Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in recent years, but approaches based purely on machine learning are still outperformed by state-of-the-art optimization methods. To close this performance gap, we propose a novel large neighborhood search (LNS) framework for vehicle routing that integrates learned heuristics for generating new solutions. The learning mechanism is based on a deep neural network with an attention mechanism and has been especially designed to be integrated into an LNS search setting. We evaluate our approach on the capacitated vehicle routing problem (CVRP), the split delivery vehicle routing problem (SDVRP), and the capacitated team orienteering problem (CTOP). We show that the NLNS approach is able to outperform a handcrafted LNS on the CVRP and SDVRP and match the performance of a standard LNS on the CTOP. NLNS is thus able to quickly and effectively learn high performance heuristics to maneuver through the search space of difficult routing problems, coming close to the performance of state-of-the-art optimization approaches.

学习如何自动解决优化问题有可能提供优化技术的下一个重大飞跃。近年来，自动学习启发式算法在路由问题上的性能一直在稳步提高，但纯粹基于机器学习的方法仍然优于最先进的优化方法。为了缩小这一性能差距，我们提出了一种新颖的大型邻域搜索 (LNS) 框架，用于车辆路径，该框架集成了学习的启发式算法以生成新的解决方案。学习机制基于具有注意力机制的深度神经网络，并专门设计用于集成到 LNS 搜索设置中。我们评估了我们在容量车辆路径问题 (CVRP)、拆分交付车辆路径问题 (SDVRP) 上的方法，和有能力的团队定向问题（CTOP）。我们展示了 NLNS 方法能够在 CVRP 和 SDVRP 上优于手工制作的 LNS，并在 CTOP 上与标准 LNS 的性能相匹配。因此，NLNS 能够快速有效地学习高性能启发式算法，以在困难路由问题的搜索空间中进行机动，接近最先进优化方法的性能。