检索结果-内蒙古大学图书馆

Unit Commitment with Joint Chance Constraints in Multi-area Power Systems with Wind Power Based on Partial sample average approximation

引用

Journal of Modern Power Systems and Clean Energy 2025年第1期13卷 241-252页

作者： Jinghua Li Hongyu Zeng Yutian Xie School of Electrical Engineering Guangxi UniversityNanning 530004China

Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in *** average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)***,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)*** address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind *** partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled *** approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being ***,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by *** results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.

关键词： Unit commitment joint chance constraint renewable energy multi-area power system wind power sample average approximation partial sample average approximation

来源：评论

学校读者我要写书评

暂无评论

A sample average approximation-based heuristic for the stochastic production routing problem

引用

CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2025年第1期33卷 121-144页

作者： Geiger, Andreas Univ Hamburg Inst Operat Res Moorweidenstr 18 D-20148 Hamburg Germany

The Production Routing Problem under demand uncertainty is an integrated problem containing production, inventory, and distribution decisions. At the planning level, the aim is to meet retailers demand, when only the demand distribution is known in advance, while minimizing the corresponding costs. In this study, a two-stage formulation is presented in which the routing can be adjusted at short notice. In the first stage, only production decisions are made, while delivery and inventory quantities and retailer visit schedules are determined in the second stage. To handle a large number of scenarios, two solution methods based on sample average approximation are introduced. Furthermore, the impact of the routing quality is explored by applying a simple heuristic and an effective metaheuristic on the routing part. It is shown that, on average, the simple heuristic within an adjustable sample average approximation approach provides better objective function values than the metaheuristic within a non-adjustable approach. Also all solution approaches outperform an expected value based approach in terms of runtime and objective function value.

关键词： Production routing problem Integrated planning Stochastic programming sample average approximation Demand uncertainty Heuristic

来源：评论

学校读者我要写书评

暂无评论

Supplier Selection for Agriculture Industry Under Uncertainty: Machine Learning Based sample average approximation Method 2nd

Supplier Selection for Agriculture Industry Under Uncertaint...

引用

2nd International Conference on Artificial Intelligence: Towards Sustainable Intelligence, AI4S 2024

作者： Yılmaz, Ömer Faruk Yılmaz, Beren Gürsoy Department of Industrial Engineering Karadeniz Technical University Trabzon61080 Turkey Department of Industrial and Systems Engineering University of Florida Gainesville32608 United States

ISBN: (纸本)9783031813689

This paper addresses the problem of supplier selection for a hazelnut producer in the agriculture industry under the uncertainty of product quality, with the objective of cost minimization. To mathematically represent the problem, a two-stage stochastic programming model is developed to make decisions both before and after the realization of uncertainty. The first stage involves supplier selection decisions, while the second stage determines the amount of product received from each supplier. After the hazelnuts are produced, if they do not meet quality standards, customers may return the products, causing significant customer satisfaction issues and increased costs. Product quality is assessed based on four features: (I) Aflatoxin, (II) Acidity, (III) Moisture, and (IV) Sifter. To address this problem within the context of intelligent agriculture, four different scenario reduction techniques are employed: (I) sample average approximation (SAA), (II) SAA combined with Machine Learning-1 (SAA + ML1), (III) SAA + ML2, and (IV) SAA + ML3. Each method utilizes the K-means clustering algorithm with specific problem-related characteristics. Computational results indicate that when the SAA approach is combined with K-means clustering and scenarios are reduced based on clustering results, better outcomes are achieved in reducing costs associated with low-quality products. Specifically, higher numbers of suppliers and higher probabilities of generating scenarios from relevant clusters contribute to improved cost reductions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Intelligent Agriculture K-means clustering sample average approximation Two-stage stochastic programming

来源：评论

学校读者我要写书评

暂无评论

sample average approximation method for a new stochastic personnel assignment problem

引用

COMPUTERS & INDUSTRIAL ENGINEERING 2017年 113卷 135-143页

作者： Pour, Amir Ghorbani Naji-Azimi, Zahra Salari, Majid Ferdowsi Univ Mashhad Dept Management Mashhad Iran Ferdowsi Univ Mashhad Dept Ind Engn POB 91775-1111 Mashhad Iran

We introduce a practical generalization of the standard personnel assignment problem. In this problem, we have a set of personnel and a set of lost and found centers. Each center receives a stochastic demand. Some constraints, namely, the work skills of different personnel, balancing workload while assigning personnel to the centers and some other practical constraints are taken into account. The objective function is to minimize the assignment cost and the cost occurred by the shortage of personnel in different centers due to the stochastic arrival of the demand over a given time period. We have developed a sample average approximation technique to solve the introduced problem. Computational tests for the studied problem show the effectiveness of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Personnel assignment problem Stochastic optimization Monte Carlo sample average approximation

来源：评论

学校读者我要写书评

暂无评论

sample average approximation with sparsity-inducing penalty for high-dimensional stochastic programming

引用

MATHEMATICAL PROGRAMMING 2019年第1-2期178卷 69-108页

作者： Liu, Hongcheng Wang, Xue Yao, Tao Li, Runze Ye, Yinyu Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Penn State Univ Harold & Inge Marcus Dept Ind & Mfg Engn University Pk PA 16802 USA Penn State Univ Dept Stat University Pk PA 16802 USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

The theory on the traditional sample average approximation (SAA) scheme for stochastic programming (SP) dictates that the number of samples should be polynomial in the number of problem dimensions in order to ensure proper optimization accuracy. In this paper, we study a modification to the SAA in the scenario where the global minimizer is either sparse or can be approximated by a sparse solution. By making use of a regularization penalty referred to as the folded concave penalty (FCP), we show that, if an FCP-regularized SAA formulation is solved locally, then the required number of samples can be significantly reduced in approximating the global solution of a convex SP: the sample size is only required to be poly-logarithmic in the number of dimensions. The efficacy of the FCP regularizer for nonconvex SPs is also discussed. As an immediate implication of our result, a flexible class of folded concave penalized sparse M-estimators in high-dimensional statistical learning may yield a sound performance even when the problem dimension cannot be upper-bounded by any polynomial function of the sample size.

关键词： sample average approximation Folded concave penalty Second order necessary condition Stochastic programming

来源：评论

学校读者我要写书评

暂无评论

sample average approximation for stochastic nonconvex mixed integer nonlinear programming via outer-approximation

引用

OPTIMIZATION AND ENGINEERING 2021年第3期22卷 1245-1273页

作者： Li, Can Bernal, David E. Furman, Kevin C. Duran, Marco A. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA ExxonMobil Upstream Res Co 22777 Springwoods Village Pkwy Spring TX 77389 USA

We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333-346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation algorithm where we iterate between a mixed-integer linear programming (MILP) master problem and a nonconvex nonlinear programming (NLP) subproblem. We prove that the optimal solutions and optimal value obtained by the SAAOA algorithm converge to the optimal solutions and the optimal value of the true SP problem as the sample size goes to infinity. The convergence rate is also given to estimate the sample size. Since the theoretical sample size estimate is too conservative in practice, we propose an SAAOA algorithm with confidence intervals for the upper bound and the lower bound at each iteration of the SAAOA algorithm. Two policies are proposed to update the sample sizes dynamically within the SAAOA algorithm with confidence intervals. The proposed algorithm works well for the special case of pure binary first stage variables and continuous stage two variables since in this case the nonconvex NLPs can be solved for each scenario independently. The proposed algorithm is tested with a stochastic pooling problem and is shown to outperform the external sampling approach where large scale MINLPs need to be solved.

关键词： Stochastic programming sample average approximation Mixed-integer nonlinear programming Outer-approximation

来源：评论

学校读者我要写书评

暂无评论

sample average approximation METHOD FOR COMPOUND STOCHASTIC OPTIMIZATION PROBLEMS

引用

SIAM JOURNAL ON OPTIMIZATION 2013年第4期23卷 2231-2263页

作者： Ermoliev, Yuri M. Norkin, Vladimir I. Int Inst Appl Syst Anal A-2361 Laxenburg Austria Natl Acad Sci Ukraine VM Glushkov Cybernet Inst UA-03187 Kiev Ukraine

The paper studies stochastic optimization (programming) problems with compound functions containing expectations and extreme values of other random functions as arguments. Compound functions arise in various applications. A typical example is a variance function of nonlinear outcomes. Other examples include stochastic minimax problems, econometric models with latent variables, and multilevel and multicriteria stochastic optimization problems. As a solution technique a sample average approximation (SAA) method (also known as statistical or empirical (sample) mean method) is used. The method consists in approximation of all expectation functions by their empirical means and solving the resulting approximate deterministic optimization problems. In stochastic optimization, this method is widely used for optimization of standard expectation functions under constraints. In this paper, SAA method is extended to general compound stochastic optimization problems. The conditions for convergence in mean, almost surely, and rate of convergence are established. The study of the convergence rate is based on properties of Rademacher averages of functional sets, concentration inequalities for bounded random functions, and the concept of uniform normalized convergence of random variables. The convergence results are applicable both for discrete and continuous stochastic optimization problems.

关键词： stochastic optimization compound functions sample average approximation normalized convergence uniform normalized convergence uniform law of large numbers concentration inequalities Rademacher averages rate of convergence

来源：评论

学校读者我要写书评

暂无评论

sample average approximation of conditional value-at-risk based variational inequalities

引用

OPTIMIZATION LETTERS 2024年第2期18卷 471-496页

作者： Cherukuri, Ashish Univ Groningen ENTEG Groningen Netherlands

This paper focuses on a class of variational inequalities (VIs), where the map defining the VI is given by the component-wise conditional value-at-risk (CVaR) of a random function. We focus on solving the VI using sample average approximation, where solutions of the VI are estimated with solutions of a sample average VI that uses empirical estimates of the CVaRs. We establish two properties for this scheme. First, under continuity of the random map and the uncertainty taking values in a bounded set, we prove asymptotic consistency, establishing almost sure convergence of the solution of the sample average problem to the true solution. Second, under the additional assumption of random functions being Lipschitz, we prove exponential convergence where the probability of the distance between an approximate solution and the true solution being smaller than any constant approaches unity exponentially fast. The exponential decay bound is refined for the case where random functions have a specific separable form in the decision variable and uncertainty. We adapt these results to the case of uncertain routing games and derive explicit sample guarantees for obtaining a CVaR-based Wardrop equilibria using the sample average procedure. We illustrate our theoretical findings by approximating the CVaR-based Wardrop equilibria for a modified Sioux Falls network.

关键词： Variational inequalities sample average approximation Conditional value-at-risk Wardrop equilibrium

来源：评论

学校读者我要写书评

暂无评论

sample average approximation for the continuous type principal-agent problem

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期275卷 1050-1057页

作者： Singham, D., I Naval Postgrad Sch Monterey Operat Res Dept Monterey CA 93943 USA

We develop a method for finding approximate solutions to the continuous agent type principal-agent problem when analytical methods are not available. The solution is calculated by solving a discrete agent type version of the problem using sample average approximation and bootstrapping. We show how a solution to the approximate problem can be used to derive a lower bound and expected upper bound for the optimal objective function, and evaluate the error associated with the approximation. Numerical examples illustrate convergence in the approximate solution to the true solution as the number of samples increases. This works yields a method for obtaining some tractability in continuous type principal-agent problems where solutions were previously unavailable. Published by Elsevier B.V.

关键词： Pricing Mechanism design Principal-agent models sample average approximation

来源：评论

学校读者我要写书评

暂无评论

sample average approximation of stochastic dominance constrained programs

引用

MATHEMATICAL PROGRAMMING 2012年第1-2期133卷 171-201页

作者： Hu, Jian Homem-de-Mello, Tito Mehrotra, Sanjay Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA Univ Illinois Dept Mech & Ind Engn Chicago IL 60607 USA

In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems allows for the modeling of optimization problems where a risk-averse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with the case of multi-variate stochastic dominance under general distributions and nonlinear functions. We introduce the concept of -dominance, which generalizes some notions of multi-variate dominance found in the literature. We apply the sample average approximation (SAA) method to this problem, which results in a semi-infinite program, and study asymptotic convergence of optimal values and optimal solutions, as well as the rate of convergence of the feasibility set of the resulting semi-infinite program as the sample size goes to infinity. We develop a finitely convergent method to find an -optimal solution of the SAA problem. An important aspect of our contribution is the construction of practical statistical lower and upper bounds for the true optimal objective value. We also show that the bounds are asymptotically tight as the sample size goes to infinity.

关键词： Stochastic programming Stochastic dominance sample average approximation Semi-infinite programming Convex programming Cutting plane algorithms

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：