AI 中文总结
本研究开发了开源软件包SDDmiP.jl，实现带ReLU割的可证收敛Benders型分解算法，结合两种割选择策略与交替割准则，经四类多阶段随机整数规划实验验证了方法性能。
AI 中文摘要
我们提出一款开源软件包，用于实现多阶段随机整数规划的可证收敛Benders型分解算法。除Benders割、强化Benders割、拉格朗日割等标准割族外，该算法还整合了整流线性单元（ReLU）割，可为一般混合整数状态变量提供收敛保证。不过，用于生成这些割的对偶问题常存在多个最优解。尽管每个解都会生成一个可分离当前可行解的有效割，但生成的割在近似子问题成本的效果上存在差异。为强化这些割，本软件包实现并评估了两种基于对偶问题归一化和正则化的割选择策略。我们还引入了交替割准则，当Benders割有效时使用成本更低的该类割，仅在必要时调用成本更高的紧割。针对四类多阶段随机整数规划的计算实验对这些方法进行了基准测试，并揭示了问题结构如何影响其实际性能。
英文摘要
We present an open-source software package that implements a provably convergent Benders-type decomposition algorithm for multistage stochastic integer programs. In addition to standard cut families, such as Benders, strengthened Benders, and Lagrangian cuts, the algorithm incorporates rectified linear unit (ReLU) cuts, which provide convergence guarantees for general mixed-integer state variables. However, the dual problems used to generate these cuts often admit multiple optimal solutions. Although each solution yields a valid cut that separates the incumbent, the resulting cuts can differ in how well they approximate the subproblem cost. To strengthen these cuts, our package implements and evaluates two cut-selection strategies based on normalization and regularization of the dual problem. We also incorporate an alternating-cut criterion that uses cheaper Benders cuts when they are effective and invokes more expensive tight cuts only when necessary. Computational experiments on four classes of multistage stochastic integer programs benchmark these methods and provide insights on how problem structure affects their practical performance.
