一种用于两阶段随机规划的L型细化链切割方法
A novel L-shaped refinement chain cuts method for two-stage stochastic programs
AI总结：
提出一种集成场景细化链与L型分解框架的新方法，通过分组求解子问题并建立理论收敛性，有效求解大规模风险厌恶两阶段随机规划问题。
摘要：
本文介绍了一种用于求解两阶段随机规划的新方法——L型细化链切割方法。该方法将场景细化链集成到经典的L型分解框架中。在所提出的方法中，完整场景集在细化链的每一层被划分为子组，每个子组求解一个子问题，而不是像经典L型方法那样为每个单独场景求解。该框架推广了经典的多切割和单切割L型公式。对于每个细化层，建立了收敛到原始两阶段随机规划最优解的理论性质。此外，用Benders切割刻画了连续细化层之间的关系，从而开发了一种基于迭代细化的求解算法，该算法在细化链的连续层之间迭代。在均值-风险公式下的两阶段随机固定费用多商品网络设计问题上评估了所提方法的有效性。基准实例上的计算实验证明了所提框架的良好性能，并突出了其在大规模风险厌恶随机优化问题中的适用性。
英文摘要：
This paper introduces the L-shaped refinement chain cuts method, a novel decomposition approach for solving two-stage stochastic programs. The proposed method generalizes the classical L-shaped framework by exploiting refinement chains of scenarios, where sequences of increasingly refined scenario partitions are considered. At each refinement level, the full scenario set is partitioned into subgroups, and one subproblem is solved for each subgroup rather than for each individual scenario as in the classical L-shaped method. The proposed framework provides a unified decomposition scheme in which the classical multi-cut and single-cut L-shaped formulations arise as special cases. Theoretical convergence properties to the optimal solution of the original two-stage stochastic program are established at each refinement level. Furthermore, the relationships between consecutive refinement levels are characterized in terms of Benders cuts, leading to the development of an iterative refinement-based solution algorithm. The effectiveness of the proposed method is evaluated on a two-stage stochastic fixed-charge multicommodity network design problem under a mean-risk formulation. Computational experiments validate the benefits of the proposed approach and highlight its applicability to large-scale risk-averse stochastic optimization problems.
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