A Novel Multi-Objective Shuffled Complex Differential Evolution Algorithm with Application to Hydrological Model Parameter Optimization

Practice experience suggests that the traditional calibration of hydrological models with single objective cannot properly measure all of the behaviors of the hydrological system. To circumvent this problem, in recent years, a lot of studies have looked into calibration of hydrological models with multi-objective. In this paper, we propose a novel multi-objective evolution algorithm entitled multi-objective shuffled complex differential evolution (MOSCDE) algorithm, which is an extension of the famous single objective algorithm, shuffled complex evolution (SCE-UA) algorithm, to the multi-objective framework. This new proposed algorithm replaces the simplex search used in SCE-UA with the differential evolution (DE) algorithm and can more thoroughly utilize the information of the individuals in the evolutionary population and improve the search ability of the algorithm. Meanwhile, the Cauchy mutation (CM) operator is employed to prevent the algorithm from falling into the local optimal region of the feasible space. Moreover, two types of archive sets are employed to further improve the performance of the algorithm. The efficacy of the MOSCDE algorithm is first tested on five benchmark problems. After achieving satisfactory performance on the test problems, the MOSCDE is applied to multi-objective parameter optimization of a hydrological model for daily runoff forecasting. The results show that the MOSCDE algorithm can be a viable alternative for multi-objective parameter optimization of hydrological model.

[1]  Bin He,et al.  Regional groundwater prediction model using automatic parameter calibration SCE method for a coastal plain of Seto Inland Sea , 2007 .

[2]  Ville Tirronen,et al.  Recent advances in differential evolution: a survey and experimental analysis , 2010, Artificial Intelligence Review.

[3]  S. Simonovic,et al.  Integrated Reservoir Management System for Adaptation to Climate Change: The Nakdong River Basin in Korea , 2010 .

[4]  John W. Nicklow,et al.  Multi-objective automatic calibration of SWAT using NSGA-II , 2007 .

[5]  W. J. Shuttleworth,et al.  Parameter estimation of a land surface scheme using multicriteria methods , 1999 .

[6]  Mark Wineberg,et al.  Selecting Model Parameter Sets from a Trade-off Surface Generated from the Non-Dominated Sorting Genetic Algorithm-II , 2010 .

[7]  Gift Dumedah,et al.  Formulation of the Evolutionary-Based Data Assimilation, and its Implementation in Hydrological Forecasting , 2012, Water Resources Management.

[8]  A. Vasan,et al.  Application of Differential Evolution for Irrigation Planning: An Indian Case Study , 2007 .

[9]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

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

[11]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[12]  Lei De.  Crowding-Measure Based Multi-Objective Evolutionary Algorithm , 2005 .

[13]  Muzaffar Eusuff,et al.  Optimal Operation of Artificial Groundwater Recharge Systems Considering Water Quality Transformations , 2004 .

[14]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[15]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[16]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[17]  Xin Yao,et al.  Fast Evolutionary Programming , 1996, Evolutionary Programming.

[18]  Yanbin Yuan,et al.  An enhanced differential evolution algorithm for daily optimal hydro generation scheduling , 2008, Comput. Math. Appl..

[19]  N. J. DE VOS,et al.  Multi-objective performance comparison of an artificial neural network and a conceptual rainfall—runoff model , 2007 .

[20]  David E. Goldberg,et al.  Simplifying multiobjective optimization: An automated design methodology for the nondominated sorted genetic algorithm‐II , 2003 .

[21]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[22]  N. Madavan.  Multiobjective optimization using a Pareto differential evolution approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[23]  Henrik Madsen,et al.  Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling , 2008 .

[24]  Ligang Xu,et al.  Modeling of Surface Runoff in Xitiaoxi Catchment, China , 2007 .

[25]  Soroosh Sorooshian,et al.  Multi-objective global optimization for hydrologic models , 1998 .

[26]  Jasper A. Vrugt,et al.  Comparison of point forecast accuracy of model averaging methods in hydrologic applications , 2010 .

[27]  Ying Wang,et al.  Multi-objective differential evolution with adaptive Cauchy mutation for short-term multi-objective optimal hydro-thermal scheduling , 2010 .

[28]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[29]  Henrik Madsen,et al.  Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. , 2000 .

[30]  L. Coelho,et al.  Differential evolution optimization combined with chaotic sequences for image contrast enhancement , 2009 .

[31]  N. J. de Vos,et al.  Multiobjective training of artificial neural networks for rainfall‐runoff modeling , 2008 .

[32]  S. Sorooshian,et al.  A multistep automatic calibration scheme for river forecasting models , 2000 .

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

[34]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[35]  Enrique Alba,et al.  SMPSO: A new PSO-based metaheuristic for multi-objective optimization , 2009, 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making(MCDM).

[36]  Xin Yao,et al.  Fast Evolution Strategies , 1997, Evolutionary Programming.

[37]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[38]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

[39]  Adam P. Piotrowski,et al.  Product-Units neural networks for catchment runoff forecasting , 2012 .

[40]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[41]  Weiyi Qian,et al.  Adaptive differential evolution algorithm for multiobjective optimization problems , 2008, Appl. Math. Comput..

[42]  Carlos Rogério de Mello,et al.  Hydrological Prediction in a Tropical Watershed Dominated by Oxisols Using a Distributed Hydrological Model , 2012, Water Resources Management.

[43]  G. I. Rashed,et al.  Application of differential evolution algorithm for optimal location and parameters setting of UPFC considering power system security , 2009 .

[44]  K. Beven,et al.  Model Calibration and Uncertainty Estimation , 2006 .

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

[46]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[47]  S. Sorooshian,et al.  Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system , 2004, Journal of Hydrology.

[48]  S. Sorooshian,et al.  Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data , 1996 .

[49]  H. Madsen,et al.  Multiobjective calibration with Pareto preference ordering: An application to rainfall‐runoff model calibration , 2005 .

[50]  Martijn J. Booij,et al.  Catchment Variability and Parameter Estimation in Multi-Objective Regionalisation of a Rainfall–Runoff Model , 2010 .

[51]  Luis A. Bastidas,et al.  Multiobjective particle swarm optimization for parameter estimation in hydrology , 2006 .

[52]  D. Boyle.  Multicriteria Calibration of Hydrologic Models , 2013 .

[53]  Jun Xia,et al.  Integration of a statistical emulator approach with the SCE-UA method for parameter optimization of a hydrological model , 2012 .

[54]  Patrick M. Reed,et al.  How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration , 2005 .

[55]  Soroosh Sorooshian,et al.  A framework for development and application of hydrological models , 2001, Hydrology and Earth System Sciences.

[56]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods , 2000 .