On Generating Lagrangian Cuts for Two-Stage Stochastic Integer Programs
研究如何快速生成拉格朗日割来加强两阶段随机整数规划的Benders松弛，实验表明新方法比已有方法更快改善松弛，并在分支割算法中显著缩小搜索树。
We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation and are derived from solving single scenario integer programming subproblems identical to those used in the nonanticipative Lagrangian dual of a stochastic integer program. Although Lagrangian cuts have the potential to significantly strengthen the Benders relaxation, generating Lagrangian cuts can be computationally demanding. We investigate new techniques for generating Lagrangian cuts with the goal of obtaining methods that provide significant improvements to the Benders relaxation quickly. Computational results demonstrate that our proposed method improves the Benders relaxation significantly faster than previous methods for generating Lagrangian cuts and, when used within a branch-and-cut algorithm, significantly reduces the size of the search tree for three classes of test problems.