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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: Numerical results demonstrate the advantages of implementing stochastic programming on the UC problem by taking into account the intermittent behavior of wind energy and load inconstancy.
Abstract: This essay performs a reliability constraint stochastic model for unit commitment problem by considering generation and transmission constraints with high wind penetration and volatility of load demands. This query is expressed as a MILP that is based on the linear direct current model. The proposed approach models uncertainty of wind generators output power, load demand fluctuations and stochastic elements outage of the system like generators and transmission lines. In this paper, stochastic interdependence between random variables like wind speed and load demand is recognized. To establish the probability distribution of these correlated random variables, Copula theory is applied. Correlation structure between wind speed of different locations and a group of loads existing in the same area is investigated and studied based on historical data. For representing these uncertainties in the stochastic unit commitment problem, possible scenarios are generated with Monte Carlo simulation method. The reliability constraints are utilized in each scenario to evaluate the feasibility of solutions from a reliability point. The introduced stochastic UC is executed on the RTS 96-bus test system. Numerical results demonstrate the advantages of implementing stochastic programming on the UC problem by taking into account the intermittent behavior of wind energy and load inconstancy.

133 citations

Book ChapterDOI
Yaochu Jin1, Bernhard Sendhoff1
TL;DR: This paper suggests a method for constructing dynamic optimization test problems using multi-objective optimization (MOO) concepts that is computationally efficient, easily tunable and functionally powerful.
Abstract: Dynamic optimization using evolutionary algorithms is receiving increasing interests. However, typical test functions for comparing the performance of various dynamic optimization algorithms still lack. This paper suggests a method for constructing dynamic optimization test problems using multi-objective optimization (MOO) concepts. By aggregating different objectives of an MOO problem and changing the weights dynamically, we are able to construct dynamic single objective and multi-objective test problems systematically. The proposed method is computationally efficient, easily tunable and functionally powerful. This is mainly due to the fact that the proposed method associates dynamic optimization with multi-objective optimization and thus the rich MOO test problems can easily be adapted to dynamic optimization test functions.

133 citations

Journal ArticleDOI
TL;DR: The method the advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution, to illustrate how well the algorithm performs.
Abstract: One of the challenging optimization problems is determining the minimizer of a nonlinear programming problem that has binary variables. A vexing difficulty is the rate the work to solve such problems increases as the number of discrete variables increases. Any such problem with bounded discrete variables, especially binary variables, may be transformed to that of finding a global optimum of a problem in continuous variables. However, the transformed problems usually have astronomically large numbers of local minimizers, making them harder to solve than typical global optimization problems. Despite this apparent disadvantage, we show that the approach is not futile if we use smoothing techniques. The method we advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution. To illustrate how well the algorithm performs we show the computational results of applying it to problems taken from the literature and new test problems with known optimal solutions.

133 citations

Book ChapterDOI
01 Jan 2006
TL;DR: In this article, the authors consider optimization problems involving coherent measures of risk and derive necessary and sufficient conditions of optimality for these problems, and discuss the nature of the non-anticipativity constraints.
Abstract: We consider optimization problems involving coherent measures of risk. We derive necessary and sufficient conditions of optimality for these problems, and we discuss the nature of the nonanticipativity constraints. Next, we introduce dynamic measures of risk, and formulate multistage optimization problems involving these measures. Conditions similar to dynamic programming equations are developed. The theoretical considerations are illustrated with many examples of mean-risk models applied in practice.

133 citations

Journal ArticleDOI
TL;DR: A stochastic programming model is introduced to address the air freight hub location and flight routes planning under seasonal demand variations and the real data based on theAir freight market in Taiwan and China is used to test the proposed model.

133 citations


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