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Column generation strategies and decomposition approaches for the two-stage stochastic multiple knapsack problem

COMPUTERS & OPERATIONS RESEARCH 2017年第Jul.期83卷 125-139页

作者： Tonissen, D. D. van den Akker, J. M. Hoogeveen, J. A. Eindhoven Univ Technol Sch Ind Engn POB 513 NL-5600 MB Eindhoven Netherlands Univ Utrecht Dept Informat & Comp Sci Princetonpl 5 NL-3584 CC Utrecht Netherlands

Many problems can be formulated by variants of knapsack problems. However, such models are deterministic, while many real-life problems include some kind of uncertainty. Therefore, it is worthwhile to develop and test knapsack models that can deal with disturbances. In this paper, we consider a two stage stochastic multiple knapsack problem. Here, we have a multiple knapsack problem together with a set of possible disturbances. For each disturbance, or scenario, we know its probability of occurrence and the resulting reduction in the sizes of the knapsacks. For each knapsack we decide in the first stage which items we take with us, and when a disturbance occurs we are allowed to remove items from the corresponding knapsack. Our goal is to find a solution where the expected revenue is maximized. We use branch-and-price to solve this problem. We present and compare two solution approaches: the separate recovery decomposition (SRD) and the combined recovery decomposition (CRD). We prove that the LP-relaxation of the CRD is stronger than the LP-relaxation of the SRD. Furthermore, we investigate numerous column generation strategies and methods to create additional columns outside the pricing problem. These strategies reduce the solution time significantly. To the best of our knowledge, there is no other paper that investigates such strategies so thoroughly. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： two-stage stochastic programming Recoverable robustness Column generation Branch-and-price Multiple knapsack problem

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Optimal Location-Allocation of TCSCs and Transmission Switch Placement Under High Penetration of Wind Power

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IEEE TRANSACTIONS ON POWER SYSTEMS 2017年第4期32卷 3006-3014页

作者： Ziaee, Omid Choobineh, Fred Univ Nebraska Dept Elect & Comp Engn Lincoln NE 68588 USA

We propose a stochastic mathematical program for finding the optimal location and compensation level of thyristor-controlled series compensators (TCSCs) and the optimal location of line switches in a transmission network. The combined uncertainty of the load and generation is captured by scenarios. The proposed problem has polynomial constraints, and we use the general linearization technique to linearize those constraints. The model becomes decomposable into a primal master and subprograms solvable by a branch-and-price procedure with the aid of column generation. The numerical results of implementing the model for the IEEE 118-bus test system show that combined investment in TCSCs and switches decreased the cost of energy and increased the penetration of wind energy more than individual investment of TCSCs or switches.

关键词： TCSC location-allocation transmission line switching two-stage stochastic programming wind power penetration

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Multi-Timescale Coordinated Voltage/Var Control of High Renewable-Penetrated Distribution Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2017年第6期32卷 4398-4408页

作者： Xu, Yan Dong, Zhao Yang Zhang, Rui Hill, David J. Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia China Southern Power Grid Res Inst Guangzhou 510000 Guangdong Peoples R China Univ Hong Kong Dept Elect & Elect Engn Pokfulam Hong Kong Peoples R China Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

This paper proposes a multi-timescale coordinated stochastic voltage/var control method for high renewable-penetrated distribution networks. It aims to utilize multiple devices to counteract uncertain voltage fluctuation and deviation. In the hourly timescale (first stage), capacitor banks and transformer tap changers are scheduled before stochastic renewable output and load variations are realized. In the 15-min timescale (second stage), inverters that interface the renewable energy resources provide var support to supplement the first-stage decision after uncertainty is observed. The coordination is model as a two-stage stochastic programming problem with scenario reduction. It is then converted to a deterministic mixed-integer quadratic programming equivalence model and solved by commercial solvers combined. Compared with existing methods, the proposed volt/var control can achieve lower expected energy loss and can sustain a secure voltage level under random load demand and renewable power injection. The proposed method is verified on the IEEE 33-bus distribution network and compared with existing practices.

关键词： Distribution network renewable energy resource two-stage stochastic programming volt/var control

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Developing a two stage stochastic programming model of the price and lead-time decision problem in the multi-class make-to-order firm

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COMPUTERS & INDUSTRIAL ENGINEERING 2011年第4期61卷 1086-1097页

作者： Chaharsooghi, S. Kamal Honarvar, Mahboobeh Modarres, M. Kamalabadi, Isa Nakhai Tarbiat Modares Univ Dept Ind Engn Sch Engn Tehran Iran Sharif Univ Technol Dept Ind Engn Tehran Iran

Pricing coordination and due-date management are managerial challenges in today's competitive marketplace. Segmenting orders into classes and allocating resources based on their sensitivity to time and price can increase a firm's profit and its capacity utilization. In addition, other parameters such as production policy, inventory holding and delivery system should be considered in pricing and due-date decisions. In this paper, we consider the role of flexibility in price, lead-time and delivery in the make-to-order environment, where limited production capacity under a stochastic demand function is allowed. We develop a two-stage stochastic programming model to determine the price, lead-time and production amount jointly in each period. The difficulty of continuous distributions is avoided by using a scenario-based approach for stochastic demand. Through numerical analyses, we indicate the benefits of flexibility in delivery, price and lead-time in various environments. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Pricing Lead-time Production two-stage stochastic programming

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Development of a fuzzy-stochastic programming with Green Z-score criterion method for planning water resources systems with a trading mechanism

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2016年第24期23卷 25245-25266页

作者： Zeng, X. T. Huang, G. H. Li, Y. P. Zhang, J. L. Cai, Y. P. Liu, Z. P. Liu, L. R. Capital Univ Econ & Business Beijing 10070 Peoples R China Univ Regina Inst Energy Environm & Sustainable Commun Regina SK S4S 0A2 Canada Beijing Normal Univ Coll Environm Beijing 100875 Peoples R China North China Elect Power Univ MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China

This study developed a fuzzy-stochastic programming with Green Z-score criterion (FSGZ) method for water resources allocation and water quality management with a trading-mechanism (WAQT) under uncertainties. FSGZ can handle uncertainties expressed as probability distributions, and it can also quantify objective/subjective fuzziness in the decision-making process. Risk-averse attitudes and robustness coefficient are joined to express the relationship between the expected target and outcome under various risk preferences of decision makers and systemic robustness. The developed method is applied to a real-world case of WAQT in the Kaidu-Kongque River Basin in northwest China, where an effective mechanism (e.g., market trading) to simultaneously confront severely diminished water availability and degraded water quality is required. Results of water transaction amounts, water allocation patterns, pollution mitigation schemes, and system benefits under various scenarios are analyzed, which indicate that a trading-mechanism is a more sustainable method to manage water-environment crisis in the study region. Additionally, consideration of anthropogenic (e.g., a risk-averse attitude) and systemic factors (e.g., the robustness coefficient) can support the generation of a robust plan associated with risk control for WAQT when uncertainty is present. These findings assist local policy and decision makers to gain insights into water-environment capacity planning to balance the basin's social and economic growth with protecting the region's ecosystems.

关键词： Fuzzy programming two-stage stochastic programming Green Z-score criterion Strategic analysis Trading-mechanism Arid basin

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stochastic programming and market equilibrium analysis of microgrids energy management systems

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ENERGY 2016年 113卷 662-670页

作者： Hu, Ming-Che Lu, Su-Ying Chen, Yen-Haw Natl Taiwan Univ Dept Bioenvironm Syst Engn 1Sect 4Roosevelt Rd Taipei 10617 Taiwan Taiwan Inst Econ Res Div Res 17F16-8 Dehuei St Taipei 104 Taiwan

Microgrids facilitate optimum utilization of distributed renewable energy, provides better local energy supply, and reduces transmission loss and greenhouse gas emission. Because the uncertainty in energy demand affects the energy demand and supply system, the aim of this research is to develop a stochastic optimization and its market equilibrium for microgrids in the electricity market. Therefore, a two-stage stochastic programming model for microgrids and the market competition model are derived in this paper. In the stochastic model, energy demand and supply uncertainties are considered. Furthermore, a case study of the stochastic model is conducted to simulate the uncertainties on the INER microgrids in Taiwanese market. The optimal investment of the generators and batteries installation and operating strategies are determined under energy demand and supply uncertainties for the INER microgrids. The results show optimal investment and operating strategies for the current INER microgrids are also determined by the proposed two-stage stochastic model in the market. In addition, trade-off between the battery capacity and microgrids performance is investigated. Battery usage and power trading between the microgrids and main grid systems are the functions of battery capacity. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Microgrids Uncertainty analysis two-stage stochastic programming Market equilibrium

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A stochastic programming with imprecise probabilities model for planning water resources systems under multiple uncertainties

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stochastic ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2016年第8期30卷 2169-2178页

作者： Wang, Y. Y. Huang, G. H. Wang, S. Li, W. North China Elect Power Univ S&C Resources & Environm Res Acad MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada

In this study, a stochastic programming with imprecise probabilities (SP-IP) model is proposed for planning water resources systems. The SP-IP model is capable of addressing multiple uncertainties in the forms of intervals with random boundaries and imprecise probability distributions. The stochastic optimization model can be transformed into a deterministic equivalence in a straightforward manner. A case study of regional water resources allocation is used to demonstrate the applicability of the proposed model. Results indicate that the total net benefits would be decreased with increased probabilities of occurrence, reflecting a potential trade-off between economic benefits and associated risks. The SP-IP model is also capable of providing a variety of decision alternatives under different scenarios of water policies, which is useful for water managers to formulate an appropriate water management policy in an uncertain environment.

关键词： Interval probability Dual uncertainties Random boundary interval two-stage stochastic programming Water resources allocation

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A Day-Ahead Joint Energy and Uncertainty Reserve Market Clearing Model to Manage VRE Uncertainty

A Day-Ahead Joint Energy and Uncertainty Reserve Market Clea...

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IEEE International Conference on Environment and Electrical Engineering

作者： Shaghayegh Zalzar Ettore Bompard Department of Energy Politecnico di Torino Turin Italy

The existing electricity market designs may be not compatible with high penetration of Variable Renewable Energy Sources (VRE) in power systems and need to be improved to address VREs' variability and uncertainty. VREs require flexibility and additional reserve capacities from conventional power plants to offset their real-time deviation from the forecasted output power. Another important issue regarding VRE market participation is the relatively low market clearing prices which in turn threatens the profitability of conventional generators. To address these issues, this paper contributes in modelling a central framework to provide uncertainty reserve service which is simultaneously optimized with energy procurement in day-ahead market. The uncertainty reserve is remunerated through day-ahead reservation price and real-time activation price. The proposed market clearing mechanism is able to provide fair and competitive supplementary revenue stream for conventional generators, while it ensures adequate reserve capacities in an hourly basis, taking into account network constraints, to address VRE variability and uncertainty.

关键词： Uncertainty Reserve Mixed Integer Linear programming Variable Renewable Energy (VRE) two-stage stochastic programming

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Sizing of energy storage systems considering uncertainty on demand and generation

Sizing of energy storage systems considering uncertainty on ...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Bucciarelli, Martina Giannitrapani, Antonio Paoletti, Simone Vicino, Antonio Zarrilli, Donato Univ Siena Dipartimento Ingn Informaz & Sci Matemat Via Roma 56 I-53100 Siena Italy

Over recent years there has been a general consensus about the necessary changes towards modernizing the existing power grid to meet environmental and socio-economic objectives. The adoption of low carbon technologies is a milestone in this process. On the other hand, the massive and uncoordinated connection of distributed generators (e.g. solar or wind) is making the operation of electrical distribution networks more challenging, e.g. causing energy balancing problems or voltage violations. Energy storage systems represent a possible means to cope with these issues. In this paper, we consider the problem of sizing the energy storage systems installed in a low voltage network with the aim of preventing voltage violations along the feeders. Since the problem is solved at the planning stage, when future realizations of demand and generation are unknown, we adopt a two-stage stochastic formulation where daily demand and generation profiles are modelled as random processes. The cost function to be minimized takes into account installation and operation costs related to storage use. By taking a scenario based approach, the two-stage problem is approximated via a multi-scenario optimal power flow. To reduce the computational burden of the latter problem, a heuristic strategy consisting of solving separately a sizing problem for each scenario, and then combining the solutions of the single problems through a worst-case criterion, is proposed. The multi-scenario approach and the heuristic strategy are compared in terms of both computation time and quality of the solution using real data from an Italian low voltage network with photovoltaic generation. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Energy storage sizing voltage control distribution network two-stage stochastic programming scenario-based approach

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Uncertainty-aware Optimization of Resource Provisioning, a Cloud End-user Perspective 7

Uncertainty-aware Optimization of Resource Provisioning, a C...

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7th International Conference on Cloud Computing and Services Science (CLOSER)

作者： Tajvidi, Masoumeh Maher, Michael J. Essam, Daryl UNSW Sch Engn & Informat Technol Canberra ACT Australia

ISBN: (纸本)9789897582431

Cloud computing offers a customer the possibility of the availability of large computational resources, while paying only for the resources used. However, because of uncertainty in the customers future demand and the future market price for the computational resources, obtaining these resources in a cost-effective and robust way is a difficult problem. The variety of pricing plans is a further complication. In this paper we solve this problem using two-stage stochastic programming, for the first time considering all three available pricing plans, i.e. on-demand, reservation, and spot pricing. Through our experimental implementation, we find that our model can lower the total operational cost by up to 1.5 percent compared to other solutions.

关键词： Cloud Computing Resource Provisioning two-stage stochastic programming

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