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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: In this paper, three deterministic reformulations of the general linear programming problem are considered in which the coefficients of the objective function to be maximized are assumed to be random variables with a known multinormal distribution.
Abstract: The general linear programming problem is considered in which the coefficients of the objective function to be maximized are assumed to be random variables with a known multinormal distribution. Three deterministic reformulations involve, respectively, maximizing the expected value, the α-fractile (α fixed, 0 < α < ½), and the probability of exceeding a predetermined level k of payoff. In this paper the author's previous work on “bi-criterion programs” is specialized to give an algorithm for routinely and efficiently solving the second and third reformulations. A by-product of the calculations in each case is the tradeoff-curve between the criterion being maximized and expected value. The intimate relationships between all three reformulations are illuminated, with the cumulative effect of considerably lessening the burden on the decision-maker to preselect with finality a particular value of α or k.

101 citations

Journal ArticleDOI
TL;DR: The proposed approach for design optimization for design problems with mixed type input uncertainties is applied and it is shown that the proposed approach provides conservative optimum design.
Abstract: The reliability based design optimization (RBDO) method is prevailing in stochastic structural design optimization by assuming the amount of input data is sufficient enough to create accurate input statistical distribution. If the sufficient input data cannot be generated due to limitations in technical and/or facility resources, the possibility-based design optimization (PBDO) method can be used to obtain reliable designs by utilizing membership functions for epistemic uncertainties. For RBDO, the performance measure approach (PMA) is well established and accepted by many investigators. It is found that the same PMA is a very much desirable approach also for the PBDO problems. In many industry design problems, we have to deal with uncertainties with sufficient data and uncertainties with insufficient data simultaneously. For these design problems, it is not desirable to use RBDO since it could lead to an unreliable optimum design. This paper proposes to use PBDO for design optimization for such problems. In order to treat uncertainties as fuzzy variables, several methods for membership function generation are proposed. As less detailed information is available for the input data, the membership function that provides more conservative optimum design should be selected. For uncertainties with sufficient data, the membership function that yields the least conservative optimum design is proposed by using the possibility-probability consistency theory and the least conservative condition. The proposed approach for design problems with mixed type input uncertainties is applied to some example problems to demonstrate feasibility of the approach. It is shown that the proposed approach provides conservative optimum design.

101 citations

Journal ArticleDOI
TL;DR: Efficient algorithms based on continuous optimization to find the bounds on second and higher moments of interval data and bounding envelopes for the family of Johnson distributions are presented, analogous to the notion of empirical p-box in the literature.

100 citations

Journal ArticleDOI
TL;DR: Two fundamental classes of problems in large-scale linear and quadratic programming are described and strong properties of duality are revealed which support the development of iterative approximate techniques of solution in terms of saddlepoints.
Abstract: Two fundamental classes of problems in large-scale linear and quadratic programming are described. Multistage problems covering a wide variety of models in dynamic programming and stochastic programming are represented in a new way. Strong properties of duality are revealed which support the development of iterative approximate techniques of solution in terms of saddlepoints. Optimality conditions are derived in a form that emphasizes the possibilities of decomposition.

100 citations

Journal ArticleDOI
TL;DR: This paper considers the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion and transforms the formulation into a nonlinear nonconvex programming problem.
Abstract: In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.

100 citations


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