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: A two-stage stochastic UC model with high renewable penetration including reserve requirements for the efficient management of uncertainty is presented, and a minimum conditional value at risk term has been included in the model formulation.
Abstract: Isolated regions and islands are facing imported fossil-fuel dependency, higher electricity prices, and vulnerability to climate change. At the same time, they are increasing their renewable penetration and, therefore, risk for electric utilities. Integrating stochastic energy resources in noninterconnected systems may take advantage of an intelligent and optimized risk-averse unit commitment (UC) model. This paper presents a two-stage stochastic UC model with high renewable penetration including reserve requirements for the efficient management of uncertainty. In order to account for the uncertainty around the true outcomes of load, wind, and photovoltaic (PV) generation, a minimum conditional value at risk term has been included in the model formulation. A stochastic measure of the value of the stochastic solution is used to evaluate the benefits of using stochastic programming. The model considers the need for reserves dependent on the forecasting horizon and the amount of renewable generation. Active power demand, and wind and PV generations are considered as probability distribution functions. The model is applied to the Lanzarote–Fuerteventura system in the Canary Islands, Spain, and Crete, Greece.
119 citations
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17 Oct 2004TL;DR: This work gives the first approximation algorithms for 2-stage discrete stochastic optimization problems with recourse for which the underlying random data is given by a "black box" and no restrictions are placed on the costs in the two stages, based on an FPRAS for the LP relaxation of the Stochastic problem (which has exponentially many variables and constraints).
Abstract: Stochastic optimization problems attempt to model uncertainty in the data by assuming that (part of) the input is specified in terms of a probability distribution. We consider the well-studied paradigm of 2-stage models with recourse: first, given only distributional information about (some of) the data one commits on initial actions, and then once the actual data is realized (according to the distribution), further (recourse) actions can be taken. We give the first approximation algorithms for 2-stage discrete stochastic optimization problems with recourse for which the underlying random data is given by a "black box" and no restrictions are placed on the costs in the two stages, based on an FPRAS for the LP relaxation of the stochastic problem (which has exponentially many variables and constraints). Among the range of applications we consider are stochastic versions of the set cover, vertex cover, facility location, multicut (on trees), and multicommodity flow problems.
119 citations
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01 Jan 1986TL;DR: A new method is proposed for solving two-stage problems in linear and quadratic stochastic programming that approximates the dual objective over the convex hull of finitely many dual feasible solutions.
Abstract: A new method is proposed for solving two-stage problems in linear and quadratic stochastic programming. Such problems are dualized, and the dual, althought itself of high dimension, is approximated by a sequence of quadratic programming subproblems whose dimensionality can be kept low. These subproblems correspond to maximizing the dual objective over the convex hull of finitely many dual feasible solutions. An optimizing sequence is produced for the primal problem that converges at a linear rate in the strongly quadratic case. An outer algorithm of augmented Lagrangian type can be used to introduce strongly quadratic terms, if desired.
119 citations
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TL;DR: The financial planning model InnoALM, developed at Innovest for the Austrian pension fund of the electronics firm Siemens, uses a multiperiod stochastic linear programming framework with a flexible number of time periods of varying length to improve pension fund performance.
Abstract: This paper describes the financial planning model InnoALM we developed at Innovest for the Austrian pension fund of the electronics firm Siemens. The model uses a multiperiod stochastic linear programming framework with a flexible number of time periods of varying length. Uncertainty is modeled using multiperiod discrete probability scenarios for random return and other model parameters. The correlations across asset classes, of bonds, stocks, cash, and other financial instruments, are state dependent using multiple correlation matrices that correspond to differing market conditions. This feature allows InnoALM to anticipate and react to severe as well as normal market conditions. Austrian pension law and policy considerations can be modeled as constraints in the optimization. The concave risk-averse preference function is to maximize the expected present value of terminal wealth at the specified horizon net of expected discounted convex (piecewise-linear) penalty costs for wealth and benchmark targets in each decision period. InnoALM has a user interface that provides visualization of key model outputs, the effect of input changes, growing pension benefits from increased deterministic wealth target violations, stochastic benchmark targets, security reserves, policy changes, etc. The solution process using the IBM OSL stochastic programming code is fast enough to generate virtually online decisions and results and allows for easy interaction of the user with the model to improve pension fund performance. The model has been used since 2000 for Siemens Austria, Siemens worldwide, and to evaluate possible pension fund regulation changes in Austria.
119 citations
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TL;DR: This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering.
Abstract: This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering. Since these methods usually require a careful tuning of the parameters which control the behavior of the strategies (strategy parameters), significant features of the algorithms implemented by the authors are presented. An analytical comparison among them is performed. Finally, results are discussed on three optimization problems.
119 citations