Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
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TL;DR: The analysis provides a unified framework for convergence of some problems where the ambiguity set is approximated in a process with increasing information on uncertainty and extends the classical convergence analysis in stochastic programming.
Abstract: In this paper, we study distributionally robust optimization approaches for a one-stage stochastic minimization problem, where the true distribution of the underlying random variables is unknown but it is possible to construct a set of probability distributions, which contains the true distribution and optimal decision is taken on the basis of the worst-possible distribution from that set. We consider the case when the distributional set (which is also known as the ambiguity set) varies and its impact on the optimal value and the optimal solutions. A typical example is when the ambiguity set is constructed through samples and we need to look into the impact of increasing the sample size. The analysis provides a unified framework for convergence of some problems where the ambiguity set is approximated in a process with increasing information on uncertainty and extends the classical convergence analysis in stochastic programming. The discussion is extended briefly to a stochastic Nash equilibrium problem wh...
95 citations
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TL;DR: This article proposes an approach that translates an expressive subset of the PPDDL representation to a first-order MDP (FOMDP) specification and then derives a domain-independent policy without grounding at any intermediate step and presents proof-of-concept results of this approach.
95 citations
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TL;DR: To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs and to deal with the “Curse of Dimensionality” of stochastically programming.
Abstract: To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the “Curse of Dimensionality” of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.
95 citations
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TL;DR: In this paper, a stochastic bilevel model is proposed, whose upper level represents the wind investment and operation decisions with the target of maximizing profits; and its lower-level represents the market clearing under differing load and wind conditions and provides LMPs.
95 citations
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TL;DR: The results show that the complementarity of hydropower and PV power in long-term operations is highly necessary, and considering the uncertainty of stochastic streamflow and PV output simultaneously improves the efficiency of complementary operations.
94 citations