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A stochastic optimization procedure to design the fair aggregation of energy users in a Renewable Energy Community

RENEWABLE ENERGY 2024年 237卷

作者： Volpato, Gabriele Carraro, Gianluca De Giovanni, Luigi Dal Cin, Enrico Danieli, Piero Bregolin, Edoardo Lazzaretto, Andrea Univ Padua Ind Engn Dept Via Venezia 1 I-35131 Padua Italy Univ Padua Dept Math Tullio Levi Civita I-35131 Padua Italy

Optimizing unit sizes and operation within a Renewable Energy Community (REC) can match intermittent renewable energy generation with variable user energy demands. These uncertain variables are often represented by pre-defined stochastic scenarios, without searching for the "best" scenarios and testing the optimization models with these scenarios. Moreover, little work both optimized RECs under uncertainty and distributed optimal life-cycle costs (investment and operation) among members. Thus, the objectives are: i) identifying the "best" set of stochastic scenarios of solar irradiance and user electricity demands and ii) assessing the accuracy of the "stochastic forecasts" of the total system costs and unit sizes, obtained by solving a stochastic programming model based on the "best" scenarios. The proposed novel procedure shifts the "present moment" back in time to split historical data into "past" and "future" periods used to identify the "best" scenarios and compare the "stochastic forecasts" with the utopic "perfect forecasts" based on the perfect knowledge of real data, respectively. The small errors between these forecasts in the optimal life-cycle costs (less than 2 %) and sizes (3-13 %) indicate good effectiveness of the suggested procedure. Also, the optimal life-cycle costs of "stochastic forecasts" are fairly distributed among users by applying the Shapley value mechanism.

关键词： Renewable energy community Multi-energy system Optimization stochastic programming Mixed-integer linear programming Fair cost allocation

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THE stochastic CONJUGATE SUBGRADIENT ALGORITHM FOR KERNEL SUPPORT VECTOR MACHINES

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SIAM Journal on Optimization 2025年第2期35卷 1194-1215页

作者： Zhang, Di Sen, Suvrajeet Department of Industrial and System Engineering University of Southern California Los AngelesCA90007 United States

stochastic first-order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where empirical evidence indicates potential performance limitations. In response, this paper proposes an innovative method specifically designed for kernel support vector machines (SVMs). This method not only achieves faster convergence per iteration but also exhibits enhanced scalability when compared to conventional SFO techniques. Diverging from traditional sample average approximation strategies that typically frame kernel SVM as an ``all-in-one"" quadratic program (QP), our approach adopts adaptive sampling. This strategy incrementally refines approximation accuracy on an ``as-needed"" basis. Crucially, this approach also inspires a decomposition-based algorithm, effectively decomposing parameter selection from error estimation, with the latter being independently determined for each data point. To exploit the quadratic nature of the kernel matrix, we introduce a stochastic conjugate subgradient method. This method preserves many benefits of first-order approaches while adeptly handling both nonlinearity and nonsmooth aspects of the SVM problem. Thus, it extends beyond the capabilities of standard SFO algorithms for nonsmooth convex optimization. The convergence rate of this novel method is thoroughly analyzed within this paper. Our experimental results demonstrate that the proposed algorithm not only maintains but potentially exceeds the scalability of SFO methods. Moreover, it significantly enhances both speed and accuracy of the optimization process. © 2025 Society for Industrial and Applied Mathematics.

关键词： stochastic programming

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Optimal bookmaking

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期295卷 560-574页

作者： Lorig, Matthew Zhou, Zhou Zou, Bin Univ Washington Dept Appl Math Seattle WA 98195 USA Univ Sydney Sch Math & Stat Sydney NSW Australia Univ Connecticut Dept Math 341 Mansfield Rd U1009 Storrs CT 06269 USA

We introduce a general framework for continuous-time betting markets, in which a bookmaker can dy-namically control the prices of bets on outcomes of random events. In turn, the prices set by the book-maker affect the rate or intensity of bets placed by gamblers. The bookmaker seeks an optimal price process that maximizes his expected (utility of) terminal wealth. We obtain explicit solutions or charac-terizations to the bookmaker's optimal bookmaking problem in various interesting models. (c) 2021 Elsevier B.V. All rights reserved.

关键词： stochastic programming Poisson process Sports betting stochastic control Utility maximization

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Logarithmic barrier decomposition-based interior point methods for stochastic symmetric programming

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2014年第2期409卷 973-995页

作者： Alzalg, Baha Ariyawansa, K. A. Univ Jordan Dept Math Amman 1194 Jordan Washington State Univ Dept Math Pullman WA 99164 USA

We introduce and study two-stage stochastic symmetric programs with recourse to handle uncertainty in data defining (deterministic) symmetric programs in which a linear function is minimized over the intersection of an affine set and a symmetric cone. We present a Benders' decomposition-based interior point algorithm for solving these problems and prove its polynomial complexity. Our convergence analysis proved by showing that the log barrier associated with the recourse function of stochastic symmetric programs behaves a strongly self-concordant barrier and forms a self-concordant family on the first stage solutions. Since our analysis applies to all symmetric cones, this algorithm extends Zhao's results [G. Zhao, A log barrier method with Benders' decomposition for solving two-stage stochastic linear programs, Math. Program. Ser. A 90 (2001) 507-536] for two-stage stochastic linear programs, and Mehrotra and Ozevin's results [S. Mehrotra, M.G. Ozevin, Decomposition-based interior point methods for two-stage stochastic semidefinite programming, SIAM J. Optim. 18 (1) (2007) 206-222] for two-stage stochastic semidefinite programs. (C) 2013 Elsevier Inc. All rights reserved.

关键词： stochastic programming Symmetric cone programming Benders' decomposition Interior point methods Primal-dual methods Euclidean Jordan algebra

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Designing profit-maximizing omnichannel distribution networks for high responsiveness

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2025年 286卷

作者： Nguyen, Dung Klibi, Walid Ben Mohamed, Imen EM Normandie Business Sch Metis Lab Clichy France Kedge Business Sch Ctr Excellence Supply Chain CESIT Bordeaux France Emlyon Business Sch AIM Res Ctr Quantitat Methods Business Quant Ecully France Kuhne Logist Univ Hamburg Germany

The network posture of omnichannel retailers, encompassing dedicated urban fulfillment centers (UFCs) and/or selected stores (omnistores) for order fulfillment, directly influences their ability to provide responsive delivery services. In turn, customers' willingness to purchase online is shaped by the responsiveness level offered, impacting overall sales revenue. To address this business context, we introduce a responsive omnichannel distribution network design problem under a probabilistic, offer-dependent customer channel choice framework. At the strategic level, our approach optimizes the selection of delivery service offers by demand zone while jointly determining the number and location of UFCs and omnistores. We formulate a two-stage stochastic distribution network design model that maximizes expected profit. Demand scenarios are derived from a discrete choice model that captures customer preferences between online and offline channels, contingent on the retailer's responsiveness level. To account for last-mile delivery complexities, we employ a refined pixelization of urban delivery areas and develop a precise calculation of Order-to-Delivery Time (ODT). Managerial insights from a case study of an omnichannel retailer in France highlight the advantages of deploying UFCs and omnistores, yielding up to an 8% profit increase under high responsiveness. Our results demonstrate the effectiveness of the proposed model in capturing customer willingness to buy online, with network offerings shifting to next-day delivery in up to 60% of demand zones.

关键词： Distribution network design Responsiveness offer Omnichannel retailing Discrete choice model stochastic programming Last-miles logistics

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Elasticity management for capacity planning in software as a service cloud computing

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IISE TRANSACTIONS 2021年第4期53卷 407-424页

作者： Stauffer, Jon M. Megahed, Aly Sriskandarajah, Chelliah Texas A&M Univ Mays Business Sch College Stn TX 77843 USA IBM Res Almaden San Jose CA USA

Applications of cloud computing are increasing as companies shift from on-premise IT environments to public, private, or hybrid clouds. Consequently, cloud providers use capacity planning to maintain the capacity of computing resources (instances) required to meet the dynamic nature of the demand (queries). However, there is a trade-off between deploying too many costly instances, and deploying too few instances and paying penalties for not being able to process queries on-time. An instance has multiple resource dimensions and executing a query consumes multiple dimensions of an instance's capacity. This detailed multi-dimensional management of cloud computing resource capacity is known as elasticity management and is an important issue faced by all cloud providers. Determining the optimal number of instances needed in a given planning horizon is challenging, due to the combinatorial nature of the optimization problem involved. We develop an optimization model and related algorithms to capture the trade-off between the resource cost versus the delayed execution penalty in software as a service applications from the cloud provider's perspective. We develop an exact approach to solve small to medium sized applications and heuristics to solve large applications. We then evaluate their performance via extensive computational analyses with real-world data and current cloud provider approaches. We also develop a stochastic framework and methodology to deal with demand uncertainty, and using two different randomly generated data sets (representing problem instances in practice), we demonstrate that robust solutions can be obtained.

关键词： Cloud computing capacity planning horizontal elasticity management stochastic programming operations research software as a service

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Asynchronous Lagrangian scenario decomposition

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MATHEMATICAL programming COMPUTATION 2021年第1期13卷 1-50页

作者： Aravena, Ignacio Papavasiliou, Anthony Lawrence Livermore Natl Lab Livermore CA 94550 USA Catholic Univ Louvain CORE Louvain La Neuve Belgium

We present a distributed asynchronous algorithm for solving two-stage stochastic mixed-integer programs (SMIP) using scenario decomposition, aimed at industrial-scale instances of the stochastic unit commitment (SUC) problem. The algorithm is motivated by large differences in run times observed among scenario subproblems of SUC instances, which can result in inefficient use of distributed computing resources by synchronous parallel algorithms. Our algorithm performs dual iterations asynchronously using a block-coordinate subgradient descent method which allows performing block-coordinate updates using delayed information, while candidate primal solutions are recovered from the solutions of scenario subproblems using heuristics. We present a high performance computing implementation of the asynchronous algorithm, detailing the operations performed by each parallel process and the communication mechanisms among them. We conduct numerical experiments using SUC instances of the Western Electricity Coordinating Council system with up to 1000 scenarios and of the Central Western European system with up to 120 scenarios. We also conduct numerical experiments on generic SMIP instances from the SIPLIB library (DCAP and SSLP). The results demonstrate the general applicability of the proposed algorithm and its ability to solve industrial-scale SUC instances within operationally acceptable time frames. Moreover, we find that an equivalent synchronous parallel algorithm would leave cores idle up to 80.4% of the time on our realistic test instances, an observation which underscores the need for designing asynchronous optimization schemes in order to fully exploit distributed computing on real world applications.

关键词： Asynchronous algorithm stochastic programming Unit commitment High performance computing

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A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs

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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

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Assessment of financial risk in the design and scheduling of multipurpose plants under demand uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2021年第20期59卷 6125-6145页

作者： Vieira, Miguel Paulo, Helena Pinto-Varela, Tania Barbosa-Povoa, Ana Paula Univ Lisboa Lisboa Inst Super Tecn CEG IST Lisbon Portugal Univ Coimbra Dept Mech Engn CEMMPRE P-3030788 Coimbra Portugal IPL ISEL Rua Conselheiro Emidio Navarro Lisboa Lisbon Portugal

Industrial companies are seeking for highly flexible strategic and operational solutions to face the requirements of current dynamic markets. The aim of this work is to provide a decision support assessment for the design and scheduling of a multipurpose plant under demand uncertainty, allowing the assessment of alternative risk profile solutions. A general two-stage mixed-integer linear programming (MILP) model is proposed with the goal to maximise the annualised profit of the plant operation under a set of scenarios while minimising the associated financial risk. Considering the long-term investment perspective, the Conditional Value at Risk (CVaR) measure is used to evaluate the likelihood that a specific loss or gain will exceed a certain value at risk. A bi-objective model is formulated using the augmented epsilon-constraint method to generate an approximation to the Pareto-optimal curve, illustrating the trade-offs between plant profit (with the corresponding design and scheduling decisions) and the associated financial risk. Addressing a set of propositions regarding a case-study, the conclusions highlight the advantages of the risk measure integration in support of the decision-making process, discussing the managerial insights in the assessment of diverse financial outcomes for the solution optimisation.

关键词： Flexible manufacturing systems design and scheduling optimisation risk assessment stochastic programming conditional value at risk (CVaR)

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Power/Hydrogen Optimal stochastic Scheduling Considering Frequency Regulation Markets 5

Power/Hydrogen Optimal Stochastic Scheduling Considering Fre...

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5th IEEE International Conference on Smart Systems and Technologies, SST 2022

作者： Khazali, Amirhossein Torkzadeh, Roozbeh Chamorro, Harold R. Makolo, Peter Sood, Vijay K. Zamora, Ramon Grid Planning Deputy Iran Grid Management Company Tehran Iran Department of Electrical Engineering Eindhoven University of Technology Eindhoven Netherlands Department of Electrical Engineering KTH Royal Institute of Technology Stockholm Sweden Department of Electrical Engineering Auckland University of Technology Auckland New Zealand Department of Electrical Engineering Ontario Tech University Oshawa Canada

ISBN: (数字)9781665482158

ISBN: (纸本)9781665482158

This paper presents a novel optimal offering framework to incorporate hydrogen system potential for frequency regulation goals. Furthermore, the presented model considers the possibility of submitting bids for a day-ahead hydrogen market. To harness the uncertainty of AGC (automatic generation control) signals, the problem is formulated as a two-level stochastic programming approach where in the first stage, the day-ahead market is cleared, and in the second stage, which is related to the real-time market, the up and down capacities of the hydrogen system are determined for each hour. The results indicate that the presented model is able to maximize the income of the integrated power/hydrogen system by determining the optimal scheduling of each of these devices and increase the income of the system by taking advantage of the frequency regulation market and dedicating a capacity of the electrolyzer and fuel cell to this market. © 2022 IEEE.

关键词： stochastic programming

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