结合积分定价的分支定价与切割算法用于具有时间窗和充电时间槽的电动车路径规划问题
A Pricing-for-Integrality Primal Heuristic for Branch-and-Price: An Application to the Electric Vehicle Routing Problem with Time Windows and Charging Time Slots
AI总结：
本文提出一种基于积分定价的启发式方法，用于解决具有时间窗和充电时间槽的电动车路径规划问题，有效缩小根节点间隙。
摘要：
分支定价与切割是解决许多车辆路径问题的最新精确方法，尤其在具有时间窗的车辆路径问题中效果显著。分支定价与切割面临的一个挑战是列的生成由主问题线性松弛的信息引导，无法保证从整数角度具有用处。因此，高质量的原解往往只能在显著的切割和分支或使用原启发式方法之后才能找到。在本工作中，基于积分定价的思想，我们提出了一种新的车辆路径问题的原启发式方法。该启发式方法旨在生成更可能成为高质量整数解组成部分的列。它首先从给定的列池中构建一个部分整数解，然后迭代搜索补充该解的列。搜索通过修改与部分解相关的定价问题、线性规划对偶信息以及之前生成的列来完成。在具有时间窗和充电时间槽的电动车路径规划问题上进行了计算测试，这是一个具有调度和路径规划方面的难题，使其非常适合评估所提启发式的性能。结果表明，所提启发式方法在比较于受限主启发式方法时，平均关闭根节点间隙30% - 40%。
英文摘要：
Branch-price-and-cut is the state-of-the-art exact method for solving many types of vehicle routing problems, and it is particularly effective for vehicle routing problems with time windows. A well-known challenge in branch-price-and-cut is that the generation of columns is guided by information from the linear relaxation of the master problem, with no guarantee that they will be useful from an integer perspective. As a consequence, high-quality primal solutions are often found only after significant cutting and branching, or the use of primal heuristics. In this work, based on the ideas of pricing-for-integrality, we propose a primal heuristic for branch-and-price and evaluate it on the electric vehicle routing problem with time windows extended with charging time slots. The heuristic first uses a destroy-and-repair phase to enrich the column pool and then applies a restricted master heuristic to obtain a primal solution. In the destroy-and-repair phase, route generation is guided by scaled dual values and heuristic feedback based on previously generated routes, with the aim of producing routes likely to contribute to high-quality integer solutions. Computational tests on the electric vehicle routing problem with time windows extended with charging time slots show that the proposed heuristic reduces the average optimality gap in the root node by around 60% compared to a restricted master heuristic and by around 25% - 30% compared to the implemented benchmark diving heuristic.
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