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Experimental Study of Methods of Scenario Lattice Construction for stochastic dual dynamic programming

Open Journal of Optimization 2021年第2期10卷 47-60页

作者： Dmitry Golembiovsky Anton Pavlov Smetanin Daniil Moscow State University Moscow Russia New Economic School Moscow Russia

The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.

关键词： stochastic dual dynamic programming Newsvendor Problem Markov Process

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stochastic dual dynamic programming to Schedule Energy Storage Units Providing Multiple Services

Stochastic Dual Dynamic Programming to Schedule Energy Stora...

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IEEE Eindhoven PowerTech Conference

作者： Olivier Megel Johanna L. Mathieu Goran Andersson ETH Zurich Power Systems Laboratory Zurich Switzerland Electrical and Computer Engineering University of Michigan Ann Arbor USA

When energy storage units, such as batteries, are installed to support photovoltaics and defer power system upgrades they are inactive or only partially used most of time. Their unused capacities could be used to provide frequency control, allowing them to generate additional revenues. However, the challenge is to decide how much of their energy and power capacities to allocate to either service. Photovoltaic generation profiles are difficult to forecast accurately, and frequency deviation is a highly stochastic process. This paper develops a stochastic dual dynamic programming (SDDP) approach to generate decision rules for determining how much capacity to assign to each service at each time step, depending on the time of day and the storage energy level. Unlike stochastic dynamic programming (SDP), our approach does not require us to discretize the state and decision spaces. We show that, when storage efficiency is high, SDDP outperforms SDP, but when short computation times are required, SDP may be preferred. We also discuss challenges associated with using SDDP when storage efficiency is lower than unity. Finally, we show that the number of tuning parameters is lower for SDDP than for SDP, and that the relation between tuning parameters and policy quality is more intuitive for SDDP than for SDP.

关键词： Batteries stochastic dynamic programming stochastic dual dynamic programming Frequency Control

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A stochastic dual dynamic integer programming based approach for remanufacturing planning under uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第17期61卷 5992-6012页

作者： Quezada, Franco Gicquel, Celine Kedad-Sidhoum, Safia Univ Santiago Chile USACH Fac Engn Ind Engn Dept Santiago 8320000 Chile Univ Santiago Chile USACH Fac Engn Program Dev Sustainable Prod Syst PDSPS Santiago 8320000 Chile Univ Paris Saclay LISN Gif Sur Yvette France CNAM CEDRIC Paris France

We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent the uncertain information structure. We introduce a new dynamic programming formulation that relies on a partial nested decomposition of the scenario tree. We then propose a new approximate stochastic dual dynamic integer programming algorithm based on this partial decomposition. Our numerical results show that the proposed solution approach is able to provide near-optimal solutions for large-size instances with a reasonable computational effort.

关键词： Production planning lot-sizing remanufacturing multi-stage stochastic integer programming stochastic dual dynamic programming

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stochastic dual dynamic integer programming

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MATHEMATICAL programming 2019年第1-2期175卷 461-502页

作者： Zou, Jikai Ahmed, Shabbir Sun, Xu Andy Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, such as nested Benders' decomposition and its stochastic variant, stochastic dual dynamic programming (SDDP), which proceed by iteratively approximating these functions by cuts or linear inequalities, have been established as effective approaches. However, it is difficult to directly adapt these algorithms to MSIP due to the nonconvexity of integer programming value functions. In this paper we propose an extension to SDDPcalled stochastic dual dynamic integer programming (SDDiP)for solving MSIP problems with binary state variables. The crucial component of the algorithm is a new reformulation of the subproblems in each stage and a new class of cuts, termed Lagrangian cuts, derived from a Lagrangian relaxation of a specific reformulation of the subproblems in each stage, where local copies of state variables are introduced. We show that the Lagrangian cuts satisfy a tightness condition and provide a rigorous proof of the finite convergence of SDDiP with probability one. We show that, under fairly reasonable assumptions, an MSIP problem with general state variables can be approximated by one with binary state variables to desired precision with only a modest increase in problem size. Thus our proposed SDDiP approach is applicable to very general classes of MSIP problems. Extensive computational experiments on three classes of real-world problems, namely electric generation expansion, financial portfolio management, and network revenue management, show that the proposed methodology is very effective in solving large-scale multistage stochastic integer optimization problems.

关键词： Multistage stochastic integer programming Binary state variables Nested decomposition stochastic dual dynamic programming

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A stochastic dual dynamic programming Model for Medium-Term Hydrothermal Scheduling in Greece

A Stochastic Dual Dynamic Programming Model for Medium-Term ...

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International Universities Power Engineering Conference

作者： Konstantina I. Ourani Costas G. Baslis Anastasios G. Bakirtzis Brunel University Heron Thermoelectric S.A. Aristotle University of Thessaloniki

ISBN: (纸本)9781467328548

This paper describes the development and application of the stochastic dual dynamic programming (SDDP) algorithm for solving the optimal medium-term hydrothermal scheduling in the Greek power system. The method aims at providing a more elaborate optimization tool compared to the traditional approaches used for medium-term hydrothermal scheduling in Greece;the latter have been developed on deterministic assumptions, while the proposed tool recognizes the impact of inflow uncertainty and provides well-hedged management strategies for each reservoir. The described method is developed using GAMS/CPLEX and tested for a power system similar to the Greek Interconnected Power System. The method proposed can be a stepping stone towards the calculation of the variable cost of each hydroplant on a monthly basis, a goal that has been officialy set forth by the Greek Regulatory Authority for Energy.

关键词： Hydrothermal Scheduling stochastic dual dynamic programming Variable Cost

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The value of nuclear power plants’ flexibility: A multistage stochastic dynamic programming approach

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European Journal of Operational Research 2025年

作者： Blanchard, Ange Massol, Olivier Laboratoire de Génie Industriel CentraleSupélec Université Paris Saclay 3 Rue Joliot Curie Gif-sur-YvetteF-91190 France Climate Economics Chair 28 Pl. de la Bourse ParisF-75002 France Chair the Economics of Gas 60 Bd Saint-Michel ParisF-75272 France Department of Economics City University of London Northampton Square LondonEC1V 0HB United Kingdom

In future power systems dominated by intermittent renewable generation, nuclear power plants will increasingly need to follow uncertain loads. However, regulatory and technical constraints limit the frequency of load-following operations, making their efficient allocation crucial. This paper explores the economic value of nuclear flexibility by modeling it as a stock constraint within a stochastic dynamic programming framework. We show how non-convex constraints at the reactor-scale translate to the fleet level through a linearized approximation, allowing for the analysis of multiple reactors operating under flexibility constraints. Applying this model to the French electricity system in 2035 using the stochastic dual dynamic programming (SDDP) algorithm, we estimate a marginal value of EUR 100/MW for the current flexibility level of the French nuclear fleet. Our results show that increased nuclear flexibility enhances system-wide cost efficiency and improves the integration of renewables, with solar generation seeing the largest benefits. However, our findings suggest a potential misalignment with the profit-maximizing goals of individual nuclear operators, which may deter them from increasing flexibility despite its necessity for the system. © 2025

关键词： dynamic programming Low-carbon power systems Nuclear power OR in energy stochastic dual dynamic programming

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dynamic order forecast sharing with dual shipping options under quantity flexibility contract

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年

作者： Zhang, Shuyang Yao, Yashu Huo, Jiazhen Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China

We study how a manufacturer shares demand information with its supplier under an important class of supply contracts known as quantity flexibility (QF) contract. In this article, we assume a manufacturer, facing evolving demand forecasts, needs to share the order forecasts to the supplier in a rolling-horizon manner. In each period, previous order forecasts can be adjusted but must remain within the flexibility outlined by the QF contract. Additionally, the manufacturer has two shipping options for transportation between the supplier and its location. We formulate this problem using stochastic dynamic programming and solve it with the stochastic dual dynamic programming (SDDP) algorithm. We carry out extensive numerical experiments and demonstrate that this method outperforms the other two benchmark methods. We also show that adopting dual shipping options can substantially reduce the overall costs of this inventory system and improve the effectiveness of information sharing. Most importantly, we find that the symmetric QF contract always leads to the exaggeration of quantities in order forecasts, while the asymmetric QF contract, with increasing flexibility slightly higher than decreasing, can facilitate unbiased order forecast sharing. Therefore, from the supplier's perspective, such asymmetric contracts are preferable.

关键词： Quantity flexibility contract dual shipping options forecast evolution rolling-horizon planning stochastic dual dynamic programming

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Trade-off between computation time and solution quality for integrated generation and transmission expansion planning with N-1 security criterion

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2025年 164卷

作者： Okamura, Lucas Y. Borges, Carmen L. T. Chicco, Gianfranco PSR Rio De Janeiro Brazil Univ Fed Rio de Janeiro Rio de Janeiro Brazil Politecn Torino Turin Italy

The generation and transmission (G&T) expansion planning of large-scale systems is usually carried out hierarchically due to the high complexity of the problem. However, this hierarchical plan may be more expensive than a fully integrated (co-optimized) G&T plan that, on the other hand, requires high computation time. Therefore, the trade-off between computation time and solution quality is of great importance, especially with the integration of renewable generation. This paper proposes and assesses alternative formulations of the integrated G&T planning problem, also considering the system operation simulation under the N-1 security criterion, seeking to balance solution optimality and computational effort. The assessments are illustrated for the Chilean electrical system. The main outcome is that one of the proposed methods, in which the future cost function is maintained fixed during the generation and transmission optimization and is recalculated only in the final simulation of the system operation, achieves results very close to the fully integrated generation, transmission, and operation optimization method. This method presents a cost reduction of 8 % compared to a hierarchical approach, which represents savings of around 700 million dollars, and 50 % less computation time compared to the fully integrated method. For the same proposed method, the preliminary calculation of an optimal solution without applying the N-1 security constraint as a starting point, followed by re-optimization with active N-1 security constraints, contributes to a 65 % reduction of the computation time without significantly impacting the quality of the solution.

关键词： Power system planning Renewable Generation Security Optimization Mixed Integer Linear programming stochastic dual dynamic programming

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A stochastic algorithm for deterministic multistage optimization problems

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ANNALS OF OPERATIONS RESEARCH 2025年第1期345卷 1-38页

作者： Akian, Marianne Chancelier, Jean-Philippe Tran, Benoit CNRS Ecole Polytech INRIA Saclay IP Paris Route Saclay F-91128 Palaiseau France CNRS Ecole Polytech CMAP IP Paris Route Saclay F-91128 Palaiseau France Ecole Ponts ParisTech CERMICS 6&8 Ave Blaise Pascal F-77455 Marne La Vallee 2 France

Several attempts to dampen the curse of dimensionality problem of the dynamic programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the stochastic dual dynamic programming method (Sddp) introduced by Pereira and Pinto (Math Program 52(1-3):359-375. https://***/10.1007/BF01582895). Assuming that the value function is convex (for a minimization problem), one builds a non-decreasing sequence of lower (or outer) convex approximations of the value function. Those convex approximations are constructed as a supremum of affine cuts. On continuous time deterministic optimal control problems, assuming that the value function is semiconvex, Zheng Qu, inspired by the work of McEneaney, introduced in 2013 a stochastic max-plus scheme that builds a non-increasing sequence of upper (or inner) approximations of the value function. In this note, we build a common framework for both the Sddp and a discrete time version of Zheng Qu's algorithm to solve deterministic multistage optimization problems. Our algorithm generates a monotone sequence of approximations of the value function as a pointwise supremum, or infimum, of basic (affine or quadratic for example) functions which are randomly selected. We give sufficient conditions on the way basic functions are selected in order to ensure almost sure convergence of the approximations to the value function on a set of interest.

关键词： Deterministic multistage optimization problem Min-plus algebra Tropical algebra stochastic dual dynamic programming dynamic programming

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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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