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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.


Papers
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Journal ArticleDOI
TL;DR: The stochastic p-hub center problem with chance constraints is presented, which is used to model the service-level guarantees of small package delivery companies and discusses analytical results, proposed solution heuristics, and the results from computational experiments.

156 citations

Journal ArticleDOI
TL;DR: Borders and algorithms are given for the case where the distributions and the variables controllinginformation discovery are discrete and an algorithmic procedure for solving problems of this type is proposed.
Abstract: In the “standard” formulation of a stochastic program with recourse, the distribution ofthe random parameters is independent of the decisions. When this is not the case, the problemis significantly more difficult to solve. This paper identifies a class of problems that are“manageable” and proposes an algorithmic procedure for solving problems of this type. Wegive bounds and algorithms for the case where the distributions and the variables controllinginformation discovery are discrete. Computational experience is reported.

156 citations

Journal ArticleDOI
TL;DR: In this paper, the authors unify the concepts of caution and probing put forth by Feldbaum [14] with the mathematical technique of stochastic dynamic programming originated by Bellman [5].
Abstract: The purpose of this paper is to unify the concepts of caution and probing put forth by Feldbaum [14] with the mathematical technique of stochastic dynamic programming originated by Bellman [5]. The decomposition of the expected cost in a stochastic control problem, recently developed in [8], is used to assess quantitatively the caution and probing effects of the system uncertainties on the control. It is shown how in some problems, because of the uncertainties, the control becomes cautious (less aggressive) while in other problems it will probe (by becoming more aggressive) in order to enhance the estimation/identification while controlling the system. Following this a classification of stochastic control problems according to the dominant effect is discussed. This is then used to point out which are the stochastic control problems where substantial improvements can be expected from using a sophisticated algorithm versus a simple one.

156 citations

Journal ArticleDOI
TL;DR: The proposed evolutionary optimization algorithm is suggested to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem and is suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region.
Abstract: Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.

155 citations

Journal ArticleDOI
TL;DR: A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other.
Abstract: A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other. The argument is based on upper bounds of the L r -distance and the filtration distance, and on quantitative stability results for multistage stochastic programs. The important difference from scenario reduction in two-stage models consists in incorporating the filtration distance. An algorithm is presented for selecting and removing nodes of a scenario tree such that a prescribed error tolerance is met. Some numerical experience is reported.

155 citations


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