Abstract
The optimal algorithm to ensure computational efficiency and accuracy remains to be challenging for the development of robust operation model to solve the optimization problem of reservoir operation, particularly for applications involving flood control with complex flood hydrograph. The dynamic programming (DP) is one of the most popular methods to solve optimization problem, but it is limited the “curse of dimensionality” problem. The improved dynamic programming (IDP) method has been proposed to overcome this defeat of DP, remaining the convergence problem. The relaxation method based on approximate monotonic relationship shows potential to ensure convergence of IDP. In this study, the theoretical search range of the relaxation method are analyzed. A stable improved dynamic programming (SIDP) method is proposed based on relaxation method and a prediction method of schedulable storage states. The proposed SIDP overcomes the complex computational problem of DP and the convergence problem of IDP. The case study on an ideal reservoir and the Guanting reservoir, shows that SIDP can achieve an accuracy as high as DP, but with a much higher efficiency than DP. This method shows a strong solution to optimization problems of reservoir flood control operation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Data and code are available from the corresponding author.
References
Ahmad A, El-Shafie A, Razali SFM, Mohamad ZS (2014) Reservoir Optimization in Water Resources: a Review. Water Resour Manag 28:3391–3405. https://doi.org/10.1007/s11269-014-0700-5
Ahmed E-SMS, Mays LW (2013) Model for determining real-time optimal dam releases during flooding conditions. Nat Hazards 65:1849–1861. https://doi.org/10.1007/s11069-012-0444-6
Bayat B, Mousavi SJ, Namin MM (2011) Optimization–simulation for short-term reservoir operation under flooding conditions. J Water Supply Res T 60:434–447. https://doi.org/10.2166/aqua.2011.038
Bellman R (1966) Dynamic Programming. Science 153:34–37. https://doi.org/10.1126/science.153.3731.34
Chen J, Zhong P-a, Xu B, Zhao Y-f (2015) Risk Analysis for Real-Time Flood Control Operation of a Reservoir. J Water Res Plan Man 141:04014092. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000490
Chen J, Qi X, Qiu G, Chen L (2022) Improved progressive optimality algorithm and its application to determination of optimal release trajectory of long-term power generation operation of cascade reservoirs. Adv Water Resour 166:104253. https://doi.org/10.1016/j.advwatres.2022.104253
Cheng C, Wang S, Chau K-W, Wu X (2014) Parallel discrete differential dynamic programming for multireservoir operation. Environ Modell Softw 57:152–164. https://doi.org/10.1016/j.envsoft.2014.02.018
Dash SS, Sahoo B, Raghuwanshi NS (2022) An adaptive multi-objective reservoir operation scheme for improved supply-demand management. J Hydrol 615:128718. https://doi.org/10.1016/j.jhydrol.2022.128718
Devkota R, Bhattarai U, Devkota L, Maraseni TN (2020) Assessing the past and adapting to future floods: a hydro-social analysis. Clim Change 163:1065–1082. https://doi.org/10.1007/s10584-020-02909-w
Draper AJ, Lund JR (2004) Optimal hedging and carryover storage value. J Water Res Plan Man 130:83–87. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(83)
Hansford MR, Plink-Björklund P, Jones ER (2020) Global quantitative analyses of river discharge variability and hydrograph shape with respect to climate types. Earth-Sci Rev 200:102977. https://doi.org/10.1016/j.earscirev.2019.102977
He S, Guo S, Chen K et al (2019) Optimal impoundment operation for cascade reservoirs coupling parallel dynamic programming with importance sampling and successive approximation. Adv Water Resour 131:103375. https://doi.org/10.1016/j.advwatres.2019.07.005
He Z, Wang C, Wang Y et al (2021) Dynamic programming with successive approximation and relaxation strategy for long-term joint power generation scheduling of large-scale hydropower station group. Energy 222:119960. https://doi.org/10.1016/j.energy.2021.119960
He Z, Wang C, Wang Y, Zhang H, Yin H (2022) An Efficient Optimization Method for Long-term Power Generation Scheduling of Hydropower Station: Improved Dynamic Programming with a Relaxation Strategy. Water Resour Manag 36:1481–1497. https://doi.org/10.1007/s11269-022-03096-2
Heidari M, Chow VT, Kokotović PV, Meredith DD (1971) Discrete Differential Dynamic Programing Approach to Water Resources Systems Optimization. Water Resour Res 7:273–282. https://doi.org/10.1029/WR007i002p00273
Howson HR, Sancho NGF (1975) A new algorithm for the solution of multi-state dynamic programming problems. Math Program 8:104–116. https://doi.org/10.1007/BF01580431
Hsieh C-D, Yang W-F (2007) Optimal nonpoint source pollution control strategies for a reservoir watershed in Taiwan. J Environ Manage 85:908–917. https://doi.org/10.1016/j.jenvman.2006.10.022
Hsu N-S, Wei C-C (2007) A multipurpose reservoir real-time operation model for flood control during typhoon invasion. J Hydrol 336:282–293. https://doi.org/10.1016/j.jhydrol.2007.01.001
Jia B, Simonovic SP, Zhong P, Yu Z (2016) A Multi-Objective Best Compromise Decision Model for Real-Time Flood Mitigation Operations of Multi-Reservoir System. Water Resour Manag 30:3363–3387. https://doi.org/10.1007/s11269-016-1356-0
Lai V, Huang YF, Koo CH, Ahmed AN, El-Shafie A (2022) A Review of Reservoir Operation Optimisations: from Traditional Models to Metaheuristic Algorithms. Arch Comput Method E 29:3435–3457. https://doi.org/10.1007/s11831-021-09701-8
Lee J-H, Labadie JW (2007) Stochastic optimization of multireservoir systems via reinforcement learning. Water Resour Res 43. https://doi.org/10.1029/2006WR005627
Li J-Q, Zhang Y-S, Ji C-M, Wang A-J, Lund JR (2013) Large-scale hydropower system optimization using dynamic programming and object-oriented programming: the case of the Northeast China Power Grid. Water Sci Technol 68:2458–2467. https://doi.org/10.2166/wst.2013.528
Li X, Wei J, Li T, Wang G, Yeh WWG (2014) A parallel dynamic programming algorithm for multi-reservoir system optimization. Adv Water Resour 67:1–15. https://doi.org/10.1016/j.advwatres.2014.01.002
Liu P, Li L, Guo S et al (2015) Optimal design of seasonal flood limited water levels and its application for the Three Gorges Reservoir. J Hydrol 527:1045–1053. https://doi.org/10.1016/j.jhydrol.2015.05.055
Rahimi H, Ardakani MK, Ahmadian M, Tang X (2020) Multi-Reservoir Utilization Planning to Optimize Hydropower Energy and Flood Control Simultaneously. Environ Process 7:41–52. https://doi.org/10.1007/s40710-019-00404-8
Su H-T, Tung Y-K (2013) Flood-Damage-Reduction Project Evaluation with Explicit Consideration of Damage Cost Uncertainty. J Water Res Plan Man 139:704–711. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000291
Tsakiris G (2014) Flood risk assessment: concepts, modelling, applications. Nat Hazard Earth Sys 14:1361–1369. https://doi.org/10.5194/nhess-14-1361-2014
van der Pol TD, Gabbert S, Weikard HP, van Ierland EC, Hendrix EMT (2017) A Minimax Regret Analysis of Flood Risk Management Strategies Under Climate Change Uncertainty and Emerging Information. Environ Resour Econ 68:1087–1109. https://doi.org/10.1007/s10640-016-0062-y
Xiong F, Guo S, Yin J, Tian J, Rizwan M (2020) Comparative study of flood regional composition methods for design flood estimation in cascade reservoir system. J Hydrol 590:125530. https://doi.org/10.1016/j.jhydrol.2020.125530
Zhang Z, Zhang S, Wang Y, Jiang Y, Wang H (2013) Use of parallel deterministic dynamic programming and hierarchical adaptive genetic algorithm for reservoir operation optimization. Comput Ind Eng 65:310–321. https://doi.org/10.1016/j.cie.2013.02.003
Zhang X, Liu P, Xu C-Y et al (2019) Real-time reservoir flood control operation for cascade reservoirs using a two-stage flood risk analysis method. J Hydrol 577:123954. https://doi.org/10.1016/j.jhydrol.2019.123954
Zhao T, Cai X, Lei X, Wang H (2012) Improved Dynamic Programming for Reservoir Operation Optimization with a Concave Objective Function. J Water Res Plan Man 138:590–596. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000205
Zhao T, Zhao J, Lei X, Wang X, Wu B (2017) Improved Dynamic Programming for Reservoir Flood Control Operation. Water Resour Manag 31:2047–2063. https://doi.org/10.1007/s11269-017-1599-4
Zhou Y, Guo S, Chang F-J, Liu P, Chen AB (2018) Methodology that improves water utilization and hydropower generation without increasing flood risk in mega cascade reservoirs. Energy 143:785–796. https://doi.org/10.1016/j.energy.2017.11.035
Zhu D, Mei Y, Xu X et al (2021) Optimal Operation of a Parallel Multireservoir System for Flood Control using a Stagewise Compensation Method. Water Resour Manag 35:1689–1710. https://doi.org/10.1007/s11269-021-02803-9
Funding
This work was supported by the Key Technologies Research and Development Program of China (No. 2016YFC0803107) and Beijing Science and Technology Planning Project (No. Z201100008220005).
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. Methods, data collection and supervision are performed by Fuxin Chai. Methods, programming and analysis were performed by Feng Peng. The first draft of the manuscript was written by Feng Peng. The first draft was reviewed by Hongping Zhang and Wenbin Zang and Hongping Zhang revised the first draft. Fuxin Chai performed the final review. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Competing Interests
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chai, F., Peng, F., Zhang, H. et al. Stable Improved Dynamic Programming Method: An Efficient and Accurate Method for Optimization of Reservoir Flood Control Operation. Water Resour Manage 37, 5635–5654 (2023). https://doi.org/10.1007/s11269-023-03622-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-023-03622-w