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Selecting Model Parameter Sets from a Trade-off Surface Generated from the Non-Dominated Sorting Genetic Algorithm-II

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  • Gift Dumedah
  • Aaron Berg
  • Mark Wineberg
  • Robert Collier

Abstract

There is increasing trend in the use of multi-objective genetic algorithms (GAs) to estimate parameter sets in the calibration of hydrological models. Multi-objective GAs facilitate the evaluation of several model evaluation objectives, and the examination of massive combinations of parameter sets. Typically, the outcome is a set of several equally-accurate parameter sets which make-up a trade-off surface between the objective functions, usually referred to as Pareto set. The Pareto set is a set of incomparable parameter sets as each solution has unique parameter values in parameter space with competing accuracy in the objective function space. As would be required for decision making purposes, a single parameter set is usually chosen to represent the model calibration procedure. An automated framework for choosing a single solution from such a trade-off surface has not been thoroughly investigated in the model calibration literature. As a result, this study has outlined an automated framework using the distribution of solutions in objective space and parameter space to select solutions with unique properties from an incomparable set of solutions. Our Pareto set was generated from the application of Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to calibrate the Soil and Water Assessment Tool (SWAT) for simulations of streamflow in the Fairchild Creek watershed in southern Ontario. Using cluster analysis to evaluate the distribution of solutions in both objective space and parameter space, we developed four auto-selection methods for choosing parameter sets from the trade-off surface to support decision making. Our method generates solutions with unique properties including a representative pathway in parameter space, a basin of attraction (or the center of mass) in objective space, a proximity to the origin in objective space, and a balanced compromise between objective space and parameter space (denoted BCOP). The BCOP method is appealing as it is an equally-weighted compromise for the distribution of solutions in objective space and parameter space. That is, the BCOP solution emphasizes stability in model parameter values and in objective function values—in a way that similarity in parameter space implies similarity in objective space. Copyright Springer Science+Business Media B.V. 2010

Suggested Citation

  • Gift Dumedah & Aaron Berg & Mark Wineberg & Robert Collier, 2010. "Selecting Model Parameter Sets from a Trade-off Surface Generated from the Non-Dominated Sorting Genetic Algorithm-II," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(15), pages 4469-4489, December.
  • Handle: RePEc:spr:waterr:v:24:y:2010:i:15:p:4469-4489
    DOI: 10.1007/s11269-010-9668-y
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    References listed on IDEAS

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    1. Robert Thorndike, 1953. "Who belongs in the family?," Psychometrika, Springer;The Psychometric Society, vol. 18(4), pages 267-276, December.
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    1. Qi Wang & Enrico Creaco & Marco Franchini & Dragan Savić & Zoran Kapelan, 2015. "Comparing Low and High-Level Hybrid Algorithms on the Two-Objective Optimal Design of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(1), pages 1-16, January.
    2. Zeinab Takbiri & Abbas Afshar, 2012. "Multi-Objective Optimization of Fusegates System under Hydrologic Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(8), pages 2323-2345, June.
    3. Ahmad Sharafati & Siyamak Doroudi & Shamsuddin Shahid & Ali Moridi, 2021. "A Novel Stochastic Approach for Optimization of Diversion System Dimension by Considering Hydrological and Hydraulic Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(11), pages 3649-3677, September.
    4. Tao Bai & Lianzhou Wu & Jian-xia Chang & Qiang Huang, 2015. "Multi-Objective Optimal Operation Model of Cascade Reservoirs and Its Application on Water and Sediment Regulation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(8), pages 2751-2770, June.
    5. Jun Guo & Jianzhong Zhou & Qiang Zou & Yi Liu & Lixiang Song, 2013. "A Novel Multi-Objective Shuffled Complex Differential Evolution Algorithm with Application to Hydrological Model Parameter Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(8), pages 2923-2946, June.
    6. Jose-Luis Molina & Raziyeh Farmani & John Bromley, 2011. "Aquifers Management through Evolutionary Bayesian Networks: The Altiplano Case Study (SE Spain)," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(14), pages 3883-3909, November.
    7. Prakash Kaini & Kim Artita & John Nicklow, 2012. "Optimizing Structural Best Management Practices Using SWAT and Genetic Algorithm to Improve Water Quality Goals," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(7), pages 1827-1845, May.
    8. Jianzhong Zhou & Shuo Ouyang & Xuemin Wang & Lei Ye & Hao Wang, 2014. "Multi-Objective Parameter Calibration and Multi-Attribute Decision-Making: An Application to Conceptual Hydrological Model Calibration," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(3), pages 767-783, February.
    9. Tian Peng & Jianzhong Zhou & Chu Zhang & Na Sun, 2018. "Modeling and Combined Application of Orthogonal Chaotic NSGA-II and Improved TOPSIS to Optimize a Conceptual Hydrological Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(11), pages 3781-3799, September.
    10. Minglong Dai & Jianzhong Zhou & Xiang Liao, 2016. "Research on Combination Forecast Mode of Conceptual Hydrological Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(13), pages 4483-4499, October.
    11. Akshay Kadu & Basudev Biswal, 2022. "A Model Combination Approach for Improving Streamflow Prediction," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(15), pages 5945-5959, December.
    12. Duan Chen & Qiuwen Chen & Arturo S. Leon & Ruonan Li, 2016. "A Genetic Algorithm Parallel Strategy for Optimizing the Operation of Reservoir with Multiple Eco-environmental Objectives," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(7), pages 2127-2142, May.
    13. Gift Dumedah, 2012. "Formulation of the Evolutionary-Based Data Assimilation, and its Implementation in Hydrological Forecasting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(13), pages 3853-3870, October.

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