Assessing the weighted multi-objective adaptive surrogate model optimization to derive large-scale reservoir operating rules with sensitivity analysis

Abstract The optimization of large-scale reservoir system is time-consuming due to its intrinsic characteristics of non-commensurable objectives and high dimensionality. One way to solve the problem is to employ an efficient multi-objective optimization algorithm in the derivation of large-scale reservoir operating rules. In this study, the Weighted Multi-Objective Adaptive Surrogate Model Optimization (WMO-ASMO) algorithm is used. It consists of three steps: (1) simplifying the large-scale reservoir operating rules by the aggregation-decomposition model, (2) identifying the most sensitive parameters through multivariate adaptive regression splines (MARS) for dimensional reduction, and (3) reducing computational cost and speeding the searching process by WMO-ASMO, embedded with weighted non-dominated sorting genetic algorithm II (WNSGAII). The intercomparison of non-dominated sorting genetic algorithm (NSGAII), WNSGAII and WMO-ASMO are conducted in the large-scale reservoir system of Xijiang river basin in China. Results indicate that: (1) WNSGAII surpasses NSGAII in the median of annual power generation, increased by 1.03% (from 523.29 to 528.67 billion kW h), and the median of ecological index, optimized by 3.87% (from 1.879 to 1.809) with 500 simulations, because of the weighted crowding distance and (2) WMO-ASMO outperforms NSGAII and WNSGAII in terms of better solutions (annual power generation (530.032 billion kW h) and ecological index (1.675)) with 1000 simulations and computational time reduced by 25% (from 10 h to 8 h) with 500 simulations. Therefore, the proposed method is proved to be more efficient and could provide better Pareto frontier.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  Chao Deng,et al.  Identifying Explicit Formulation of Operating Rules for Multi-Reservoir Systems Using Genetic Programming , 2014, Water Resources Management.

[3]  S. Sorooshian,et al.  Shuffled complex evolution approach for effective and efficient global minimization , 1993 .

[4]  Alcigeimes B. Celeste,et al.  Evaluation of stochastic reservoir operation optimization models , 2009 .

[5]  Virginia M. Johnson,et al.  Accuracy of Neural Network Approximators in Simulation-Optimization , 2000 .

[6]  Ignacio E. Grossmann,et al.  An Iterative Aggregation/Disaggregation Approach for the Solution of a Mixed-Integer Nonlinear Oilfield Infrastructure Planning Model , 2000 .

[7]  Pan Liu,et al.  Derivation of Aggregation-Based Joint Operating Rule Curves for Cascade Hydropower Reservoirs , 2011 .

[8]  Chen Wang,et al.  Multiobjective adaptive surrogate modeling‐based optimization for parameter estimation of large, complex geophysical models , 2016 .

[9]  P. R. H. Sales,et al.  Coordinating the Energy Generation of the Brazilian National Hydrothermal Electrical Generating System , 1986 .

[10]  A. Turgeon,et al.  Fuzzy Learning Decomposition for the Scheduling of Hydroelectric Power Systems , 1996 .

[11]  R. P. Oliveira,et al.  Operating rules for multireservoir systems , 1997 .

[12]  V. Singh,et al.  Global Experiences on Wastewater Irrigation: Challenges and Prospects , 2016 .

[13]  Wei Chu,et al.  A comprehensive evaluation of various sensitivity analysis methods: A case study with a hydrological model , 2014, Environ. Model. Softw..

[14]  Pan Liu,et al.  A Bayesian model averaging method for the derivation of reservoir operating rules , 2015 .

[15]  M. Valipour.  Comparison of Surface Irrigation Simulation Models: Full Hydrodynamic, Zero Inertia, Kinematic Wave , 2012 .

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Christos Makropoulos,et al.  Multiobjective optimisation on a budget: Exploring surrogate modelling for robust multi-reservoir rules generation under hydrological uncertainty , 2015, Environ. Model. Softw..

[18]  Wei Gong,et al.  An Intercomparison of Sampling Methods for Uncertainty Quantification of Environmental Dynamic Models , 2015 .

[19]  A. Turgeon.  Optimal operation of multireservoir power systems with stochastic inflows , 1980 .

[20]  Yuanyuan Liu,et al.  Optimal Operation of Multi-reservoir Systems Considering Time-lags of Flood Routing , 2015, Water Resources Management.

[21]  S. Sorooshian,et al.  Effective and efficient algorithm for multiobjective optimization of hydrologic models , 2003 .

[22]  R. Srinivasan,et al.  A global sensitivity analysis tool for the parameters of multi-variable catchment models , 2006 .

[23]  William W.-G. Yeh,et al.  Reservoir Management and Operations Models: A State‐of‐the‐Art Review , 1985 .

[24]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[25]  Stefan Banzhaf,et al.  Groundwater and Surface Water Interaction at the Regional-scale – A Review with Focus on Regional Integrated Models , 2015, Water Resources Management.

[26]  Pan Liu,et al.  Evaluation of Estimation of Distribution Algorithm to Calibrate Computationally Intensive Hydrologic Model , 2016 .

[27]  Wei Gong,et al.  Multi-objective parameter optimization of common land model using adaptive surrogate modeling , 2014 .

[28]  A. Owen.  Controlling correlations in latin hypercube samples , 1994 .

[29]  Wei Gong,et al.  Assessing parameter importance of the Common Land Model based on qualitative and quantitative sensitivity analysis , 2013 .

[30]  Bryan A. Tolson,et al.  Review of surrogate modeling in water resources , 2012 .

[31]  Abhay Anand,et al.  Coordinating multiple model predictive controllers for the management of large-scale water systems , 2013 .

[32]  Soroosh Sorooshian,et al.  Optimal use of the SCE-UA global optimization method for calibrating watershed models , 1994 .

[33]  M. Valipour,et al.  Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir , 2013 .

[34]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

[35]  Wang Li,et al.  Evolution of Water Lifting Devices (Pumps) over the Centuries Worldwide , 2015 .

[36]  Pan Liu,et al.  Deriving multiple near‐optimal solutions to deterministic reservoir operation problems , 2011 .

[37]  M. Valipour.  Optimization of neural networks for precipitation analysis in a humid region to detect drought and wet year alarms , 2016 .

[38]  Pan Liu,et al.  Derivation of water and power operating rules for multi-reservoirs , 2016 .

[39]  Piet Demeester,et al.  A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design , 2010, J. Mach. Learn. Res..

[40]  D. E. Rheinheimer,et al.  Parameter uncertainty analysis of reservoir operating rules based on implicit stochastic optimization. , 2014 .

[41]  Liping Li,et al.  Multi-Objective Operating Rules for Danjiangkou Reservoir Under Climate Change , 2016, Water Resources Management.

[42]  Quentin W. Martin.  Optimal Operation of Multiple Reservoir Systems , 1983 .

[43]  J. Lund,et al.  Derived Operating Rules for Reservoirs in Series or in Parallel , 1999 .

[44]  Guangtao Fu,et al.  Improving multi-objective reservoir operation optimization with sensitivity-informed dimension reduction , 2015 .

[45]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice , 2002 .

[46]  Chong-Yu Xu,et al.  Derivation of operation rules for reservoirs in parallel with joint water demand , 2015 .

[47]  K Ang,et al.  A NOTE ON UNIFORM DISTRIBUTION AND EXPERIMENTAL DESIGN , 1981 .

[48]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[49]  Juan B. Valdés,et al.  Aggregation‐Disaggregation Approach to multireservoir operation , 1992 .

[50]  Kourosh Behzadian,et al.  Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks , 2009, Environ. Model. Softw..

[51]  Wolfgang Ponweiser,et al.  Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted -Metric Selection , 2008, PPSN.

[52]  Arthur van Dam,et al.  Flood inference simulation using surrogate modelling for the Yellow River multiple reservoir system , 2014, Environ. Model. Softw..

[53]  Miguel A. Mariño,et al.  Optimal Operation of a Multiple Reservoir System , 1983 .

[54]  A. Turgeon,et al.  Learning disaggregation technique for the operation of long‐term hydroelectric power systems , 1994 .

[55]  Mario Paruggia,et al.  Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , 2006 .

[56]  Christopher K. I. Williams,et al.  Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) , 2005 .