发表机构
Cornell Tech; Jacobs Technion-Cornell Institute, Cornell Tech and Technion – IIT; Department of Industrial and Enterprise Systems Engineering, University of Illinois Urbana-Champaign（康奈尔科技; 雅各布泰康-康奈尔学院、康奈尔科技和以色列理工学院; 伊利诺伊大学厄巴纳-香槟分校工业与企业系统工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出输入凸神经网络与神经-本德斯校正相结合的方法，学习两阶段随机机组组合问题的凸代理，实现快速求解并保证质量，在IEEE基准上达到零最优性差距，加速高达214倍。
AI 中文摘要
两阶段随机混合整数线性规划是在不确定性下优化电力系统运行的典型建模工具，然而其扩展形式（extensive-form）的规模随场景数量线性增长，在日前时间约束下很快变得计算上不可行。我们提出了一种输入凸神经网络（Input Convex Neural Network）架构，用于学习第二阶段价值函数的凸代理（convex surrogate），从而在保持凸性的同时实现快速的第一阶段优化。我们将该代理与神经-本德斯（Neural-Benders）校正循环相结合，该循环事后细化第一阶段解，无论网络是高估还是低估了追索成本（recourse cost），都能恢复精确最优解，并且独立于代理精度对解质量进行认证。我们在IEEE随机机组组合基准（case9-case118）上，在连续和整数追索两种设置下评估了该方法。所提出的方法在所有测试案例和场景维度K∈{10,50,100}下，在K场景实例上实现了零最优性差距的解，在整数设置下相比扩展形式（Extensive Form）加速高达214倍。求解时间在不同场景实现中保持稳定，并且在所测试的基准实例上兼容于日前时间窗口。
英文摘要
Two-stage stochastic Mixed-Integer Linear Programs are a canonical modeling tool to optimize power system operations under uncertainty, yet their extensive-form counterparts scale linearly with the number of scenarios and quickly become computationally prohibitive under day-ahead time constraints. We propose an Input Convex Neural Network architecture to learn a convex surrogate of the second-stage value function, enabling fast first-stage optimization while preserving convexity by construction. We couple the surrogate with a Neural-Benders correction loop that refines the first-stage solution a posteriori, recovering the exact optimum whether the network overestimates or underestimates the recourse cost, and certifying solution quality independently of surrogate accuracy. We evaluate the method on IEEE Stochastic Unit Commitment benchmarks (case9-case118) under both continuous and integer recourse. The proposed approach achieves solutions with zero optimality gap on the $K$-scenario instance across all test cases and scenario dimensions $K \in \{10, 50, 100\}$, with speedups up to $214\times$ over the Extensive Form in the integer setting. Solve times are stable across scenario realizations and compatible with day-ahead time windows on the tested benchmark instances.
Comments11 pages, 2 figures, 3 tables, 1 algorithm. Submitted to IEEE Transactions on Power Systems
