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Two simplex-based approximate stochastic dynamic programming schemes for a real hydropower management problem

ANNALS OF OPERATIONS RESEARCH 2025年 1-32页

作者： Zephyr, Luckny Lamond, Bernard F. Demeester, Kenjy Latraverse, Marco Laurentian Univ Sch Business Adm Barthi Sch Engn & Comp Sci 935 Ramsey Lake Rd Sudbury ON P3E 2C6 Canada Univ Laval Fac Sci Adm Dept Operat & Syst Decis 2325 Rue Univ Quebec City PQ G1V 0A6 Canada Rio Tinto Tech Serv 1955 Blvd MellonEd 100A Saguenay PQ G7S 4L2 Canada

We present an approximate stochastic dynamic programming methodology for a real-world hydropower management problem, in which water must be released from reservoirs to produce electricity to power aluminum smelters over a planning horizon of a year (three-day time step). In each period, decisions are constrained by limits on the releases and the level of the four reservoirs, among others. The approach is a revisit of our previous work on simplicial approximate stochastic dynamic programming, in which the so-called cost-to-go or value functions are approximated over grid points chosen as vertices of simplices. The latter are constructed by first partitioning the reservoir level space into simplices and then iteratively subdividing existing simplices until a desired approximation error or a fixed number of grid points is reached. For each simplex, the approximation error is given by the difference between an upper and a lower bound. This scheme requires storing the list of created simplices in memory. In each iteration, the list is searched to find the existing simplex with the highest approximation error. This may be time-consuming as the number of existing simplices may be very large. In the new proposal, we avoid creating a long list of simplices by combining the original simplicial scheme with Monte Carlo simulation, similar to an exploration strategy in reinforcement learning. We benchmark the new method against its ancestor and an internal software package developed and used by an industrial partner, based on operational metrics and the concept of super-efficiency in data envelopment analysis. The Monte Carlo simplex-based scheme (the new method) outperforms the former method on all metrics considered. In addition, we compare the computational efficiency of both methods for different grid sizes. The average CPU time (over 15 replications) of the Monte Carlo simplicial approach varies between 78% and 98% of that of the simplicial method. As the grid sizes increas

关键词： Hydropower stochastic dynamic programming Approximate stochastic dynamic programming Data envelopment analysis Simplex Monte Carlo simulation

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stochastic dynamic programming model for optimal resource allocation in vehicular ad hoc networks

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2018年第4期43卷 1-8页

作者： Bhuvaneswari, M. Paramasivan, B. Kandasamy, A. Natl Engn Coll Dept Comp Sci & Engn Kovilpatti 628503 India Natl Inst Technol Karnataka Dept Math & Computat Sci Mangalore 575025 India

Vehicular ad hoc network (VANET) is an emerging trend where vehicles communicate with each other and possibly with a roadside unit to assist various applications like monitoring, managing and optimizing the transportation system. Collaboration among vehicles is significant in VANET. Resource constraint is one of the great challenges of VANETs. Because of the absence of centralized management, there is pitfall in optimal resource allocation, which leads to ineffective routing. Effective reliable routing is quite essential to achieve intelligent transportation. stochastic dynamic programming is currently employed as a tool to analyse, develop and solve network resource constraint and allocation issues of resources in VANET. We have considered this work as a geographical-angular-zone-based two-phase dynamic resource allocation problem with a homogeneous resource class. This work uses a stochastic dynamic programming algorithm based on relaxed approximation to generate optimal resource allocation strategies over time in response to past task completion status history. The second phase resource allocation uses the observed outcome of the first phase task completion to provide optimal viability in resulting decisions. The proposed work will be further extended for the scenario that deals with heterogeneous resource class. Simulation results show that the proposed scheme works significantly well for the problems with identical resources.

关键词： stochastic dynamic programming relaxed formulation vehicular ad hoc networks resource allocation

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stochastic dynamic programming for the energy management of a serial hybrid electric bus

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INTERNATIONAL JOURNAL OF VEHICLE DESIGN 2015年第1-4期69卷 88-112页

作者： Elbert, Philipp Widmer, Martin Gisler, Hans-Joerg Onder, Christopher ETH Inst Dynam Syst & Control Dept Mech & Proc Engn CH-8092 Zurich Switzerland Carrosserie Hess AG CH-4512 Bellach Solothurn Switzerland

Hybrid electric vehicles require an energy management strategy to determine how the requested power is to be split up between the combustion engine and the electric energy buffer. The energy management significantly influences the overall efficiency of the vehicle. A careful design and implementation is thus crucial to achieve good fuel economy. This paper proposes a strategy based on stochastic dynamic programming with the following advantages: First, optimal performance is guaranteed with respect to the available information. Second, the resulting controller is a look-up table and the computational burden of its evaluation is very light. Third, controller synthesis is a systematic procedure allowing to trade off multiple objectives, e.g., fuel economy and drivability. Simulation results show 3-5% close to global optimal performance. During practice, a hybrid bus with the proposed energy management yields a fuel consumption reduction of 22-29% compared to a Diesel bus with comparable specifications.

关键词： hybrid electric vehicles energy management stochastic dynamic programming public transportation electric double layer capacitor

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stochastic dynamic programming-Based Online Algorithm for Energy Management of Integrated Energy Buildings With Electric Vehicles and Flexible Thermal Loads

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IEEE ACCESS 2021年 9卷 58780-58789页

作者： Cheng, Renli Cheng, Weijie Li, Jie Chen, Zeqi Shi, Jun Pan, Zhenning Wu, Yufeng Yu, Tao Shenzhen Power Supply Bur Co Ltd Shenzhen 518000 Peoples R China South China Univ Technol Coll Elect Power Guangzhou 510640 Peoples R China

With the rapid development of economy and technology, large-scale integrated energy buildings account for an increasing proportion of urban load. However, the randomness of EV owner behaviors, electricity price and outdoor temperature have brought challenges to the energy management of integrated energy buildings. This paper proposes a stochastic dynamic programming-based online algorithm to address the energy management of integrated energy buildings with electric vehicles and flexible thermal loads under multivariate uncertainties. First, an online energy management framework is established, which is further formulated as a multi-stage stochastic sequential decision-making problem. To address the complexities of the problem, a novel stochastic dynamic programming is employed to develop a distribution-free, computationally efficient, and scalable solution. By using extensive training samples, the algorithm is trained offline to learn how to deal with multivariate uncertainties and get the approximate optimal solution, which no longer depends on intraday forecast information. Numerical tests demonstrate the effectiveness of the proposed algorithm compared with other online algorithms in terms of optimality and computation efficiency.

关键词： Buildings Resistance heating Uncertainty Heuristic algorithms Energy management Water heating stochastic processes stochastic dynamic programming online algorithm energy management integrated energy building multivariate uncertainties

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stochastic dynamic programming (SDP) with a conditional value-at-risk (CVaR) criterion for management of storm-water

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JOURNAL OF HYDROLOGY 2008年第3-4期348卷 320-329页

作者： Piantadosi, J. Metcalfe, A. V. Howlett, P. G. Univ S Australia Ctr Ind & Appl Math Mawson Lakes CampusMawson Lakes Blvd Mawson Lakes SA 5095 Australia Univ Adelaide Sch Math Adelaide SA 5005 Australia

We present a new approach to stochastic dynamic programming (SDP) to determine a policy for management of urban storm-water that minimises conditional value-at-risk (CVaR). Storm-water flows into a large capture dam and is subsequently pumped to a holding dam. Water is then supplied directly to users or stored in an underground aquifer. We assume random inflow and constant demand. SDP is used to find a pumping policy that minimises CVaR, with a penalty for increased risk of environmental damage, and a pumping policy that maximises expected monetary value (EMV). We use both value iteration and policy improvement to show that the optimal policy under CVaR differs from the optimal policy under EMV. (c) 2007 Elsevier B.V. All rights reserved.

关键词： water management connected dams stochastic dynamic programming conditional value-at-risk

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stochastic dynamic programming based optimal energy scheduling for a hybrid fuel cell/PV/battery system under uncertainty

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PROCESS SAFETY AND ENVIRONMENTAL PROTECTION 2022年第0期165卷 380-386页

作者： Wang, Xianlian Hua, Qingsong Liu, Ping Sun, Li Southeast Univ Natl Engn Res Ctr Power Generat Control & Safety Sch Energy & Environm Nanjing 210096 Peoples R China Sun Yat Sen Univ Sch Aeronaut & Astronaut Guangdong 510275 Peoples R China

Hybrid green energy system, consisting of photovoltaic (PV), fuel cell and battery, receives wide attention because of its autonomy, flexibility and promising potential in accelerating the development of carbon neutrality in the field of power generation. However, the efficient power dispatching of the hybrid energy system is challenging due to the inevitable uncertainties of the solar energy. To this end, stochastic dynamic programming (SDP) is used in this paper to find the optimal solution to minimize the total fuel consumption during a 72-hour operating cycle, with constraints on the magnitude and rate of the fuel cell and battery operation, in which the stochastic characteristics of the solar power are described by Markov chain. The influence of sampling time and number of states on the solar prediction accuracy is discussed. For comparison, the traditional rule-based al-gorithm and dynamic programming (DP) algorithms are also utilized to describe and solve the power distribution problem, corresponding to different decision results in terms of how to distribute the energy flow for each time period. Numerical optimization results within the 72-hour period demonstrate that, the SDP has a 20.61% economy and 66.34% battery SOC improvement than that of rule-based algorithm, and in most uncertain cases, the SDP produces superior economic performance than those of both the rule-based algorithm and DP, benefited from the inclusion of the solar power probabilities into the optimization framework. The results of this paper lay a solid foundation for the efficient energy management of the hydrogen and solar hybrid energy system.

关键词： Energy management Markov chain stochastic dynamic programming Hybrid energy system

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stochastic dynamic programming with Non-linear Discounting

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APPLIED MATHEMATICS AND OPTIMIZATION 2021年第3期84卷 2819-2848页

作者： Baeuerle, Nicole Jaskiewicz, Anna Nowak, Andrzej S. Karlsruhe Inst Technol Dept Math Karlsruhe Germany Wroclaw Univ Sci & Technol Fac Pure & Appl Math Wyspianskiego 27 PL-50370 Wroclaw Poland Univ Zielona Gora Fac Math Comp Sci & Econometr Licealna 9 PL-65417 Zielona Gora Poland

In this paper, we study a Markov decision process with a non-linear discount function and with a Borel state space. We define a recursive discounted utility, which resembles non-additive utility functions considered in a number of models in economics. Non-additivity here follows from non-linearity of the discount function. Our study is complementary to the work of Jaskiewicz et al. (Math Oper Res 38:108-121, 2013), where also non-linear discounting is used in the stochastic setting, but the expectation of utilities aggregated on the space of all histories of the process is applied leading to a non-stationary dynamic programming model. Our aim is to prove that in the recursive discounted utility case the Bellman equation has a solution and there exists an optimal stationary policy for the problem in the infinite time horizon. Our approach includes two cases: (a) when the one-stage utility is bounded on both sides by a weight function multiplied by some positive and negative constants, and (b) when the one-stage utility is unbounded from below.

关键词： stochastic dynamic programming Non-linear discounting Bellman equation Optimal stationary policy

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stochastic dynamic programming heuristics for influence maximization-revenue optimization

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INTERNATIONAL JOURNAL OF DATA SCIENCE AND ANALYTICS 2019年第1期8卷 1-14页

作者： Lawrence, Trisha Hosein, Patrick Univ West Indies Dept Math & Stat St Augustine Trinidad Tobago Univ West Indies Dept Comp Sci St Augustine Trinidad Tobago

The well-known influence maximization (IM) problem has been actively studied by researchers over the past decade with emphasis on marketing and social networks. Existing research has determined solutions to the IM problem by obtaining the influence spread and utilizing the property of submodularity. This paper is based on a novel approach to the IM problem geared toward optimizing clicks, and consequently revenue, within an online social network (OSN). Our approach differs from existing approaches by adopting a novel, decision-making perspective using stochastic dynamic programming (SDP). Thus, we define a new problem, influence maximization-revenue optimization and propose SDP as a solution method. The SDP method has lucrative gains for an advertiser in terms of optimizing clicks and generating revenue, but one drawback to the method is its associated "curse of dimensionality" particularly for large OSNs. Thus, we introduce the L-degree heuristic, adaptive hill-climbing heuristic and the multistage particle swarm optimization heuristic as methods which are orders of magnitude faster than the SDP method while achieving near-optimal results. We compare these heuristics on both synthetic and real-world networks.

关键词： Online social networks stochastic dynamic programming Influence maximization Revenue Optimization

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stochastic dynamic programming Illuminates the Link Between Environment, Physiology, and Evolution

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BULLETIN OF MATHEMATICAL BIOLOGY 2015年第5期77卷 857-877页

作者： Mangel, Marc Univ Calif Santa Cruz Ctr Stock Assessment Res Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Appl Math & Stat Santa Cruz CA 95064 USA Univ Bergen Dept Biol Bergen Norway

I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

关键词： stochastic dynamic programming Parasitoids

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stochastic dynamic programming for energy management of an overplanted offshore wind farm with dynamic thermal rating and storage

Stochastic dynamic programming for energy management of an o...

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IEEE Belgrade PowerTech Conference

作者： Faye-Bedrin, Alexandre Blavette, Anne Haessig, Pierre Bourguet, Salvy Daminov, Ildar Univ Rennes CNRS ENS Rennes SATIE Lab Bruz France CentraleSupelec IETR Lab Rennes France Nantes Univ UR 4642 IREENA F-44600 St Nazaire France

ISBN: (纸本)9781665487788

We study the optimal energy management of an offshore wind farm which combines "overplanting" (more production than transmission capacity), "dynamic thermal rating" (DTR, transiently exporting more than the steady-state transmission capacity thanks to the large thermal inertia of the soil surrounding the export cable) and an energy storage (to mitigate both curtailements and forecast errors). This forward-looking setting, which aims at further reducing the Levelized Cost of Energy of offshore wind power, creates an optimization problem with both temporal couplings and uncertain inputs. The difficulty of this energy management problem comes from having time constants separated by several orders of magnitude due the thermal inertia of the cable surroundings. We propose an approximate solution based on large GPU implementation of stochastic dynamic programming (SDP). In our performance comparisons, SDP outperforms simpler rule-based energy management schemes while we also explore the benefit of DTR in the context of overplanting.

关键词： overplanting dynamic thermal rating energy storage optimal energy management stochastic dynamic programming

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