Study on Optimization of Hydrological Watershed Model using Multi-Objective Programming

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The multi-objective optimization is very useful for parameter estimation of multi-output-flux hydrological models and even in the case of single-output rainfall-runoff models, it is applicable and useful for parameter calibration using different objectives simultaneously. e.g. minimization of errors of peak flows, low flows and overall volume. In this study, parameter optimization of a conceptual rainfall-runoff model, the Sugawara Tank Model using the multi-objectives was investigated. The root mean square error (RMSE) and the root mean square of relative error (RR), which show obvious trade-off relationship, were adopted as objective functions and these objectives were minimized under the constraint of the permitted water balance error. The discrete Pareto optimal solutions were obtained by using the classical weighting method based on the SCE-UA method of the single-objective global optimization algorithm and then a new simple approach based on the random search was applied to estimate a large number of Pareto solutions efficiently and approximate the entire Pareto space. Moreover, the use of the Evolution Strategy (ES) which is one of the global search methods was discussed. The ES was applied to the single- and multi-objective optimization of the Tank Model. Results showed that the ES is more effective than the GA and the SCE-UA in the single-objective optimization and the Pareto solutions of multi-objective optimization can be obtained quite efficiently by using the ES. The relationship between the selection of objective functions used in calibration of rainfall-runoff models and the goodness of fit of simulated hydrograph was also investigated. Results showed that the RMSE emphasizes most the goodness of fit at high flows and the RR emphasizes estimated errors at low flows.