用Transformer加速大规模随机优化求解，突破以往计算瓶颈。
Learning to Optimize at Scale: A Benders Decomposition-TransfORmers Framework for Stochastic Combinatorial Optimization
- 用预训练Transformer快速生成场景子问题的优质近似解
- 在T=270的实例上实现零不可行性，收敛速度显著提升
- 模型可扩展至任意时长问题，适合大规模生产调度场景
我们提出一种学习增强的Benders分解框架，用于求解大规模两阶段随机混合整数规划。针对需求不确定性下的两阶段随机容量限制生产计划问题（TSSCLSP），通过预训练Transformer模型快速生成高质量的场景子问题近似解，加速分解算法收敛。该方法利用Transformer预测结果生成强最优性和可行性割平面，有效指导主问题求解。框架包含一种新型可扩展生成机制，使在固定时长下训练的模型可处理任意长度实例。测试中，该方法成功求解达T=270的实例，此前此类规模难以处理，且生成的子问题解保持零不可行性，验证了Transformer作为嵌入经典分解算法的高效代理求解器的潜力。
原文摘要 · Abstract (English)
We propose a learning-augmented Benders decomposition framework to solve large-scale two-stage stochastic mixed-integer programs. We focus on the two-stage stochastic capacitated lot-sizing problem (TSSCLSP) under demand uncertainty. Our method accelerates the convergence of the decomposition by using a pre-trained TransfORmer model to rapidly generate high-quality approximate solutions for the scenario subproblems. This hybrid strategy uses the TransfORmer predictions to generate strong optimality and feasibility cuts, effectively guiding the Benders master problem. Our framework includes a novel expandable generation mechanism, allowing a model trained on a fixed horizon to solve instances of arbitrary length. For the test set considered, our method solves instances up to T = 270, a scale previously intractable for this approach, while maintaining zero infeasibility in the generated subproblem solutions. This demonstrates the potential of TransfORmers as powerful surrogate solvers embedded within classical decomposition algorithms.
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