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Application of the Elitist-Mutated PSO and an Improved GSA to Estimate Parameters of Linear and Nonlinear Muskingum Flood Routing Models

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  • Ling Kang
  • Song Zhang

Abstract

Heuristic search algorithms, which are characterized by faster convergence rates and can obtain better solutions than the traditional mathematical methods, are extensively used in engineering optimizations. In this paper, a newly developed elitist-mutated particle swarm optimization (EMPSO) technique and an improved gravitational search algorithm (IGSA) are successively applied to parameter estimation problems of Muskingum flood routing models. First, the global optimization performance of the EMPSO and IGSA are validated by nine standard benchmark functions. Then, to further analyse the applicability of the EMPSO and IGSA for various forms of Muskingum models, three typical structures are considered: the basic two-parameter linear Muskingum model (LMM), a three-parameter nonlinear Muskingum model (NLMM) and a four-parameter nonlinear Muskingum model which incorporates the lateral flow (NLMM-L). The problems are formulated as optimization procedures to minimize the sum of the squared deviations (SSQ) or the sum of the absolute deviations (SAD) between the observed and the estimated outflows. Comparative results of the selected numerical cases (Case 1–3) show that the EMPSO and IGSA not only rapidly converge but also obtain the same best optimal parameter vector in every run. The EMPSO and IGSA exhibit superior robustness and provide two efficient alternative approaches that can be confidently employed to estimate the parameters of both linear and nonlinear Muskingum models in engineering applications.

Suggested Citation

  • Ling Kang & Song Zhang, 2016. "Application of the Elitist-Mutated PSO and an Improved GSA to Estimate Parameters of Linear and Nonlinear Muskingum Flood Routing Models," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-20, January.
  • Handle: RePEc:plo:pone00:0147338
    DOI: 10.1371/journal.pone.0147338
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    Cited by:

    1. Nazanin Farahani & Hojat Karami & Saeed Farzin & Mohammad Ehteram & Ozgur Kisi & Ahmad Shafie, 2019. "A New Method for Flood Routing Utilizing Four-Parameter Nonlinear Muskingum and Shark Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(14), pages 4879-4893, November.
    2. Wen-chuan Wang & Wei-can Tian & Dong-mei Xu & Kwok-wing Chau & Qiang Ma & Chang-jun Liu, 2023. "Muskingum Models’ Development and their Parameter Estimation: A State-of-the-art Review," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(8), pages 3129-3150, June.
    3. Ling Kang & Liwei Zhou & Song Zhang, 2017. "Parameter Estimation of Two Improved Nonlinear Muskingum Models Considering the Lateral Flow Using a Hybrid Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4449-4467, November.

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