A Linear Approximation for Chance-Constrained Programming

Olson, David L.; Swenseth, Scott R.

doi:10.1057/jors.1987.42

Cited by 41 publications

(6 citation statements)

References 15 publications

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“…The objective function is linear, and the constraint set is convex for

α_{j} ⩾ 0 MathClass-punc. 5

. Therefore, global optimal solution of mathematical models in this form can be found by using GAMS/Baron solver, which implements deterministic global optimization algorithms of the branch‐and‐bound type that are guaranteed to provide global optimal under fairly general assumptions .…”

Section: The Ccp Approachmentioning

confidence: 99%

A simulated annealing approach for reliability‐based chance‐constrained programming

Sakallı

2013

Appl Stoch Models Bus & Ind

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The chance-constrained programming (CCP) is a well-known and widely used stochastic programming approach. In the CCP approach, determining the confidence levels of the constraints at the beginning of solution process is a critical issue for optimality. On one hand, it is possible to obtain better solutions at different confidence levels. On the other hand, the decision makers prefer to simplify their choices instead of grappling with the details such as determining confidence levels for all chance constraints. Reliability is an effective tool that enables the decision maker to look over the system integrity. In this paper, the CCP is considered as a reliability-based nonlinear multiobjective model, and a simulated annealing (SA) algorithm is developed to solve the model. The SA represents different solution alternatives at the different reliability degrees to the decision makers by performing different confidence levels. Thus, the decision makers have the opportunity to make more effective decisions.

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“…The objective function is linear, and the constraint set is convex for

α_{j} ⩾ 0 MathClass-punc. 5

Section: The Ccp Approachmentioning

confidence: 99%

A simulated annealing approach for reliability‐based chance‐constrained programming

Sakallı

2013

Appl Stoch Models Bus & Ind

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“…An alternative assumption could be to enforce the constraint with some probability. This is called a chance constraint and can be often approximated as a linear constraint as in [8]. Similar to the alternative treatments of the objective function, we could use some measure of the distribution on the bound.…”

Section: [End][dry] <= Res[1] -Flow[1] + Inflow[dry]; Subject To Conservation[1][wet]: Res[end] [Wet] <= Res[1] -Flow[1] + Inflow[wet];mentioning

confidence: 99%

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Entriken

2001

Annals of Operations Research

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This paper introduces two tokens of syntax for algebraic modeling languages that are sufficient to model a wide variety of stochastic optimization problems. The tokens are used to declare random parameters and to define a precedence relationship between different random events. It is necessary to make a number of assumptions in order to use this syntax, and it is through these assumptions, which cover the areas of model structure, time, replication, and stages, that we can attain a deeper understanding of this class of problem.

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“…But when we focus on continuous uncertainties, results from random scenarios cannot reflect the real influence on the objective, as a result of the absence of probability density/distribution of uncertainties. Thus, the approach of chance-constrained optimization was introduced by Charnes (1958) and further discussed by many researchers, − and recently Prékopa (2013) takes the probability density and distribution of uncertain parameters into consideration and defines confidence intervals of the objective. The chance-constrained approach also has to face difficulties in the reformulation and calculation of the original model, such as reformulation of chance-constrained problems with different kinds of uncertain parameters; estimation of probability density/distribution of uncertainties; choosing confidence coefficients of chance constraints; solving individual and joint chance-constrained problems. …”

Section: Introductionmentioning

confidence: 99%

Data-Driven Chance Constrained and Robust Optimization under Matrix Uncertainty

Zhang

Feng

2016

Ind. Eng. Chem. Res.

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To solve optimization problems with matrix uncertainty, a novel optimization approach is proposed based on chance-constrained and robust optimization, which focuses on constraints with continuous uncertainty, especially with matrix uncertainty. In chance-constrained approach, constraints with matrix uncertainty are always regarded as joint chance constraints, which can be simplified into individual chance constraints and can be further reformulated into algebraic constraints by robust methods. Motivated by reformulation of chance constraints with right-hand side uncertainty, a novel formulation of constraints with left-hand side uncertainty is proposed, where the uncertainty is described as intervals related to the confidence level of chance constraints. Through using kernel density estimation, confidence sets of uncertain parameters are built to approximate unknown true probability density functions. The approach is illustrated with a motivating and process industry scheduling example with energy consumption uncertainties.

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A Linear Approximation for Chance-Constrained Programming

Cited by 41 publications

References 15 publications

A simulated annealing approach for reliability‐based chance‐constrained programming

A simulated annealing approach for reliability‐based chance‐constrained programming

Untitled

Data-Driven Chance Constrained and Robust Optimization under Matrix Uncertainty

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