Worst-Case-Expectation Approach to Optimization Under Uncertainty
Alexander Shapiro, Wajdi Tekaya, Murilo Pereira Soares, Joari Paulo da Costa
Operations Research · 2013 · Volume 61 · Issue 6
Abstract
In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation where the data process can be naturally separated into two components: one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst-case) point of view. We formulate this in a time consistent way and derive the corresponding dynamic programming equations. To solve the obtained multistage problem, we develop a variant of the stochastic dual dynamic programming method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.
Keywords
multistage stochastic programming, robust optimization, time consistency, dynamic equations, stochastic dual dynamic programming, sample average approximation, risk-neutral and risk-averse approaches, case studies
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