Application of differential evolutionary optimization methodology for parameter structure identification in groundwater modeling

Parameter structure identification is formulated in terms of solving an inverse problem, which allows for a determination of an appropriate level of parameter structure complexity, and the identification of its pattern and the associated parameter values. With the increasing complexity of parameter structure identification in groundwater modeling, demand for robust, fast, and accurate optimizers is on the rise among researchers from groundwater hydrology fields. A novel global optimizer, differential evolution (DE), has been proposed to solve the parameter-structure-identification problem. The Voronoi tessellation is adopted for the automatic parameterization. The stepwise regression method and the error covariance matrix are used to determine the optimal structure complexity. Numerical experiments with a continuous hydraulic conductivity distribution are conducted to demonstrate the proposed methodology. The results indicate that the DE can identify the global optimum effectively and efficiently. A sensitivity analysis of the control parameters and mutation schemes implemented in the DE is employed to examine their influence on the objective function. The comparison between DE and genetic algorithm shows the advantage of DE in terms of robustness and efficiency. The proposed methodology is also applied to a real groundwater system, Pingtung Plain in Taiwan, and the properties of aquifers are successfully identified.