检索结果-内蒙古大学图书馆

A Framework for Solving chance-constrained Linear Matrix Inequality Programs

INFORMS JOURNAL ON COMPUTING 2021年第3期33卷 1015-1036页

作者： Karimi, Roya Cheng, Jianqiang Lejeune, Miguel A. Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA George Washington Univ George Washington Business Sch Dept Decis Sci Washington DC 20052 USA George Washington Univ Sch Engn & Appl Sci Dept Elect & Comp Engn Washington DC 20052 USA

We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions that ensure convexity for the two most popular-normal and uniform-continuous distributions. We derive several semidefinite programming PSAA reformulations efficiently solved by off-the-shelf solvers and design a sequential convex approximation method for the PSAA formulations containing bilinear matrix inequalities. The proposed methods can be generalized to other continuous random variables whose cumulative distribution function can be easily computed. We carry out a comprehensive numerical study on three practical CCLMI problems: robust truss topology design, calibration, and robust control. The tests attest to the superiority of the PSAA reformulation and algorithmic framework over the scenario and sample average approximation methods. Summary of Contribution: In line with the mission and scope of IJOC, we study an important type of optimization problems, chance-constrained linear matrix inequality (CCLMI) problems, which require stochastic linear matrix inequality (LMI) constraints to be satisfied with high probability. To solve CCLMI problems, we propose a novel partial sample average approximation (PSAA) framework: (i) develop a series of computationally tractable PSAA-based approximations for CCLMI problems, (ii) analyze their properties, (iii) derive sufficient conditions ensuring convexity, and (iv) design a sequential convex approximation method. We evaluate our proposed method via a comprehensive numerical study on three practical CCLMI problems. The tests attest the superiority of the PSAA reformulation and algorithmic framework over standard benchmarks.

关键词： stochastic programming chance-constrained programming linear matrix inequalities sampling-based approximation semidefinite programming

来源：评论

学校读者我要写书评

暂无评论

Scenario Grouping and Decomposition Algorithms for chance-constrained Programs

引用

INFORMS JOURNAL ON COMPUTING 2021年第2期33卷 757-773页

作者： Deng, Yan Jia, Huiwen Ahmed, Shabbir Lee, Jon Shen, Siqian Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario sub-problems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. We also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size. Summary of Contribution: chance-constrained programs are in general NP-hard but widely used in practice for lowering the risk of undesirable outcomes during decision making under uncertainty. Assuming finite scenarios of uncertain parameter, chance-constrained programs can be reformulated as mixed-integer linear programs with binary variables representing whether or not the constraints are satisfied in corresponding scenarios. A useful quantile bound for solving chance-constrained programs can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. In this paper, we develop algorithms for optimally and heuristically grouping scenarios to tighten the quantile bounds. We aim to improve both the computation and solution quality of a variety of chance-constrained programs formulated for different Operations Research problems.

关键词： chance-constrained programming quantile bounds scenario grouping mixed-integer programming branch-and-cut scenario decomposition

来源：评论

学校读者我要写书评

暂无评论

Stochastic inventory-routing problem with lateral transshipment for perishable product

引用

JOURNAL OF MODELLING IN MANAGEMENT 2022年第2期17卷 539-568页

作者： Fattahi, Parviz Tanhatalab, Mehdi Alzahra Univ Dept Ind Engn Tehran Iran Bu Ali Sina Univ Dept Ind Engn Hamadan Hamadan Iran

Purpose This study aims to design a supply chain network in an uncertain environment while exists two options for distribution of the perishable product and production lot-sizing is concerned. Design/methodology/approach Owing to the complexity of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds. Findings The model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs in the solution procedure. Practical implications This paper covers the modeling of some real-world problems in which demand is uncertain and managers face making some concurrent decisions related to supply chain management, transportation and logistics and inventory control issues. Furthermore, considering the perishability of product in modeling makes the problem more practically significant as these days there are many supply chains handling dairy and other fresh products. Originality/value Considering uncertainty, production, transshipment and perishable product in the inventory-routing problem makes a new variant that has not yet been studied. The proposed novel solution is based on the LR approach that is enhanced by some heuristics and some valid inequalities that make it different from the current version of the LR used by other studies.

关键词： Optimization Inventory management Mathematical programming Inventory routing problem IRP Lagrangian relaxation Transshipment chance-constrained programming

来源：评论

学校读者我要写书评

暂无评论

chance-constrained Economic Dispatch Considering Curtailment Strategy of Renewable Energy

引用

IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第6期36卷 5792-5802页

作者： Yang, Yue Wu, Wenchuan Wang, Bin Li, Mingjie Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China State Grid Corp China Natl Elect Power Control Ctr Beijing 100031 Peoples R China

chance-constrained economic dispatch (CCED) is widely used to cope with uncertainties brought by renewable energy sources. In CCED, security of power system is guaranteed by restricting risks under permitted level. As the penetration rate of renewable energy increases rapidly, the CCED model may be infeasible because of inadequate system reserve and/or transmission congestion under certain circumstances. Therefore, the curtailment of renewable energy is indispensable to guarantee security in some scenarios for power systems with high penetration of renewable energy. To address this crucial issue, this paper proposes a novel CCED model, where generation of conventional units and curtailment strategies of renewable energy are co-optimized to minimize total operational cost and restrict operational risks. An efficient solution method is developed to schedule generation and curtailment sequentially, in which tractable optimization models are formulated for each step. Numerical tests demonstrate that the proposed model can significantly reduce the probability of emergency control of curtailment compared with conventional CCED models. Furthermore, this solution method also outperforms scenario-based method with significantly improved computational efficiency and higher-quality solution.

关键词： Renewable energy sources Schedules Power systems Generators Security Optimization Mathematical model Renewable energy chance-constrained programming economic dispatch

来源：评论

学校读者我要写书评

暂无评论

A data-driven chance-constrained BESS planning in distribution networks by a decoupling solution method

引用

JOURNAL OF ENERGY STORAGE 2024年 80卷

作者： Wang, Wei Zhang, Xiaoqi Fu, Lin Liao, Mengke Xu, Xingming Shandong Univ Sci & Technol Coll Intelligent Equipment Tai An 271019 Peoples R China Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China State Grid Xinjiang Elect Power Corp Econ Res Inst Urumqi 830002 Peoples R China

In this study, a novel approach for the battery energy storage system (BESS) planning considering the integration of photovoltaic (PV) is proposed. A data-driven chance-constrained BESS programming model including the dynamic network reconfiguration (DNR) is developed. Then, a decoupling solution approach for sitting selection and sizing optimization is proposed to obtain optimal solution. According to the approach, comprehensive cost sensitivity factor (CCSF) is formulated for the sitting selection, and the particle swarm optimization (PSO) combined with the Minty algorithm and the switch operation time reduction algorithm is developed to obtain more accurate sizing. In addition, based on the scenarios generated by the spectral clustering approach, a continuous scenario increment approach is proposed to handle chance-constrained constraints. The numerical simulations on a practical 31-bus distribution network show the superiority of the proposed algorithm over existing methods.

关键词： Distribution network Battery energy storage system planning chance-constrained programming The decoupling solution method Dynamic network reconfiguration (DNR)

来源：评论

学校读者我要写书评

暂无评论

Data-Driven Scheduling of Energy Storage in Day-Ahead Energy and Reserve Markets With Probabilistic Guarantees on Real-Time Delivery

引用

IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第4期36卷 2815-2828页

作者： Toubeau, Jean-Francois Bottieau, Jeremie De Greve, Zacharie Vallee, Francois Bruninx, Kenneth Univ Mons Fac Polytech Power Elect Engn B-7000 Mons Belgium Katholieke Univ Leuven Energy Inst B-3001 Leuven Belgium

Energy storage systems (ESS) may provide the required flexibility to cost-effectively integrate weather-dependent renewable generation, in particular by offering operating reserves. However, since the real-time deployment of these services is uncertain, ensuring their availability requires merchant ESS to fully reserve the associated energy capacity in their day-ahead schedule. To improve such conservative policies, we propose a data-driven probabilistic characterization of the real-time balancing stage to inform the day-ahead scheduling problem of an ESS owner. This distributional information is used to enforce a tailored probabilistic guarantee on the availability of the scheduled reserve capacity via chance constrained programming, which allows a profit-maximizing participation in energy, reserve and balancing markets. The merit order-based competition with rival resources in reserve capacity and balancing markets is captured via a bi-level model, which is reformulated as a computationally efficient mixed-integer linear problem. Results show that a merchant ESS owner may leverage the competition effect to avoid violations of its energy capacity limits, and that the proposed risk-aware method allows sourcing more reserve capacity, and thus more value, from storage, without jeopardizing the real-time reliability of the power system.

关键词： Real-time systems Probabilistic logic Indexes Energy storage Capacity planning Schedules programming Balancing markets chance-constrained programming data-driven optimization energy storage energy-operating reserve markets

来源：评论

学校读者我要写书评

暂无评论

New chance-constrained models for U-type stochastic assembly line balancing problem

引用

SOFT COMPUTING 2021年第14期25卷 9559-9573页

作者： Pinarbasi, Mehmet OSTIM Tech Univ Ind Engn Dept TR-06374 Ankara Turkey

U-shaped assembly lines are widely encountered in contemporary JIT systems. Unlike presumptions of deterministic studies, task times may vary according to a probability distribution. In this study, a stochastic U-type assembly line balancing problem (ALBP) is considered. For this purpose, two new chance-constrained nonlinear models are proposed. While the first model belongs to the mixed-integer programming (MIP) category, the other is constraint programming (CP). The linearized chance-constrained counterparts are developed using a transformation approach to reduce the model complexity and solve the models linearly. Several numerical experiments are performed to test the effectiveness of the proposed models. The results are compared with the results of modified ant colony optimization and a piecewise-linear programming model. The numerical results demonstrate that the proposed CP and MIP models are more effective and successful in solving stochastic U-type ALBP.

关键词： Stochastic assembly line balancing U-type problem Constraint programming Mixed integer programming chance-constrained programming

来源：评论

学校读者我要写书评

暂无评论

Deterministic global optimization with Gaussian processes embedded

引用

MATHEMATICAL programming COMPUTATION 2021年第3期13卷 553-581页

作者： Schweidtmann, Artur M. Bongartz, Dominik Grothe, Daniel Kerkenhoff, Tim Lin, Xiaopeng Najman, Jaromil Mitsos, Alexander Rhein Westfal TH Aachen Proc Syst Engn AVT SVT Aachen Germany JARA CSD D-52056 Aachen Germany Forschungszentrum Julich Inst Energy & Climate Res Energy Syst Engn IEK 10 D-52425 Julich Germany

Gaussian processes (Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization problems. These optimization problems are nonconvex and global optimization is desired. However, previous literature observed computational burdens limiting deterministic global optimization to Gaussian processes trained on few data points. We propose a reduced-space formulation for deterministic global optimization with trained Gaussian processes embedded. For optimization, the branch-and-bound solver branches only on the free variables and McCormick relaxations are propagated through explicit Gaussian process models. The approach also leads to significantly smaller and computationally cheaper subproblems for lower and upper bounding. To further accelerate convergence, we derive envelopes of common covariance functions for GPs and tight relaxations of acquisition functions used in Bayesian optimization including expected improvement, probability of improvement, and lower confidence bound. In total, we reduce computational time by orders of magnitude compared to state-of-the-art methods, thus overcoming previous computational burdens. We demonstrate the performance and scaling of the proposed method and apply it to Bayesian optimization with global optimization of the acquisition function and chance-constrained programming. The Gaussian process models, acquisition functions, and training scripts are available open-source within the "MeLOn-MachineLearning Models for Optimization" toolbox (https://***/***/public/MeLOn).

关键词： Kriging Machine learning Bayesian optimization Acquisition function chance-constrained programming Reduced-space Expected improvement

来源：评论

学校读者我要写书评

暂无评论

Green closed-loop supply chain network design: a novel bi-objective chance-constraint approach

引用

RAIRO-OPERATIONS RESEARCH 2021年第2期55卷 811-840页

作者： Abad, Amin Reza Kalantari Khalil Pasandideh, Seyed Hamid Reza Kharazmi Univ Fac Engn Dept Ind Engn Tehran Iran

In this paper, a novel chance-constrained programming model has been proposed for handling uncertainties in green closed loop supply chain network design. In addition to locating the facilities and establishing a flow between them, the model also determines the transportation mode between facilities. The objective functions are applied to minimize the expected value and variance of the total cost CO2 released is also controlled by providing a novel chance-constraint including a stochastic upper bound of emission capacity. To solve the mathematical model using the General Algebraic Modeling System (GAMS) software, four multi-objective decision-making (MODM) methods were applied. The proposed methodology was subjected to various numerical experiments. The solutions provided by different methods were compared in terms of the expected value of cost, variance of cost, and CPU time using Pareto-based analysis and optimality-based analysis. In Pareto-based analysis, a set of preferable solutions were presented using the Pareto front;then optimality-based optimization was chosen as the best method by using a Simple Additive Weighting (SAW) method. Experimental experiments and sensitivity analysis demonstrated that the performance of the goal attainment method was 13% and 24% better that of global criteria and goal programming methods, respectively.

关键词： Bi-objective optimization green closed-loop supply chain network design chance-constrained programming Pareto-based analysis Lp-metrics multi-objective decision-making

来源：评论

学校读者我要写书评

暂无评论

A Precedence constrained Knapsack Problem with Uncertain Item Weights for Personalized Learning Systems

引用

OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2023年 115卷

作者： Aslan, Ayse Ursavas, Evrim Romeijnders, Ward Edinburgh Napier Univ Sch Engn & Built Environm Edinburgh EH10 5DT Scotland Univ Groningen Dept Operat NL-9747 AD Groningen Netherlands

This paper studies a unique precedence constrained knapsack problem in which there are two meth-ods available to place an item in the knapsack. Whether or not an item weight is uncertain depends on which one of the two methods is selected. This knapsack problem models students' decisions on choos-ing subjects to study in hybrid personalized learning systems in which students can study either under teacher supervision or in an unsupervised self-study mode by using online tools. We incorporate the un-certainty in the problem using a chance-constrained programming framework. Under the assumption that uncertain item weights are independently and normally distributed, we focus on the deterministic refor-mulation in which the capacity constraint involves a nonlinear and convex function of the decision vari-ables. By using the first-order linear approximations of this function, we propose an exact cutting plane method that iteratively adds feasibility cuts. To supplement this, we develop novel approximate cutting plane methods that converge quickly to high-quality feasible solutions. To improve the computational ef-ficiency of our methods, we introduce new pre-processing procedures to eliminate items beforehand and cover cuts to refine the feasibility space. Our computational experiments on small and large problem in-stances show that the optimality gaps of our approximate methods are very small overall, and that they are even able to find solutions with no optimality gaps as the number of items increases in the instances. Moreover, our experiments demonstrate that our pre-processing methods are particularly effective when the precedence relations are dense, and that our cover cuts may significantly speed up our exact cutting plane approach in challenging instances.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Knapsack Problems chance-constrained programming Cutting Plane Methods Personalized Learning OR in Education Precedence Constraints

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：