Incorporating Filters in Random Search Algorithms for the Hourly Operation of a Multireservoir System
Publication: Journal of Water Resources Planning and Management
Volume 144, Issue 2
Abstract
Optimization of short-term reservoir operation normally involves ramping constraints of outflows and water elevations at short time steps (e.g., hourly). Random search algorithms, such as genetic algorithms, have been widely used in optimization of reservoir operation. When applying random search algorithms to hourly reservoir operation, two important issues arise. The first one is the frequent violation of ramping constraints on the hourly reservoir outflows because of the random nature of the optimization algorithm. In other words, the optimization struggles to meet the ramping constraints when finding feasible solutions. The second issue is the zigzag fluctuation of the hourly decision variables as a result of the random search, which is unrealistic to implement in practice. In this study, the Savitzky-Golay smoothing filter (also known as least-squares filter) is incorporated periodically within the routine of the Nondominated Sorting Genetic Algorithm (NSGA-II). The goal of this study is to smooth out the decision variable functions without deteriorating the performance of the optimization algorithm. The performance of the proposed approach is quantified through three indexes using a multireservoir system with 3,360 decision variables as the test case. The results show that use of the Savitzky-Golay filter not only provides a solution to the two aforementioned issues, but also significantly improves the performance of the NSGA-II for hourly reservoir operation. The optimal decisions obtained using the proposed approach display similar hourly variability to decisions of actual reservoir operation.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank the editor and two anonymous referees for their insightful and constructive comments. This work was supported by the Bonneville Power Administration Projects TIP258 and TIP342. The authors would also thank the support from the National Natural Science Foundation of China (51479188, 51425902, and 91647114) and of Hubei Province (2017CFB613).
References
Afshar, A., Haddad, O. B., Mariño, M. A., and Adams, B. J. (2007). “Honey-bee mating optimization (HBMO) algorithm for optimal reservoir operation.” J. Franklin Inst., 344(5), 452–462.
Akaike, H. (1973). “Maximum likelihood identification of Gaussian autoregressive moving average models.” Biometrika, 60(2), 255–265.
Atiquzzaman, M., Liong, S. Y., and Yu, X. (2006). “Alternative decision making in water distribution network with NSGA-II.” J. Water Resour. Plann. Manage., 122–126.
Berndt, D. J., and Clifford, J. (1994). “Using dynamic time warping to find patterns in time series.” KDD Workshop, 10(16), 359–370.
Blasco, X., Herrero, J. M., Sanchis, J., and Martínez, M. (2008). “A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization.” Inform. Sci., 178(20), 3908–3924.
Catalão, J. P. S., Pousinho, H. M. I., and Mendes, V. M. F. (2010). “Scheduling of head-dependent cascaded reservoirs considering discharge ramping constraints and start/stop of units.” Int. J. Electr. Power Energy Syst., 32(8), 904–910.
Celeste, A. B., and Billib, M. (2010). “The role of spill and evaporation in reservoir optimization models.” Water Resour. Manage., 24(4), 617–628.
Chen, D., Leon, A. S., Gibson, N. L., and Hosseini, P. (2016). “Dimension reduction of decision variables for multireservoir operation: A spectral optimization model.” Water Resour. Res., 52(1), 36–51.
Chen, D., Leon, A. S., and Hosseini, P. (2014). “Optimizing short-term operation of a multireservoir system during transition of objectives and constraints.” World Environmental and Water Resources Congress, Environmental and Water Resources Institute, ASCE, Reston, VA, 1093–1105.
Chen, D., Leon, A. S., Hosseini, P., Gibson, N. L., and Fuentes, C. (2017). “Application of cluster analysis for finding operational patterns of multireservoir system during transition period.” J. Water Resour. Plann. Manage., 04017028.
Chen, D., Li, R., Chen, Q., and Cai, D. (2015). “Deriving optimal daily reservoir operation scheme with consideration of downstream ecological hydrograph through a time-nested approach.” Water Resour. Manage., 29(9), 3371–3386.
Chen, Q., Chen, D., Li, R., Ma, J., and Blanckaert, K. (2013). “Adapting the operation of two cascaded reservoirs for ecological flow requirement of a de-watered river channel due to diversion-type hydropower stations.” Ecol. Modell., 252, 266–272.
Chou, F. N. F., and Wu, C. W. (2015). “Stage-wise optimizing operating rules for flood control in a multi-purpose reservoir.” J. Hydrol., 521, 245–260.
Deane, J. P., Drayton, G., and Gallachóir, B. Ó. (2014). “The impact of sub-hourly modelling in power systems with significant levels of renewable generation.” Appl. Energy, 113, 152–158.
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002). “A fast and elitist multi-objective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput., 6(2), 182–197.
DTW (Dynamic Time Warping) version 1.4 [Computer software]. MathWorks, Natick, MA.
Edwards, B. K. (2003). The economics of hydroelectric power, Edward Elgar, Northampton, MA.
Emmerich, M., and Deutz, A. (2006). Multicriteria optimization and decision making, LIACS, Leiden Univ., Leiden, Netherlands.
Finardi, E. C., and da Silva, E. L. (2006). “Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming.” IEEE Trans. Power Syst., 21(2), 835–844.
Fonseca, V. G., Fonseca, C. M., and Hall, A. O. (2001). “Inferential performance assessment of stochastic optimisers and the attainment function.” Int. Conf. on Evolutionary Multi-Criterion Optimization, Springer, Berlin, 213–225.
Fu, G., Kapelan, Z., and Reed, P. (2011). “Reducing the complexity of multiobjective water distribution system optimization through global sensitivity analysis.” J. Water Resour. Plann. Manage., 196–207.
Giron-Sierra, J. M. (2017). “Digital filters.” Digital signal processing with MATLAB examples, Vol. 1, Springer, Singapore, 239–310.
Guisández, I., Pérez-Díaz, J. I., and Wilhelmi, J. R. (2016). “Influence of the maximum flow ramping rates on the water value.” Energy Procedia, 87, 100–107.
Hidalgo, I. G., et al. (2014). “Hybrid model for short-term scheduling of hydropower systems.” J. Water Resour. Plann. Manage., 04014062.
Hrstka, O., and Kučerová, A. (2004). “Improvements of real coded genetic algorithms based on differential operators preventing premature convergence.” Adv. Eng. Software, 35(3), 237–246.
Knowles, J., and Corne, D. (2002). “On metrics for comparing nondominated sets.” Proc., 2002 Congress on Evolutionary Computation, Vol. 1, IEEE, Washington, DC, 711–716.
Kumar, D. N., and Reddy, M. J. (2006). “Ant colony optimization for multi-purpose reservoir operation.” Water Resour. Manage., 20(6), 879–898.
Labadie, J. W. (2004). “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plann. Manage., 93–111.
Lund, J. R., and Ferreira, I. (1996). “Operating rule optimization for Missouri River reservoir system.” J. Water Resour. Plann. Manage., 122(4), 287–295.
Malekmohammadi, B., Zahraie, B., and Kerachian, R. (2010). “A real-time operation optimization model for flood management in river-reservoir systems.” Natl. Hazards, 53(3), 459–482.
MATLAB [Computer software]. MathWorks, Natick, MA.
Müller, M. (2007). Dynamic time warping. Information retrieval for music and motion, Springer, Berlin, 69–84.
Nandalal, K. D. W., and Bogardi, J. J. (2007). Dynamic programming based operation of reservoirs: Applicability and limits, Cambridge University Press, New York.
Needham, J. T., Watkins, D. W., Jr., Lund, J. R., and Nanda, S. K. (2000). “Linear programming for flood control in the Iowa and Des Moines Rivers.” J. Water Resour. Plann. Manage., 126(3), 118–127.
Niu, S., and Insley, M. (2013). “On the economics of ramping rate restrictions at hydro power plants: Balancing profitability and environmental costs.” Energy Econ., 39, 39–52.
NOAA Fisheries. (2008). “Executive summary of the FCRPS 2008 biological opinion.” Silver Spring, MD.
NOAA Fisheries. (2008). “Supplemental comprehensive analysis of the federal Columbia river power system and mainstem effects of the upper snake and other tributary actions.” Silver Spring, MD.
Oliveira, R., and Loucks, D. P. (1997). “Operating rules for multireservoir systems.” Water Resour. Res., 33(4), 839–852.
Petitjean, F., Forestier, G., Webb, G. I., Nicholson, A. E., Chen, Y., and Keogh, E. (2014). “Dynamic time warping averaging of time series allows faster and more accurate classification.” 2014 IEEE Int. Conf. on Data Mining, IEEE, Washington, DC, 470–479.
Prasad, T. D., and Park, N. S. (2004). “Multiobjective genetic algorithms for design of water distribution networks.” J. Water Resour. Plann. Manage., 73–82.
Press, W. H. (2007). Numerical recipes: The art of scientific computing, 3rd Ed., Cambridge University Press, New York.
Reddy, M. J., and Kumar, D. N. (2006). “Optimal reservoir operation using multi-objective evolutionary algorithm.” Water Resour. Manage., 20(6), 861–878.
Reed, P. M., Hadka, D., Herman, J., Kasprzyk, J., and Kollat, J. (2013). “Evolutionary multiobjective optimization in water resources: The past, present, and future.” Adv. Water Resour., 51, 438–456.
Savitzky, A., and Golay, M. J. (1964). “Smoothing and differentiation of data by simplified least squares procedures.” Anal. Chem., 36(8), 1627–1639.
Schafer, R. W. (2011). “What is a Savitzky-Golay filter?” Signal Process Mag., 28(4), 111–117.
Schwanenberg, D., Xu, M., Ochterbeck, T., Allen, C., and Karimanzira, D. (2014). “Short-term management of hydropower assets of the Federal Columbia River power system.” J. Appl. Water Eng. Res., 2(1), 25–32.
Sindhya, K., Deb, K., and Miettinen, K. (2011). “Improving convergence of evolutionary multi-objective optimization with local search: A concurrent-hybrid algorithm.” Natl. Comput., 10(4), 1407–1430.
Veselka, T. D., Hamilton, S., and McCoy, J. (1995). “Optimizing hourly hydro operations at the Salt Lake City area integrated projects.”, Argonne National Laboratory, Argonne, IL.
Vivó-Truyols, G., and Schoenmakers, P. J. (2006). “Automatic selection of optimal Savitzky-Golay smoothing.” Anal. Chem., 78(13), 4598–4608.
Wang, J., and Liu, S. (2011). “Quarter-hourly operation of hydropower reservoirs with pumped storage plants.” J. Water Resour. Plann. Manage., 138(1), 13–23.
Wang, J., and Zhang, Y. (2011). “Short-term optimal operation of hydropower reservoirs with unit commitment and navigation.” J. Water Resour. Plann. Manage., 3–12.
Wardlaw, R., and Sharif, M. (1999). “Evaluation of genetic algorithms for optimal reservoir system operation.” J. Water Resour. Plann. Manage., 25–33.
Yandamuri, S. R., Srinivasan, K., and MurtyBhallamudi, S. (2006). “Multiobjective optimal waste load allocation models for rivers using Nondominated Sorting Genetic Algorithm-II.” J. Water Resour. Plann. Manage., 133–143.
Zabinsky, Z. B. (2009). “Random search algorithms.” Wiley encyclopedia of operations research and management science, Wiley, Hoboken, NJ.
Zabinsky, Z. B. (2015). “Stochastic adaptive search methods: Theory and implementation.” Handbook of simulation optimization, Springer, New York, 293–318.
Zitzler, E., Deb, K., and Thiele, L. (2000). “Comparison of multiobjective evolutionary algorithms: Empirical results.” Evol. Comput., 8(2), 173–195.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 144 • Issue 2 • February 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 9, 2017
Accepted: Jul 25, 2017
Published online: Dec 4, 2017
Published in print: Feb 1, 2018
Discussion open until: May 4, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.