Robust Dual Dynamic Programming

• 成果类型: Article
• 署名作者: Georghiou, Angelos; Tsoukalas, Angelos; Wiesemann, Wolfram
• 署名单位: McGill University; American University of Beirut; Imperial College London
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2018.1835
• 发表日期: 2019
• 页码: 813-830
• 关键词: unit commitment; optimization; DECOMPOSITION; uncertainty

摘要

Multistage robust optimization problems, where the decision maker can dynamically react to consecutively observed realizations of the uncertain problem parameters, pose formidable theoretical and computational challenges. As a result, the existing solution approaches for this problem class typically determine suboptimal solutions under restrictive assumptions. In this paper, we propose a robust dual dynamic programming (RDDP) scheme for multistage robust optimization problems. The RDDP scheme takes advantage of the decomposable nature of these problems by bounding the costs arising in the future stages through lower and upper cost-to-go functions. For problems with uncertain technology matrices and/or constraint right-hand sides, our RDDP scheme determines an optimal solution in finite time. Also, if the objective function and/or the recourse matrices are uncertain, our method converges asymptotically (but deterministically) to an optimal solution. Our RDDP scheme does not require a relatively complete recourse, and it offers deterministic upper and lower bounds throughout the execution of the algorithm. We show the promising performance of our algorithm in a stylized inventory management problem.