Vehicle routing problem with simultaneous pickup–delivery and time window (VRPSPDTW) is computationally challenging as it generalizes the classical and NP-hard vehicle routing problem. According to the state-of-the-art, VRPSPDTW usually has two hierarchical optimization objectives: a primary objective of minimizing the number of vehicles (NV) and a secondary objective of reducing the transportation distance (TD). Given the existing research and our trial results, we find that the optimization of TD is not necessarily a promotion for reducing NV. In this paper, an effective learning-based two-stage algorithm, which has never been studied before, is proposed to solve the VRPSPDTW. In the first stage, a modified variable neighborhood search with a learning-based objective function is proposed to minimize the primary objective with retaining the potential structures. In the second stage, a bi-structure based tabu search (BSTS) is designed to optimize the primary and secondary objectives further. The experimental results on 93 benchmark instances demonstrate that the proposed algorithm performs remarkably well both in terms of computational efficiency and solution quality. In particular, the proposed two-stage algorithm improve several best known solutions (either a better NV or a better TD when NV are the same) from the state-of-the-art. To our knowledge, this is the first learning-based two-stage algorithm for solving VRPSPDTW reaching such a performance. Finally, we empirically analyze several critical components of the algorithm to highlight their impacts on the performance of the proposed algorithm.

具有同时取货-交货和时间窗口（VRPSPDTW）的车辆路径问题在计算上具有挑战性，因为它概括了经典的和NP难的车辆路径问题。根据最新技术，VRPSPDTW通常具有两个层次优化目标：将车辆数量降至最少的主要目标（NV）和减少运输距离的次要目标（TD）。根据现有的研究和我们的试验结果，我们发现TD的优化不一定有助于降低NV。本文提出了一种有效的基于学习的两阶段算法，以解决VRPSPDTW问题。在第一阶段 提出了一种基于学习的目标函数的改进的可变邻域搜索，以在保留潜在结构的情况下最大程度地减少主要目标。在第二阶段，基于双结构的禁忌搜索（BSTS）被设计为进一步优化主要和次要目标。在93个基准实例上的实验结果表明，该算法在计算效率和解决方案质量方面均表现出色。特别地，所提出的两阶段算法从最新技术改进了几种最著名的解决方案（当NV相同时，是更好的NV或更好的TD）。据我们所知，这是解决此类问题的第一个基于学习的两阶段算法，可以解决VRPSPDTW问题。最后，