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Mathematical Problems in Engineering
Volume 2016, Article ID 8215308, 13 pages
Research Article

Multiobjective Optimal Algorithm for Automatic Calibration of Daily Streamflow Forecasting Model

1School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2Hubei Key Laboratory of Digital Valley Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
3State Key Laboratory of Disaster Prevention and Reduction for Power Grid Transmission and Distribution Equipment, Changsha 410129, China
4State Grid Hunan Electric Company Disaster Prevention and Reduction Center, Changsha 410129, China
5School of Engineering and Technology, Hubei University of Technology, Wuhan 430068, China

Received 15 March 2016; Accepted 28 July 2016

Academic Editor: Marco Mussetta

Copyright © 2016 Yi Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Single-objection function cannot describe the characteristics of the complicated hydrologic system. Consequently, it stands to reason that multiobjective functions are needed for calibration of hydrologic model. The multiobjective algorithms based on the theory of nondominate are employed to solve this multiobjective optimal problem. In this paper, a novel multiobjective optimization method based on differential evolution with adaptive Cauchy mutation and Chaos searching (MODE-CMCS) is proposed to optimize the daily streamflow forecasting model. Besides, to enhance the diversity performance of Pareto solutions, a more precise crowd distance assigner is presented in this paper. Furthermore, the traditional generalized spread metric (SP) is sensitive with the size of Pareto set. A novel diversity performance metric, which is independent of Pareto set size, is put forward in this research. The efficacy of the new algorithm MODE-CMCS is compared with the nondominated sorting genetic algorithm II (NSGA-II) on a daily streamflow forecasting model based on support vector machine (SVM). The results verify that the performance of MODE-CMCS is superior to the NSGA-II for automatic calibration of hydrologic model.