Deriving operating rules for multi-objective cascade reservoir systems is an important challenge in water resources management. To address, this study combines a radial basis function network with an evolutionary algorithm to propose a heuristic input variable selection (HIS) method that extracts reservoir operating rules based on feature selection. For a case study of the Hanjiang cascade reservoirs in China, we initially describe the operating rules with radial basis functions and subsequently refine them based on the HIS method. We select the most suitable input variables for each reservoir conditioned on water supply and power generation targets to derive and optimize the rules with a Pareto-archived dynamically dimensioned search algorithm. From this we can analyze input variable selection and the corresponding impact on multi-objective cascade reservoir operations. The results demonstrate that the HIS method selects the input variables accurately and the reservoir operating rules refined by the method could increase water supply by up to 6.6% and power generation by up to 1.2%. The most suitable input variables for reservoir operation vary depending on reservoir objective, however the HIS method appears effective at selecting the appropriate input variables for individual reservoirs in a cascade system.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bolouri-Yazdeli Y, Haddad OB, Fallah-Mehdipour E, Mariño M (2014) Evaluation of real-time operation rules in reservoir systems operation. Water Resour Manag 28(3):715–729
Buşoniu L, Ernst D, De Schutter B, Babuška R (2011) Cross-entropy optimization of control policies with adaptive basis functions. IEEE Trans Syst Man Cybern B Cybern 41(1):196–209
Chang FJ, Chen L, Chang LC (2005) Optimizing the reservoir operating rule curves by genetic algorithms. Hydrol Process 19(11):2277–2289
Cheng C-T, Shen J-J, Wu X-Y, Chau K-w (2012) Operation challenges for fast-growing China’s hydropower systems and respondence to energy saving and emission reduction. Renew Sust Energ Rev 16(5):2386–2393
Chow TW, Huang D (2005) Estimating optimal feature subsets using efficient estimation of high-dimensional mutual information. IEEE Trans Neural Netw 16(1):213–224
Darken C, Moody J (1990) Fast adaptive k-means clustering: some empirical results. In: 1990 IJCNN international joint conference on neural networks, pp 233–238
Dorigo M, Di Caro G (1999) Ant colony optimization: a new meta-heuristic. In: Proceedings of the 1999 congress on evolutionary computation, CEC 99, pp 1470–1477
Draper AJ, Lund JR (2004) Optimal hedging and carryover storage value. J Water Resour Plan Manag 130(1):83–87
El-Shafie A, Abdin AE, Noureldin A, Taha MR (2009) Enhancing inflow forecasting model at Aswan high dam utilizing radial basis neural network and upstream monitoring stations measurements. Water Resour Manag 23(11):2289–2315
Galelli S, Castelletti A (2013) Tree-based iterative input variable selection for hydrological modeling. Water Resour Res 49(7):4295–4310
Giuliani M, Mason E, Castelletti A, Pianosi F, Soncini-Sessa R (2014) Universal approximators for direct policy search in multi-purpose water reservoir management: a comparative analysis. IFAC Proc Vol 47(3):6234–6239
Giuliani M, Pianosi F, Castelletti A (2015) Making the most of data: an information selection and assessment framework to improve water systems operations. Water Resour Res 51(11):9073–9093
Giuliani M, Quinn JD, Herman JD, Castelletti A, Reed PM (2017) Scalable multiobjective control for large-scale water resources systems under uncertainty. IEEE Trans Control Syst Technol
Gleick PH, Palaniappan M (2010) Peak water limits to freshwater withdrawal and use. Proc Natl Acad Sci 107(25):11155–11162
Govindaraju RS, Rao AR (2013) Artificial neural networks in hydrology. Springer
Goyal MK, Ojha C, Singh R, Swamee P, Nema R (2013) Application of ANN, fuzzy logic and decision tree algorithms for the development of reservoir operating rules. Water Resour Manag 27(3):911–925
Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182
Ham FM, Kostanic I (2000) Principles of neurocomputing for science and engineering. McGraw-Hill Higher Education
Heidari M, Chow VT, Kokotović PV, Meredith DD (1971) Discrete differential dynamic programing approach to water resources systems optimization. Water Resour Res 7(2):273–282
Houck CR, Joines J, Kay MG (1995) A genetic algorithm for function optimization: a Matlab implementation. NCSU-IE TR 95(09)
Ji C, Li C, Wang B, Liu M, Wang L (2017) Multi-stage dynamic programming method for short-term cascade reservoirs optimal operation with flow attenuation. Water Resour Manag 31(14):4571–4586
Karami H, Mousavi SF, Farzin S, Ehteram M, Singh VP, Kisi O (2018) Improved krill algorithm for reservoir operation. Water Resour Manag 32(10):3353–3372
Karamouz M, Houck MH, Delleur JW (1992) Optimization and simulation of multiple reservoir systems. J Water Resour Plan Manag 118(1):71–81
Lund JR, Guzman J (1999) Derived operating rules for reservoirs in series or in parallel. J Water Resour Plan Manag 125(3):143–153
Maier HR, Jain A, Dandy GC, Sudheer KP (2010) Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ Model Softw 25(8):891–909
Malekmohammadi B, Kerachian R, Zahraie B (2009) Developing monthly operating rules for a cascade system of reservoirs: application of Bayesian networks. Environ Model Softw 24(12):1420–1432
Mashor MY (2000) Hybrid training algorithm for RBF network. Int J Comput Internet Manag 8(2):50–65
Nagelkerke NJ (1991) A note on a general definition of the coefficient of determination. Biometrika 78(3):691–692
Oliveira R, Loucks DP (1997) Operating rules for multireservoir systems. Water Resour Res 33(4):839–852
Ostadrahimi L, Mariño MA, Afshar A (2012) Multi-reservoir operation rules: multi-swarm PSO-based optimization approach. Water Resour Manag 26(2):407–427
Peng H, Long F, Ding C (2005) Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Pattern Anal Mach Intell 27(8):1226–1238
Rani D, Moreira MM (2010) Simulation–optimization modeling: a survey and potential application in reservoir systems operation. Water Resour Manag 24(6):1107–1138
Revelle C, Joeres E, Kirby W (1969) The linear decision rule in reservoir management and design: 1, development of the stochastic model. Water Resour Res 5(4):767–777
Samadi-koucheksaraee A, Ahmadianfar I, Bozorg-Haddad O, Asghari-pari SA (2019) Gradient evolution optimization algorithm to optimize reservoir operation systems. Water Resour Manag 33(2):603–625
Sudheer K, Srinivasan K, Neelakantan T, Srinivas V (2008) A nonlinear data-driven model for synthetic generation of annual streamflows. Hydrol Process 22(12):1831–1845
Tolson BA, Shoemaker CA (2007) Dynamically dimensioned search algorithm for computationally efficient watershed model calibration. Water Resour Res 43(1)
Trelea IC (2003) The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf Process Lett 85(6):317–325
Wang Y-m, Chang J-x, Huang Q (2010) Simulation with RBF neural network model for reservoir operation rules. Water Resour Manag 24(11):2597–2610
Yang G, Guo S, Li L, Hong X, Wang L (2016) Multi-objective operating rules for Danjiangkou reservoir under climate change. Water Resour Manag 30(3):1183–1202
Yang G, Guo S, Liu P, Li L, Liu Z (2017a) Multiobjective cascade reservoir operation rules and uncertainty analysis based on PA-DDS algorithm. J Water Resour Plan Manag:04017025
Yang G, Guo S, Liu P, Li L, Xu C (2017b) Multiobjective reservoir operating rules based on cascade reservoir input variable selection method. Water Resour Res 53(4):3446–3463
This study was financially supported by the National Natural Science Foundation of China (grants 51539009 and 51422907) and the National Key Research and Development Plan of China (grant 2016YFC0402206). The authors thank the editor and the anonymous reviewers for their valuable comments.
Conflict of Interest
The authors declared that they have no conflicts of interest to this work.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
About this article
Cite this article
Yang, G., Guo, S., Liu, P. et al. Heuristic Input Variable Selection in Multi-Objective Reservoir Operation. Water Resour Manage (2020). https://doi.org/10.1007/s11269-019-02456-9
- Cascade reservoirs
- Reservoir operating rules
- Input variables selection
- Radial basis function network
- Heuristic optimization