做大规模优化或运筹学的团队终于有了加速Benders分解的实用方案——Proxy-BD用代理模型替代重复求解，理论保证不变但速度提升百倍，处理2000x2000规模问题的可以直接试。
Benders分解是求解大规模混合整数优化问题的经典框架，但传统方法反复求解相似子问题，收敛慢。本文提出代理Benders分解（Proxy-BD），用自监督的预测-投影-补全机制生成对偶可行解，产生有效的Benders割，保证理论有效性。在大规模设施选址和网络设计问题上，Proxy-BD实现中位最优性差距低于0.5%，加速高达161倍，割数量减少240倍以上。该方法在子问题复杂度高时加速效果更显著，适合大规模分解场景。
The Proxy Benders Decomposition
Benders decomposition is a fundamental framework for solving large-scale mixed-integer optimization problems with complicating variables that, when fixed, yield significantly easier subproblems. However, classical Benders decomposition repeatedly solves highly similar subproblems and often exhibits zigzagging behavior across iterations, leading to slow convergence in large-scale settings. Motivated by the repetitive structure and parametric nature of Benders subproblems, this paper introduces the proxy Benders decomposition (Proxy-BD), a new decomposition framework in which subproblem optimization is replaced by certified optimization proxies rather than repeated exact solves. The proposed proxy follows a self-supervised predict-project-and-complete mechanism that produces dual-feasible solutions for generating provably valid Benders cuts. The framework preserves the theoretical validity of the decomposition independently of prediction quality through a projection-and-completion certification layer. A formal characterization of proxy-induced cuts is established, and the framework naturally extends to modern decomposition schemes, including branch-and-Benders-cut algorithms. Computational experiments on large-scale facility location and network design problems demonstrate that Proxy-BD substantially reduces the computational effort of subproblems while maintaining near-optimal solution quality. On large-scale uncapacitated facility location instances up to 2000x2000, Proxy-BD achieves median optimality gaps below 0.5%, yields up to 161x median speedups, and reduces the number of generated cuts by more than 240x on the largest instances. The computational gains consistently increase with recourse complexity, indicating that proxy-based inference scales substantially more favorably than repeated exact subproblem optimization in large-scale decomposition settings.