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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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Journal ArticleDOI
TL;DR: A new variant of the stochastic comparison method is proved that it is guaranteed to converge almost surely to the set of global optimal solutions and a result is presented that demonstrates that this method is likely to perform well in practice.
Abstract: We discuss the choice of the estimation of the optimal solution when random search methods are applied to solve discrete stochastic optimization problems. At the present time, such optimization methods usually estimate the optimal solution using either the feasible solution the method is currently exploring or the feasible solution visited most often so far by the method. We propose using all the observed objective function values generated as the random search method moves around the feasible region seeking an optimal solution to obtain increasingly more precise estimates of the objective function values at the different points in the feasible region. At any given time, the feasible solution that has the best estimated objective function value (largest one for maximization problems; the smallest one for minimization problems) is used as the estimate of the optimal solution. We discuss the advantages of using this approach for estimating the optimal solution and present numerical results showing that modifying an existing random search method to use tnhis approach for estimating the optimal soluation appears to yield improved performance. We also present sereval rate of convergence results for random search methods using our approach for estimating the optimal solution. One these random search methods is a new variant of the stochastic comparison method; in addition to specifying the rate of convergence of this method, we prove that it is guaranteed to converge almost surely to the set of global optimal solutions and present a result that demonstrates that this method is likely to perform well in practice.

128 citations

Journal ArticleDOI
TL;DR: A decomposition algorithm for solving the finite horizon problems and a heuristic procedure that is based on the structure of the optimal policy for two-period problems, which parallels the decision rules used by managers in practice.
Abstract: In this paper, we model production problems where yields are stochastic, demands are substitutable, and several items are jointly produced. We formulate this problem as a profit maximizing convex program, and study two approximation procedures. The first method solves finite horizon stochastic programs on a rolling horizon basis. We develop a decomposition algorithm for solving the finite horizon problems. The finite horizon problems are linear programs. Our algorithm utilizes the network-like structure of the coefficient matrix of the linear programs. The second method is a heuristic procedure that is based on the structure of the optimal policy for two-period problems. The heuristic parallels the decision rules used by managers in practice. The computational results suggest that the performance of this heuristic is comparable to that of the rolling horizon approach.

128 citations

Proceedings ArticleDOI
01 Oct 2003
TL;DR: An overview of the genetic algorithm (GA) and a new stochastic algorithm called particle swarm optimization (PSO) has been shown to be a valuable addition to the electromagnetic design engineer's toolbox.
Abstract: Modern antenna designers are constantly challenged to seek for optimum solutions for complex electromagnetic device designs. The temptation has grown because of ever increasing advances in computational power. The standard brute force design techniques are systematically being replaced by the state-of-the-art optimization techniques. The ability of using numerical methods to accurately and efficiently characterizing the relative quality of a particular design has excited the EM engineers to apply stochastic global optimizers. The genetic algorithm (GA) is the most popular of the so-called evolutionary methods in the electromagnetics community. Recently, a new stochastic algorithm called particle swarm optimization (PSO) has been shown to be a valuable addition to the electromagnetic design engineer's toolbox. In this paper we provide an overview of both techniques and present some representative examples. Most of the material incorporated in this invited plenary session paper is based on the earlier publication work by the author and his students at UCLA.

128 citations

Journal ArticleDOI
01 Sep 2011-Networks
TL;DR: A two‐stage stochastic programming formulation, where design decisions make up the first stage, while recourse decisions are made in the second stage to distribute the commodities according to observed demands, which is numerically shown to be computationally efficient and to yield high‐quality solutions under various problem characteristics and demand correlations.
Abstract: We consider the stochastic fixed-charge capacitated multicommodity network design (S-CMND) problem with uncertain demand. We propose a two-stage stochastic programming formulation, where design decisions make up the first stage, while recourse decisions are made in the second stage to distribute the commodities according to observed demands. The overall objective is to optimize the cost of the first-stage design decisions plus the total expected distribution cost incurred in the second stage. To solve this formulation, we propose a metaheuristic framework inspired by the progressive hedging algorithm of Rockafellar and Wets. Following this strategy, scenario decomposition is used to separate the stochastic problem following the possible outcomes, scenarios, of the random event. Each scenario subproblem then becomes a deterministic CMND problem to be solved, which may be addressed by efficient specialized methods. We also propose and compare different strategies to gradually guide scenario subproblems to agree on the status of design arcs and aim for a good global design. These strategies are embedded into a parallel solution method, which is numerically shown to be computationally efficient and to yield high-quality solutions under various problem characteristics and demand correlations. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011. © 2011 Wiley Periodicals, Inc.

128 citations

Proceedings ArticleDOI
12 Dec 2005
TL;DR: This paper takes a different route to solve MPC problems under uncertainty and shows that this formulation guarantees robust constraint fulfillment and that the expected value of the optimum cost function of the closed loop system decreases at each time step.
Abstract: Many robust model predictive control (MPC) schemes are based on min-max optimization, that is, the future control input trajectory is chosen as the one which minimizes the performance due to the worst disturbance realization In this paper we take a different route to solve MPC problems under uncertainty Disturbances are modelled as random variables and the expected value of the performance index is minimized The MPC scheme that can be solved using Stochastic Programming (SP), for which several efficient solution techniques are available We show that this formulation guarantees robust constraint fulfillment and that the expected value of the optimum cost function of the closed loop system decreases at each time step

128 citations


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