通过基于强化学习的超启发式方法增强列生成在车辆路径与调度问题中的性能
Enhancing Column Generation by Reinforcement Learning-Based Hyper-Heuristic for Vehicle Routing and Scheduling Problems
AI总结：
提出基于强化学习的超启发式框架RLHH嵌入列生成中，通过选择低级启发式构建缩减网络加速收敛，在VRPTW和BDSP上分别降低最多27.9%和15.4%的总成本，是首个在解质量上超越传统方法的RL-based CG方法。
摘要：
列生成（CG）是一种通过动态生成变量来解决大规模问题的重要方法。它在常见的组合优化问题中有着广泛的应用，例如车辆路径和调度问题，其中每一步迭代都需要求解一个NP难约束的最短路径问题。尽管已有一些加速的启发式方法，但它们不够通用，无法解决不同的问题。在这项工作中，我们提出了一种基于强化学习的超启发式框架，称为RLHH，以增强CG的性能。RLHH是一个嵌入在CG中的选择模块，用于加速收敛并获得更好的整数解。在每次CG迭代中，RL代理选择一个低级启发式来构建一个缩减网络，仅包含更有可能成为最优解一部分的边。此外，我们将RLHH具体应用于解决两个典型的组合优化问题：带时间窗的车辆路径问题（VRPTW）和公交驾驶员调度问题（BDSP）。在我们测试的场景中，与最佳低级启发式相比，总成本在VRPTW中最多可降低27.9%，在BDSP中最多可降低15.4%，且计算时间相当或更少。所提出的RLHH是首个在解质量上超越传统方法的基于RL的CG方法，这可以促进CG在组合优化中的应用。
英文摘要：
Column generation (CG) is a vital method to solve large-scale problems by dynamically generating variables. It has extensive applications in common combinatorial optimization, such as vehicle routing and scheduling problems, where each iteration step requires solving an NP-hard constrained shortest path problem. Although some heuristic methods for acceleration already exist, they are not versatile enough to solve different problems. In this work, we propose a reinforcement learning-based hyper-heuristic framework, dubbed RLHH, to enhance the performance of CG. RLHH is a selection module embedded in CG to accelerate convergence and get better integer solutions. In each CG iteration, the RL agent selects a low-level heuristic to construct a reduced network only containing the edges with a greater chance of being part of the optimal solution. In addition, we specify RLHH to solve two typical combinatorial optimization problems: Vehicle Routing Problem with Time Windows (VRPTW) and Bus Driver Scheduling Problem (BDSP). The total cost can be reduced by up to 27.9\% in VRPTW and 15.4\% in BDSP compared to the best lower-level heuristic in our tested scenarios, within equivalent or even less computational time. The proposed RLHH is the first RL-based CG method that outperforms traditional approaches in terms of solution quality, which can promote the application of CG in combinatorial optimization.
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