Global optimization techniques for the calibration of conceptual rainfall-runoff models

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Abstract
In this study we present the results of the comparison of three different algorithms: the Genetic Algorithm coupled with Sequential Quadratic Programming (GA-SQP), the Pattern Search also coupled with SQP (PS-SQP) and the Shuffled Complex Evolution (SCE-UA). The analyses were conducted using a conceptual rainfall-runoff model applied both to a single basin and to a complex basin. For both types of basin, a theoretical case without model and data errors was considered, in which the true values of the parameters are known a priori, and several real-world cases where model and data errors exist. With reference to the single basin, the SCE-UA algorithm was the most reliable while the other two algorithms gave solutions equivalent to those of the SCE-UA in the theoretical case, but in the real-world cases they showed an increasing tendency (particularly the PS-SQP) to be trapped in local minima. With reference to the complex basin, none of the three algorithms identified the exact solution in the theoretical case. However, the SCEUA was the one which systematically approximated it better than the others. In the real-world case its solutions were stable but characterized by many parameter values set at the boundary of their own range. The other two algorithms produced a very unstable set of parameters.