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Improving operating policies in stochastic optimization: An application to the medium-term hydrothermal scheduling problem

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APPLIED ENERGY 2024年 359卷

作者： Gomez-Perez, Jesus D. Latorre-Canteli, Jesus M. Ramos, Andres Perea, Alejandro Sanz, Pablo Hernandez, Francisco Comillas Pontifical Univ Inst Res Technol Calle Alberto Aguilera 23 Madrid 28015 Spain Iberdrola Generac Tomas Redondo 1 Madrid 28033 Spain

In decision -making under uncertainty, a robust representation of uncertainty is vital for optimal operational and strategic solutions. We extend existing methods by utilizing Fourier decomposition to create multivariate synthetic time series, capturing stochastic seasonal patterns while preserving correlations. These synthetic time series are transformed into a recombining scenario tree via K -means clustering. To enhance the resulting policy in the stochastic Dual Dynamic programming (SDDP) framework, we propose an additional sampling within scenario -tree nodes to consider a better representation of the cost -to -go function. A convergence proof for this sampling technique is provided. Moreover, two new stopping criteria are introduced for better solution accuracy and robustness. The first criterion extends traditional stopping rules to all scenario -tree nodes. The second criterion enforces a minimum count of Benders cuts per node, promoting accurate and robust solutions. Our approach is evaluated on the Spanish hydrothermal system, incorporating synthetic time series with seasonal -trend uncertainty in optimization and simulation. Policies from traditional SDDP and our technique were tested over a thousand realizations, demonstrating that our proposals yield reservoir operation policies closer to the thresholds set by the operator compared to traditional SDDP. Computational efficiency is maintained. The proposed sampling mitigates the impact of discretizing stochastic variables into scenario trees by evaluating more scenarios per node. Our framework offers robust policies under uncertainty through stochastic seasonal patterns by Fourier analysis, novel SDDP sampling, and additional stopping criteria.

关键词： Time series Fourier analysis Optimization methods stochastic programming SDDP Sampling methods

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Stability and Sample-Based Approximations of Composite stochastic Optimization Problems

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OPERATIONS RESEARCH 2023年第5期71卷 1871-1888页

作者： Dentcheva, Darinka Lin, Yang Penev, Spiridon Stevens Inst Technol Dept Math Sci Hoboken NJ 07030 USA Univ New South Wales Sch Math & Stat Sydney NSW 2052 Australia Univ New South Wales Data Sci Hub Sydney NSW 2052 Australia

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals that are subjected to multiple measure perturbations. Our main focus is the asymptotic behavior of data-driven formulations with empirical or smoothing estimators such as kernels or wavelets applied to some or to all functions of the compositions. We analyze the properties of the new estimators and we establish strong law of large numbers, consistency, and bias reduction potential under fairly general assumptions. Our results are germane to risk-averse optimization and to data science in general.

关键词： stochastic programming bias coherent measures of risk kernel estimation wavelet estimation consistency strong law of large numbers

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A Multiple Objective Genetic Algorithm Approach for stochastic Open Pit Production Scheduling Optimisation

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INTERNATIONAL JOURNAL OF MINING RECLAMATION AND ENVIRONMENT 2023年第6期37卷 460-487页

作者： Amponsah, Shadrach Yaw Takouda, Pawoumodom Matthias Ben-Awuah, Eugene Laurentian Univ Min Optimizat Lab MOL Sch Engn & Comp Sci Sudbury ON Canada Laurentian Univ Sch Business Adm Res Grp Operat Analyt & Decis Sci RGinOADS Sudbury ON Canada

The conventional approach to mine planning is to use a single estimated orebody model as the basis for production scheduling. This approach, however, does not consider grade uncertainties associated with grade estimation. These uncertainties have a significant impact on the net present value (NPV) and can only be accounted for when modelled as part of the production scheduling optimisation problem. In this research, a set of equally probable simulated orebodies generated through Sequential Gaussian Simulation is used as input to a stochastic optimisation model solved with genetic algorithm (GA). Grade variability is considered as part of the stochastic model. The problem definition and resource constraints are formulated and optimised using a specially designed mining-specific GA. This GA is employed to handle partial block processing through a specialised chromosome encoding technique resulting in near-optimal solutions. Two case studies are presented which compare results from the stochastic model solved with GA (SGA) and a stochastic Mixed Integer Linear programming (SMILP) model solved with CPLEX. For the second case study, while the SMILP model was at an optimality gap of 101% after 28 days, the SGA model generated an NPV of $10,045 M at 10.16% optimality gap after 1.5 h.

关键词： Combinatorial optimisation genetic algorithm open-pit production scheduling optimisation stochastic programming grade uncertainty

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Regularized sample average approximation for high-dimensional stochastic optimization under low-rankness

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JOURNAL OF GLOBAL OPTIMIZATION 2023年第2期85卷 257-282页

作者： Lee, Hung Yi Hernandez, Charles Liu, Hongcheng Univ Florida Ind & Syst Engn Gainesville FL 32611 USA

This paper concerns a high-dimensional stochastic programming (SP) problem of minimizing a function of expected cost with a matrix argument. To this problem, one of the most widely applied solution paradigms is the sample average approximation (SAA), which uses the average cost over sampled scenarios as a surrogate to approximate the expected cost. Traditional SAA theories require the sample size to grow rapidly when the problem dimensionality increases. Indeed, for a problem of optimizing over a p-by-p matrix, the sample 2 complexity of the SAA is given by (O) over tilde (1) . p(2)/epsilon(2) . polylog(1/epsilon) to achieve an epsilon-suboptimality gap, for some poly-logarithmic function polylog(.) and some quantity (O) over tilde (1) independent of dimensionality p and sample size n. In contrast, this paper considers a regularized SAA (RSAA) with a low-rankness-inducing penalty. We demonstrate that, when the optimal solution to the SP is of low rank, the sample complexity of RSAA is (O) over tilde (1) . p/epsilon(3) . polylog(p, 1/epsilon), which is almost linear in p and thus indicates a substantially lower dependence on dimensionality. Therefore, RSAA can be more advantageous than SAA especially for larger scale and higher dimensional problems. Due to the close correspondence between stochastic programming and statistical learning, our results also indicate that high-dimensional low-rank matrix recovery is possible generally beyond a linear model, even if the common assumption of restricted strong convexity is completely absent.

关键词： stochastic programming Sample average approximation Low-rankness

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Integrated reinforcement and repair of interdependent infrastructure networks under disaster-related uncertainties

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 369-384页

作者： Suticen, Tugce Canbilen Batun, Sakine Celik, Melih Middle East Tech Univ Dept Ind Engn Univ MhDumlupinar Bl 1 TR-06800 Ankara Turkiye Univ Bath Sch Management Convocat AveClaverton Down Bath BA2 7AZ Avon England

Natural or human-inflicted disasters may cause large-scale disruptions in the services of infrastructure networks including power, water, and telecommunication. Restoring the services of these infrastructures is vital in the aftermath of the disaster, so that search-and-rescue activities, relief transportation, and restoration efforts can be efficiently facilitated. On the other hand, operations of these infrastructures may depend on receiving services from one another, resulting in an interdependent network structure. Consequently, addressing the decisions of network reinforcement before the disaster and the repairs in its aftermath needs to take into account this interdependent structure, as well as the uncertainties arising from the timing, location, and magnitude of the *** paper introduces the stochastic Interdependent Infrastructure Reinforcement and Repair Problem, which considers the pre-disaster reinforcement of interdependent network components and post-disaster repair scheduling in an integrated manner. In making these decisions, the uncertainty on which network components will be disrupted is incorporated into the problem definition. The problem is modeled using scenario-based two-stage stochastic programming. A heuristic based on a genetic algorithm and partial optimization is proposed to solve realistically-sized instances of the problem. Computational experiments not only show that the heuristic is able to find near-optimal solutions within reasonable times, but also illustrate the ability of the approach to help derive managerial insights.(c) 2022 Elsevier B.V. All rights reserved.

关键词： OR in societal problem analysis Disaster management Interdependent infrastructures stochastic programming Genetic algorithms

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DQC²O: Distributed Quantum Computing for Collaborative Optimization in Future Networks

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IEEE COMMUNICATIONS MAGAZINE 2023年第5期61卷 188-194页

作者： Ngoenriang, Napat Xu, Minrui Kang, Jiawen Niyato, Dusit Yu, Han Shen, Xuemin (Sherman) Vidyasirimedhi Inst Sci & Technol Sch Informat Sci & Technol Rayong Thailand Nanyang Technol Univ Sch Comp Sci & Engn Singapore Singapore Guangdong Univ Technol Sch Automat Guangzhou Peoples R China Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

With the advantages of high-speed parallel processing, quantum computers can efficiently solve large-scale complex optimization problems in future networks. However, due to the uncertain qubit fidelity and quantum channel noise, distributed quantum computing, which relies on quantum networks connected through entanglement, faces many challenges in exchanging information across quantum computers. In this article, we propose an adaptive distributed quantum computing approach, called DQC(2)O, to manage quantum computers and quantum networks for solving optimization tasks in future networks. Firstly, we describe the fundamentals of quantum computing and its distributed concept in quantum networks. Secondly, to address the uncertainty of future demands of collaborative optimization tasks and instability over quantum networks, we propose a quantum resource allocation scheme based on stochastic programming for minimizing quantum resource consumption. Finally, based on the proposed approach, we discuss the potential military applications of collaborative optimization in future networks, such as smart grid management, IoT cooperation, and semantic communications. Promising research directions that can lead to the design and implementation of future distributed quantum computing frameworks are also highlighted.

关键词： Distributed quantum computing quantum networks resource allocation stochastic programming

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Electricity procurement of large consumers considering power-purchase agreements

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ENERGY REPORTS 2023年 9卷 5384-5396页

作者： Arellano, Jose Carrion, Miguel UCLM Escuela Ingn Ind & Aerosp Toledo Spain

In an environment with high energy costs worldwide, the adequate determination of electricity procurement strategies by large electricity consumers is vital. This study intends to determine the best procurement strategy for electricity consumers by considering their participation in the pool and the possibility of signing different types of power purchase agreements, which can be physical/financial, on-site/off-site, with conventional/renewable energy suppliers. Additionally, the construction of a photovoltaic self-production unit is considered. This medium-term decision-making problem is formulated using a stochastic programming approach. A realistic case study is solved by considering an existing cement producer, actual pool price and renewable production data pertaining to the Spanish power system. The numerical results indicate that a risk-averse strategy obtained by the proposed model can maintain an increase in the procurement cost below 9% in a situation in which pool prices are 3.3 times higher.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Large consumer Power-purchase agreements Self-consumption facility stochastic programming

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stochastic planning of integrated energy system based on correlation scenario generation method via Copula function considering multiple uncertainties in renewable energy sources and demands

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IET RENEWABLE POWER GENERATION 2023年第12期17卷 2978-2996页

作者： Chen, Jinfan Mao, Chengxiong Liu, Zhe Ma, Chunyan Sha, Guanglin Duan, Qing Fan, Hua Qiu, Shushan Wang, Dan Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 430074 Peoples R China State Grid Shanghai Municipal Elect Power Co Shanghai Peoples R China China Elect Power Res Inst Beijing Peoples R China

The main goal of integrated energy service providers (IESP) in the future is to pursue profitability and reduce carbon emissions while ensuring sufficient energy supply. However, the multiple uncertainties associated with renewable energy resources and the multi-energy consumers pose significant challenges in the optimal planning of the integrated energy system (IES) based on energy hubs (EH). This includes the global optimization of device types, EH capacity, and the optional interconnections between adjacent EHs. This study aims to develop a comprehensive mathematical model of EH that considers the temperature limitations on device operation. The thermal bus and associated devices are divided into high and low temperature parts, and a multi-scenario stochastic programming model is proposed for IES planning. Scenarios are generated using non-parametric kernel density estimation and the Copula function, a scenario reduction technique is implemented to alleviate computational burden. Additionally, case studies illustrate effectiveness of the proposed approach, the operation and forms of EHs, effect of the interconnections and the trade-off between carbon emissions and economic costs are further studied by extensive simulations. This study can be a good guide for IESPs to invest in the construction of the EH-based IES.

关键词： distributed power generation energy management systems planning renewable energy sources stochastic programming

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The complexity of branch-and-price algorithms for the capacitated vehicle routing problem with stochastic demands

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OPERATIONS RESEARCH LETTERS 2023年第1期51卷 11-16页

作者： Fukasawa, Ricardo Gunter, Joshua Univ Waterloo Dept Combinator & Optimizat Waterloo ON Canada

The capacitated vehicle routing problem with stochastic demands (CVRPSD) is a variant of the deterministic capacitated vehicle routing problem where customer demands are random variables. While the most successful formulations for several deterministic vehicle-routing problem variants are based on a set-partitioning formulation, adapting such formulations for the CVRPSD under mild assumptions on the demands remains challenging. In this work we provide an explanation to such challenge, by proving that when demands are given as a finite set of scenarios, solving the LP relaxation of such formulation is strongly NP-Hard. We also prove a hardness result for the case of independent normal demands. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Vehicle routing stochastic programming Branch-and-price

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A bi-criteria moving-target travelling salesman problem under uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期309卷 271-285页

作者： Maskooki, Alaleh Kallio, Markku Univ Turku Vesilinnantie 5 FI-20014 Turku Finland Aalto Univ Sch Business Ekonominaukio 1 FI-00076 Espoo Finland

This article concerns a variant of moving target travelling salesman problem where the number and lo-cations of targets vary with time and realizations of random trajectories. Managerial objectives are to maximize the number of visits to different targets and to minimize the total travel distance. Employing a linear value function for finding supported Pareto-efficient solutions, we develop a two-stage stochastic programming model. We propose an iterative randomized dynamic programming (RDP ) algorithm which converges to a global optimum with probability one. Each iteration in RDP involves a randomized back-ward and forward recursion stage as well as options for improving any given schedule: swaps of targets and optimization of timing for visits. An integer linear programming (ILP) model is developed and solved by a standard ILP solver to evaluate the performance of RDP on instances of real data for scheduling an environmental surveillance boat to visit ships navigating in the Baltic Sea. Due to a huge number of binary variables, the ILP model in practice becomes intractable. For small to medium size data sets, the Pareto-efficiency of solutions found by RDP and ILP solver are equal within a reasonable tolerance;however, RDP is significantly faster and able to deal with large-scale problems in practice.& COPY;2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Travelling salesman Moving target stochastic programming Dynamic programming Integer programming

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