面向可行性的模仿学习用于Benders分解
Feasibility-Aware Imitation Learning for Benders Decomposition
AI总结：
本文提出一种面向可行性的模仿学习框架，用于加速Benders分解，通过预测主问题的整数变量值并考虑约束条件下的可行性，提升求解效率并保持准确性。
摘要：
混合整数优化问题广泛应用于控制领域。Benders分解是一种用于解决此类问题的常用算法，通过将其分解为主问题和连续子问题。关键的计算瓶颈是迭代过程中反复求解日益复杂的主问题。本文提出了一种面向可行性的模仿学习框架，能够在每次迭代中预测主问题的整数变量值，同时考虑约束条件下的可行性以及累积的Benders可行性切割。代理通过两阶段程序进行训练，结合行为克隆和基于可行性的logit调整，使预测偏向满足演变切割集的分配。该代理部署在基于代理的Benders分解框架中，结合显式的可行性检查和限时求解器计算有效的下界。所提出的方法保留了有限收敛性，因为下界在每次迭代中都被证明。在典型案例研究中的应用表明，所提出的方法在加速Benders分解方面比现有模仿学习方法更有效，同时保持了解的准确性。
英文摘要：
Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous subproblem. A key computational bottleneck is the repeated solution of increasingly complex master problems across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the values of the integer variables of the master problem at each iteration while accounting for feasibility with respect to constraints governing admissible integer assignments and the accumulated Benders feasibility cuts. The agent is trained using a two-stage procedure that combines behavioral cloning with a feasibility-based logit adjustment to bias predictions toward assignments that satisfy the evolving cut set. The agent is deployed within an agent-based Benders decomposition framework that combines explicit feasibility checks with a time-limited solver computation of a valid lower bound. The proposed approach retains finite convergence properties, as the lower bound is certified at each iteration. Application to a prototypical case study shows that the proposed method improves solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
