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: (stability) theory-based heuristics for generating scenario trees out of an initial set of scenarios based on forward or backward algorithms for tree generation consisting of recursive scenario reduction and bundling steps are developed.
Abstract: An important issue for solving multistage stochastic programs consists in the approximate representation of the (multivariate) stochastic input process in the form of a scenario tree. In this paper, we develop (stability) theory-based heuristics for generating scenario trees out of an initial set of scenarios. They are based on forward or backward algorithms for tree generation consisting of recursive scenario reduction and bundling steps. Conditions are established implying closeness of optimal values of the original process and its tree approximation, respectively, by relying on a recent stability result in Heitsch, Romisch and Strugarek (SIAM J Optim 17:511–525, 2006) for multistage stochastic programs. Numerical experience is reported for constructing multivariate scenario trees in electricity portfolio management.
271 citations
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TL;DR: In this article, a robust optimization approach for transmission network expansion planning (TNEP) under uncertainties of renewable generation and load is presented. But this approach does not require knowledge of the probability distribution of the uncertain net injections; rather the uncertainties of the net injections are specified by a simple uncertainty set.
Abstract: This paper presents a robust optimization approach for transmission network expansion planning (TNEP) under uncertainties of renewable generation and load. Unlike conventional stochastic programming, the proposed approach does not require knowledge of the probability distribution of the uncertain net injections; rather the uncertainties of the net injections are specified by a simple uncertainty set. The solution algorithm is exact and produces expansion plans that are robust against all possible realizations of the net injections defined in the uncertainty set; it is based on a Benders decomposition scheme that iterates between a master problem that minimizes the cost of the expansion plan and a slave problem that minimizes the maximum curtailment of load and renewable generation. The paper demonstrates that when adopting the dc load flow model, both the master and the dual slave can be formulated as mixed-integer linear programs for which commercial solvers exist. Numerical results on several networks with uncertainties in their loads and renewable generation show that the proposed approach produces solutions that are superior to those from two recent techniques for robust TNEP design.
271 citations
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TL;DR: In this paper, a stochastic programming model for an integrated forward/reverse logistics network design under uncertainty is developed to avoid the sub-optimality caused by the separate design of the forward and reverse networks.
270 citations
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TL;DR: The structure of the value function of the second-stage integer problem is exploited to develop a novel global optimization algorithm that avoids explicit enumeration of the search space while guaranteeing finite termination.
Abstract: This paper addresses a general class of two-stage stochastic programs with integer recourse and discrete distributions. We exploit the structure of the value function of the second-stage integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination. Computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature.
266 citations
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TL;DR: The results show that the performance of the multi-stage stochastic program could be improved drastically by choosing an appropriate scenario generation method.
266 citations