用强化学习自动选切割，让优化算法跑得更快更稳。
Learning to Cut: Reinforcement Learning for Benders Decomposition
- 用神经网络策略+REINFORCE算法动态选择最优切割
- 在电动汽车充电站选址问题上提速超50%，且泛化性强
- 适合处理大规模随机规划问题的工程师和研究者
Benders分解（BD）是求解现实世界中不确定性决策问题的两阶段随机规划的常用方法。然而，随着切割数量增加，主问题规模膨胀，导致收敛缓慢。本文提出基于强化学习的BD框架（RLBD），通过神经网络构建随机策略，自适应选择切割，并采用REINFORCE算法进行策略梯度训练。在两阶段随机电动汽车充电站选址问题上评估，结果表明RLBD显著提升计算效率，相比原始BD和基于支持向量机的监督学习方法LearnBD，在不同数据输入与变量维度下均表现出强泛化能力。
原文摘要 · Abstract (English)
Benders decomposition (BD) is a widely used solution approach for solving two-stage stochastic programs arising in real-world decision-making under uncertainty. However, it often suffers from slow convergence as the master problem grows with an increasing number of cuts. In this paper, we propose Reinforcement Learning for BD (RLBD), a framework that adaptively selects cuts using a neural network-based stochastic policy. The policy is trained using a policy gradient method via the REINFORCE algorithm. We evaluate the proposed approach on a two-stage stochastic electric vehicle charging station location problem and compare it with vanilla BD and LearnBD, a supervised learning approach that classifies cuts using a support vector machine. Numerical results demonstrate that RLBD achieves substantial improvements in computational efficiency and exhibits strong generalization to problems with similar structures but varying data inputs and decision variable dimensions.
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