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An asymptotically efficient simulation-based algorithm for finite horizon stochastic dynamic programming

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2007年第1期52卷 89-94页

作者： Chang, Hyeong Soo Fu, Michael C. Hu, Jiaqiao Marcus, Steven I. Sogang Univ Dept Comp Sci & Engn Seoul 121742 South Korea Univ Maryland Robert H Smith Sch Business College Pk MD 20742 USA Univ Maryland Syst Res Inst College Pk MD 20742 USA SUNY Stony Brook Dept Appl Math & Stat Stony Brook NY 11794 USA Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA

We present a simulation-based algorithm called "Simulated Annealing Multiplicative Weights" (SAMW) for solving large finite-horizon stochastic dynamic programming problems. At each iteration of the algorithm, a probability distribution over candidate policies is updated by a simple multiplicative weight rule, and with proper annealing of a control parameter, the generated sequence of distributions converges to a distribution concentrated only on the best policies. The algorithm is "asymptotically efficient," in the sense that for the goal of estimating the value of an optimal policy, a provably convergent finite-time upper bound for the sample mean is obtained.

关键词： learning algorithms Markov decision processes simulation simulated annealing stochastic dynamic programming

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Incorporating Penalty Function to Reduce Spill in stochastic dynamic programming Based Reservoir Operation of Hydropower Plants

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2010年第5期5卷 531-538页

作者： Jha, Deependra Kumar Yorino, Naoto Zoka, Yoshifumi Sasaki, Yutaka Hayashi, Yuki Iwata, Kajunoni Oe, Ryuji Hiroshima Univ Grad Sch Engn Artificial Complex Syst Operat Lab Higashihiroshima 7398527 Japan Chugoku Elect Power Co Inc Hiroshima Japan

This paper proposes a framework that includes a penalty function incorporated stochastic dynamic programming (SDP) model in order to derive the operation policy of the reservoir of a hydropower plant, with an aim to reduce the amount of spill during operation of the reservoir. SDP models with various inflow process assumptions (independent and Markov-I) are developed and executed in order to derive the reservoir operation policies for the case study of a storage type hydropower plant located in Japan. The policy thus determined consists of target storage levels (end-of-period storage levels) for each combination of the beginning-of-period storage levels and the inflow states of the current period. A penalty function is incorporated ill the classical SDP model with objective function that maximizes annual energy generation through operation of the reservoir. Due to the inclusion of the penalty function, operation policy of the reservoir changes in a way that ensures reduced spill. Simulations are carried out to identify reservoir storage guide curves based on the derived operation policies. Reservoir storage guide curves for different values of the coefficient of penalty function a are plotted for a study horizon of 64 years, and the corresponding average annual spill values are compared. It is observed that, with increasing values of a, the average annual spill decreases;however, the simulated average annual energy value is marginally reduced. The average annual energy generation can be checked vis-a-vis the average annual spill reduction, and the optimal value of a can be identified based on the cost functions associated with energy and spill. (C) 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

关键词： reservoir operation policy stochastic dynamic programming hydropower plants Markov chain penalty function

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Applying unweighted least-squares based techniques to stochastic dynamic programming: theory and application

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IET CONTROL THEORY AND APPLICATIONS 2019年第15期13卷 2387-2398页

作者： Forootani, Ali Iervolino, Raffaele Tipaldi, Massimo Univ Sannio Dept Engn Piazza Roma 21 I-82100 Benevento Italy Univ Naples Federico II Dept Elect Engn & Informat Technol Via Claudio 21 I-80125 Naples Italy

Big data and the curse of dimensionality are common vocabularies that researchers in different communities have recently been dealing with, e.g. dynamic programming (DP) in automatic control system society. A novel unweighted sampled based least square projection approach is proposed in this study to address the issue of the large state space in the DP optimisation problem. The method, in particular, takes into account both contraction mapping and monotonicity properties of the DP algorithm for value function approximation. Specifically, the batch of samples are gathered by uniform probability distribution at first, and an unweighted LS sub-problem in the subspace is solved. As the case study, a new Markov decision process model associated with a resource allocation problem is considered to illustrate the technique and evaluate its effectiveness. It is noted that the approach can be employed for different applications as well. Moreover, a MATLAB based software is developed to implement and examine different parts of the proposed method. Simulation examples are considered to support the results of the approach via developed software. The idea makes a connection between the recent advances in big data analysis and approximate DP as well.

关键词： mathematics computing stochastic processes function approximation Markov processes data analysis probability Big Data resource allocation dynamic programming least squares approximations stochastic dynamic programming automatic control system society square projection approach DP optimisation problem monotonicity properties DP algorithm value function approximation uniform probability distribution unweighted LS sub-problem Markov decision process model resource allocation problem MATLAB based software big data analysis contraction mapping unweighted least-squares based techniques

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Efficient control for a multi-product quasi-batch process via stochastic dynamic programming

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IIE TRANSACTIONS 2011年第3期43卷 192-206页

作者： Eren, Ezgi C. Gautam, Natarajan Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA

This article considers a quasi-batch process where items are continuously processed while they move on a conveyor belt. In addition, the products arriving into the processor require variable amounts of processing, which translate into different processor levels. Keeping the processing level constant in such a system results in severe inefficiency in terms of consumption of energy and resources with high production costs and a poor level of environmental performance. A stochastic dynamic programming model is formulated that strikes a balance between consumption of energy and material, processor performance, and product quality. The model minimizes total system-wide cost, which is essentially a unified measure across all the objectives. The structural properties of the optimal policy and value functions are analyzed taking into account high-dimensionality of the state space. Based on some of these results, efficient heuristic methodologies are developed to solve large instances of the problem. It is shown using several numerical experiments that a significant amount of energy or material resources can be saved and total costs can be reduced considerably compared to the current practices in the process industry. Insights on the sensitivity of results with respect to the cost parameters are provided.

关键词： Efficient process control energy conservation environmental impact process industry multi-product quasi-batch processing stochastic dynamic programming MDP multi-dimensional state space

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Computational improvement for stochastic dynamic programming models of urban water supply reservoirs

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1998年第2期34卷 267-278页

作者： Perera, BJC Codner, GP Victoria Univ Technol Dept Civil & Bldg Engn Melbourne Vic 8001 Australia Monash Univ Dept Civil Engn Clayton Vic 3168 Australia

This paper describes two methods that are introduced to improve the computational effort of stochastic dynamic programming (SDP) as applicable to the operation of multiple urban water supply reservoir systems. The stochastic nature of streamflow is incorporated explicitly by considering it in the form of a multivariate probability distribution. The computationally efficient Gaussian Legendre quadrature method is employed to compute the conditional probabilities of streamflow, which accounts for the serial correlation of streamflow into each storage and the cross correlation between the streamflow into various storages. A realistic assumption of cross correlation of streamflow is introduced to eliminate the need to consider the streamflow combinations which are unlikely to occur in the SDP formulation. A "corridor" approach is devised to eliminate the need to consider the infeasible and/or inferior storage volume combinations in the preceding stage in computing the objective function in the recursive relation. These methods are verified in terms of computational efficiency and accuracy by using a hypothetical example of three interconnected urban water supply reservoirs. Therefore, it can be concluded that these methods allow SDP to be more attractive for deriving optimal operating rules for multiple urban water supply reservoir systems.

关键词： stochastic dynamic programming urban water supply reservoirs optimum operation computational improvement conditional probabilities of stream flow

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A stochastic dynamic programming Approach to Optimize Short-Rotation Coppice Systems Management Scheduling: An Application to Eucalypt Plantations under Wildfire Risk in Portugal

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FOREST SCIENCE 2012年第4期58卷 353-365页

作者： Ferreira, Liliana Constantino, Miguel F. Borges, Jose G. Garcia-Gonzalo, Jordi Ctr Invest Operac Polytech Inst Leiria Sch Technol & Management Morro Do Lena Alto Do Vi Leiria Portugal Univ Lisbon Fac Ciencias Dept Estatist & Invest Operac Ctr Invest Operac P-1699 Lisbon Portugal Univ Tecn Lisboa Inst Super Agron Ctr Estudos Florestais P-1100 Lisbon Portugal

This article presents and discusses research with the aim of developing a stand-level management scheduling model for short-rotation coppice systems that may take into account the risk of wildfire. The use of the coppice regeneration method requires the definition of both the optimal harvest age in each cycle and the optimal number of coppice cycles within a full rotation. The scheduling of other forest operations such as stool thinning and fuel treatments (e.g., shrub removals) must be further addressed. In this article, a stochastic dynamic programming approach is developed to determine the policy (e.g., fuel treatment, stool thinning, coppice cycles, and rotation length) that maximizes expected net revenues. stochastic dynamic programming stages are defined by the number of harvests, and state variables correspond to the number of years since the stand was planted. Wildfire occurrence and damage probabilities are introduced in the model to analyze the impact of the wildfire risk on the optimal stand management schedule policy. For that purpose, alternative wildfire occurrence and postfire mortality scenarios were considered at each stage. A typical Eucalyptus globulus Labill. stand in Central Portugal was used as a test case. Results suggest that the proposed approach may help integrate wildfire risk in short-rotation coppice systems management scheduling. They confirm that the maximum expected discounted revenue decreases with and is very sensitive to the discount rate and further suggest that the number of cycles within a full rotation is not sensitive to wildfire risk. Nevertheless, the expected rotation length decreases when wildfire risk is considered. FOR. SCI. 58(4):353-365.

关键词： stochastic dynamic programming wildfire risk forest management eucalypt coppice system

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Improving stochastic dynamic programming on hydrothermal systems through an iterative process

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ELECTRIC POWER SYSTEMS RESEARCH 2015年 123卷 147-153页

作者： Brandi, Rafael Bruno S. Ramos, Tales Pulinho Dias, Bruno Henriques Marques Marcato, Andre Luis da Silva Junior, Ivo Chaves Univ Fed Juiz de Fora Dept Elect Energy Juiz De Fora Brazil Fed Inst Educ Sci & Technol Southeast Minas Gerai Elect Grp Educ & Technol Dept Juiz De Fora Brazil

This paper proposes an iterative process to select the cuts that model the cost-to-go functions of stochastic dynamic programming (SDP) and stochastic dual dynamic programming (SDDP) algorithms. This approach is applied to the medium/long-term operation planning of hydrothermal systems. The main idea of the proposed algorithm is to improve the performance of the SDP and SDDP methods applied to the problem by iteratively adding cuts to the linear programming instances. Also, some case studies considering the Brazilian power system are presented. The results show a significant reduction in computational time with few modifications to the original algorithm. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Hydrothermal power systems stochastic dynamic programming stochastic dual dynamic programming Long-term operation planning Cut selection Multistage stochastic optimization

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A stochastic dynamic programming approach for multi-site capacity planning in TFT-LCD manufacturing under demand uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2014年 148卷 21-36页

作者： Lin, James T. Chen, Tzu-Li Chu, Hsiao-Ching Natl Tsing Hua Univ Dept Ind Engn & Engn Management Hsinchu 300 Taiwan Fu Jen Catholic Univ Dept Informat Management New Taipei City 24205 Taiwan

The study focuses on the dynamic multi-site capacity planning problem in the thin film transistor liquid crystal display (TFT-LCD) industry under stochastic demand. Capacity planning refers to the process of simultaneously implementing a robust capacity allocation plan and capacity expansion policy across multiple sites against stochastic demand. In addition, the demand situation in TFT-LCD manufacturing follows Markov properties, in which the correlations of the demand variations in the consecutive periods are high, and the demand status in the next period is stochastically determined by the present one. Therefore, this study constructs a stochastic dynamic programming (SDP) model with an embedded linear programming (LP) to generate a capacity planning policy as the demand in each period is revealed and updated. Using the backward induction algorithm, the SDP model considers several capacity expansion and budget constraints to determine a robust and dynamic capacity expansion policy in response to newly available demand information. The LP model then considers numerous TFT-LCD practical characteristics and constraints to decide a capacity allocation plan, and generate a one-period immediate reward used by the optimality recursion equation of the SDP model. Numerical results are also illustrated to prove the feasibility and robustness of the proposed SDP model compared to the traditional deterministic capacity planning model currently applied by the industry. (C) 2013 Elsevier B.V. All rights reserved.

关键词： TFT-LCD manufacturing Multi-site capacity planning Capacity expansion stochastic dynamic programming stochastic Markovian demand

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Multi-period asset allocation by stochastic dynamic programming

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APPLIED MATHEMATICS AND COMPUTATION 2008年第1期199卷 341-348页

作者： Kung, James J. Ming Chuan Univ Dept Int Business Taipei Taiwan

This study makes use of stochastic dynamic programming to set up a multi-period asset allocation model and derives an analytic formula for the optimal proportions invested in short and long bonds. Then maximum likelihood method is employed to estimate the relevant parameters. Finally, we implement the model through backward recursion algorithm to find numerically the optimal allocation of funds between short and long bonds for an investor with power utility and an investment horizon of ten years. Our results show that an investor will hold a larger proportion of short bond if his/her investment horizon gets shorter and/or if he/she is more risk averse. (C) 2007 Elsevier Inc. All rights reserved.

关键词： multi-period asset allocation stochastic dynamic programming Bellman function power utility two-factor vasicek model backward recursion algorithm

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Ensemble of Markovian stochastic dynamic programming models in different time scales for long term hydropower scheduling

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ELECTRIC POWER SYSTEMS RESEARCH 2017年 150卷 129-136页

作者： Scarcelli, R. O. C. Zambelli, M. S. Soares, S. Carneiro, A. A. F. M. Fed Inst Sao Paulo IFSP Sao Joao Da Boa Vista SP Brazil Univ Estadual Campinas UNICAMP Campinas SP Brazil Univ Sao Paulo Sao Carlos SP Brazil

This paper presents a new approach for long term hydropower scheduling. In opposition to the standard Markovian stochastic dynamic programming approach, where monthly inflows are modeled according to probability distribution functions, conditioned to some occurrence of inflow in the previous month, in the proposed approach the monthly inflows are aggregated in different time scales and then submitted to the Markovian model. The discharge decisions are then calculated by a deterministic model that optimizes the problem for one year ahead according to inflows provided by a combination of each Markovian model. Tests were conducted on hypothetical single-reservoirs hydrothermal systems using data from four real Brazilian hydro plants, with distinct hydrological regimes. The performance of the proposed method was evaluated through simulation, using the historical inflow data, in comparison with the standard Markovian model. The results have shown that the proposed approach has provided spillage reduction and increase on hydro productivity as well as power generation, which incurred in up to 2.1% reduction in operational costs. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Hydrothermal systems Long term scheduling stochastic dynamic programming Aggregated inflows

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