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Comparing Single-Objective Optimization Protocols for Calibrating the Birds Nest Aquifer Model—A Problem Having Multiple Local Optima

Author

Listed:
  • Richard T. Lyons

    (Department of Civil and Environmental Engineering, Utah State University, Logan, UT 84322-4110, USA)

  • Richard C. Peralta

    (Department of Civil and Environmental Engineering, Utah State University, Logan, UT 84322-4110, USA)

  • Partha Majumder

    (College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 211100, Jiangsu, China)

Abstract

To best represent reality, simulation models of environmental and health-related systems might be very nonlinear. Model calibration ideally identifies globally optimal sets of parameters to use for subsequent prediction. For a nonlinear system having multiple local optima, calibration can be tedious. For such a system, we contrast calibration results from PEST, a commonly used automated parameter estimation program versus several meta-heuristic global optimizers available as external packages for the Python computer language—the Gray Wolf Optimization (GWO) algorithm; the DYCORS optimizer framework with a Radial Basis Function surrogate simulator (DRB); and particle swarm optimization (PSO). We ran each optimizer 15 times, with nearly 10,000 MODFLOW simulations per run for the global optimizers, to calibrate a steady-state, groundwater flow simulation model of the complex Birds Nest aquifer, a three-layer system having 8 horizontal hydraulic conductivity zones and 25 head observation locations. In calibrating the eight hydraulic conductivity values, GWO averaged the best root mean squared error (RMSE) between observed and simulated heads—20 percent better (lower) than the next lowest optimizer, DRB. The best PEST run matched the best GWO RMSE, but both the average PEST RMSE and the range of PEST RMSE results were an order of magnitude larger than any of the global optimizers.

Suggested Citation

  • Richard T. Lyons & Richard C. Peralta & Partha Majumder, 2020. "Comparing Single-Objective Optimization Protocols for Calibrating the Birds Nest Aquifer Model—A Problem Having Multiple Local Optima," IJERPH, MDPI, vol. 17(3), pages 1-10, January.
    • Handle: RePEc:gam:jijerp:v:17:y:2020:i:3:p:853-:d:314330
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    References listed on IDEAS

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    1. Regis, Rommel G. & Shoemaker, Christine A., 2007. "Parallel radial basis function methods for the global optimization of expensive functions," European Journal of Operational Research, Elsevier, vol. 182(2), pages 514-535, October.
    2. Partha Majumder & T.I. Eldho, 2020. "Artificial Neural Network and Grey Wolf Optimizer Based Surrogate Simulation-Optimization Model for Groundwater Remediation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(2), pages 763-783, January.
    3. Rommel G. Regis & Christine A. Shoemaker, 2007. "A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 497-509, November.
    4. O. Haddad & M. Tabari & E. Fallah-Mehdipour & M. Mariño, 2013. "Groundwater Model Calibration by Meta-Heuristic Algorithms," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2515-2529, May.
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