自适应鲁棒优化的软分离方法
Soft Separation for Adaptive Robust Optimization
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中文总结 AI 辅助
提出一种基于软分离机制的自适应鲁棒优化算法框架，通过时间非齐次马尔可夫链识别最坏情况，实现多项式时间收敛到全局最优，并适用于混合整数决策。
中文摘要 AI 辅助
我们提出了一种求解自适应鲁棒优化的算法框架，该框架在可处理性和解精度方面均具有可证明的保证。该框架引入了软分离，这是一种通过时间非齐次马尔可夫链识别最坏情况不确定性实现的概率机制。该框架不求解每次迭代中精确的分离问题（这在一般情况下是难以处理的），而是通过该链在迭代之间传递对抗性信息，与优化迭代共同演化，并在终端迭代处以高概率恢复精确分离。对于连续的第一阶段（此处即现在）决策，我们设计了一种使用软分离生成自适应梯度估计的一阶方法。值得注意的是，我们证明了在期望意义上多项式时间收敛到全局最优。对于混合整数此处即现在决策，我们将软分离嵌入分支切割框架中，为鲁棒目标生成有效割，并获得全局最优性的高概率证书。数值实验表明，与最先进的方法相比，所提出的方法在问题维度和场景规模方面具有良好的扩展性。实例和代码可在该https URL在线获取。
英文摘要
We propose an algorithmic framework for solving adaptive robust optimization with provable guarantees on both tractability and solution accuracy. The framework introduces soft separation, a probabilistic mechanism for identifying worst-case uncertainty realizations via a time-inhomogeneous Markov chain. Rather than solving an exact separation problem in each iteration, which is intractable in general, the chain carries adversarial information across iterations, co-evolves with the optimization iterates, and recovers exact separation at terminal iterates with high probability. For continuous first-stage (here-and-now) decisions, we design a first-order method that uses soft separation to produce adaptive gradient estimates. Notably, we prove polynomial-time convergence in expectation to the global optimum. For mixed-integer here-and-now decisions, we embed soft separation within a branch-and-cut framework to generate valid cuts for the robust objective and obtain a high-probability certificate of global optimality. Numerical experiments demonstrate that the proposed methods scale favorably with problem dimension and scenario size relative to state-of-the-art approaches. The instances and code are available online at https://github.com/xuqy2002/SoftSeparationARO.
发表机构
- University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。
