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

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 ar...

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Vydáno v:	Annals of operations research Ročník 351; číslo 1; s. 333 - 364
Hlavní autoři:	Zephyr, Luckny, Lamond, Bernard F., Demeester, Kenjy, Latraverse, Marco
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.08.2025 Springer Nature B.V
Témata:	Algorithms Apexes Approximation Artificial intelligence Business and Management Combinatorics Decomposition Dynamic programming Electricity Errors Hydroelectric power Hydrology Lower bounds Monte Carlo simulation Operations Research/Decision Theory Original Research Reservoirs Smelters Theory of Computation Water Water shortages Canada Approximate stochastic dynamic programming Simplex Stochastic dynamic programming Hydropower Monte Carlo simulation Data envelopment analysis
ISSN:	0254-5330, 1572-9338
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Abstract	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 increase above 3,000 points, the simplicial method becomes intractable, in contrast to the Monte Carlo version, which confirms the advantage of the latter. Lastly, to further justify the Monte Carlo simplicial method, we create an artificial system by duplicating each component of the original system. In contrast to the new proposal, under the simplicial approach, the problem is tractable only for relatively modest size grids (up to 1,500 points), for which the average CPU time under the Monte Carlo approach varies between 2% and 5% of that of its simplicial counterpart.
AbstractList	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 increase above 3,000 points, the simplicial method becomes intractable, in contrast to the Monte Carlo version, which confirms the advantage of the latter. Lastly, to further justify the Monte Carlo simplicial method, we create an artificial system by duplicating each component of the original system. In contrast to the new proposal, under the simplicial approach, the problem is tractable only for relatively modest size grids (up to 1,500 points), for which the average CPU time under the Monte Carlo approach varies between 2% and 5% of that of its simplicial counterpart.
Author	Demeester, Kenjy Latraverse, Marco Zephyr, Luckny Lamond, Bernard F.
Author_xml	– sequence: 1 givenname: Luckny orcidid: 0000-0002-7611-5192 surname: Zephyr fullname: Zephyr, Luckny email: lzephyr@laurentian.ca organization: School of Business Administration/Barthi School of Engineering and Computer Science, Laurentian University – sequence: 2 givenname: Bernard F. surname: Lamond fullname: Lamond, Bernard F. organization: Département d’opérations et système de décisions, Faculté des sciences de l’administration, Université Laval – sequence: 3 givenname: Kenjy surname: Demeester fullname: Demeester, Kenjy organization: Technical Services, Rio Tinto – sequence: 4 givenname: Marco surname: Latraverse fullname: Latraverse, Marco organization: Technical Services, Rio Tinto
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Snippet	We present an approximate stochastic dynamic programming methodology for a real-world hydropower management problem, in which water must be released from...
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SubjectTerms	Algorithms Apexes Approximation Artificial intelligence Business and Management Combinatorics Decomposition Dynamic programming Electricity Errors Hydroelectric power Hydrology Lower bounds Monte Carlo simulation Operations Research/Decision Theory Original Research Reservoirs Smelters Theory of Computation Water Water shortages
Title	Two simplex-based approximate stochastic dynamic programming schemes for a real hydropower management problem
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