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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: This paper proves asymptotic convergence of the new NP method and presents a numerical example to illustrate its potential and adapt the original NP method to stochastic optimization where the performance is estimated using simulation.
Abstract: The nested partitions (NP) method is a recently proposed new alternative for global optimization. Primarily aimed at problems with large but finite feasible regions, the method employs a global sampling strategy that is continuously adapted via a partitioning of the feasible region. In this paper we adapt the original NP method to stochastic optimization where the performance is estimated using simulation. We prove asymptotic convergence of the new method and present a numerical example to illustrate its potential.

149 citations

Journal ArticleDOI
TL;DR: In this paper, a simple but effective solution method capable of tackling problems with large numbers of potential members (e.g. >100,000,000) is presented. But this method requires a ground structure with minimal connectivity to be used in the first iteration; members are then added as required in subsequent iterations until the (provably) optimal solution is found.
Abstract: Computerized layout (or “topology”) optimization was pioneered almost four decades back. However, despite dramatic increases in available computer power and the application of increasingly efficient optimization algorithms, even now only relatively modest sized problems can be tackled using the traditional “ground structure” approach. This is because of the need, in general, for the latter to contain every conceivable member connecting together the nodes in a problem. A simple, but effective solution method capable of tackling problems with large numbers of potential members (e.g. >100,000,000) is presented. Though the method draws on the linear programming technique of “column generation”, since layout optimization specific heuristics are employed it is presented as an iterative “member adding” method. The method requires a ground structure with minimal connectivity to be used in the first iteration; members are then added as required in subsequent iterations until the (provably) optimal solution is found.

148 citations

Journal ArticleDOI
TL;DR: This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines and introduces a risk factor by means of the mean-variance Markowitz theory.
Abstract: In this paper, a new model for generation and transmission expansion is presented. This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines. In order to incorporate these random events into an optimization model, stochastic programming and probabilistic constraints are used. A risk factor is introduced in the objective function by means of the mean-variance Markowitz theory. The solved optimization problem is a mixed integer nonlinear program. The expected value of perfect information is obtained in order to show the cost of ignoring uncertainty. The proposed model is illustrated by a six- and a 21-node network using a dc approximation.

148 citations

Journal ArticleDOI
TL;DR: A stochastic dynamic programming model is developed that co-optimizes the use of energy storage for multiple applications, such as energy, capacity, and backup services, while accounting for market and system uncertainty.
Abstract: We develop a stochastic dynamic programming model that co-optimizes the use of energy storage for multiple applications, such as energy, capacity, and backup services, while accounting for market and system uncertainty. Using the example of a battery that has been installed in a home as a distributed storage device, we demonstrate the ability of the model to co-optimize services that ‘compete’ for the capacity of the battery. We also show that these multiple uses of a battery can provide substantive value.

148 citations

Journal ArticleDOI
TL;DR: In this paper, the sample average approximation (SAA) method is applied to a class of stochastic mathematical programs with variational (equilibrium) constraints, and it is shown almost sure convergence of optimal values, optimal solutions, and generalized Karush-Kuhn-Tucker points of the SAA program to their true counterparts.
Abstract: In this article, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both–the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and generalized Karush–Kuhn–Tucker points of the SAA program to their true counterparts. We also study uniform exponential convergence of the sample average approximations, and as a consequence derive estimates of the sample size required to solve the true problem with a given accuracy. Finally, we present some preliminary numerical test results.

148 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532