.

中文翻译：

---

具有单位需求的车辆路径问题的指数多重插入邻域

摘要 在本文中，我们扩展、分析和评估了最初由 Angel 等人提出的具有单位需求的车辆路径问题的指数多插入邻域。(2008)。在这个邻域中，邻居解是通过从解中移除一组移动节点和随后的最佳重新插入来获得的。首先，我们检查邻域的理论属性，例如它的连通性以及可以选择多少节点作为移动节点的问题。此外，我们证明找到一组最佳移动节点是 NP 难的。然后，我们提出了一种两阶段方法，其中先启发式地选择第一个移动节点，然后以最佳方式重新插入。最后，