PEST - Model-Independent Parameter Estimation and Uncertainty Analysis

Global Optimisers


CMAES_P is a PEST compatible implementation of the powerful and robust CMA-ES global optimisation scheme. For details of this scheme see, for example, Hansen and Ostermeier (2001) and Hansen et al (2003). See also Nikolaus Hansen's web pages for further details, including a tutorial as well as MATLAB and OCTAVE source code.

CMAES_P is fully compatible with PEST. It can read a PEST input dataset. It can undertake model runs in parallel across nodes within a cluster, or across PCs in an office network.


Hansen, N. and Ostermeier, A., 2001. Completely derandomized self-adaptation in evolution strategies. Evol. Comput., 9, 159-195.

Hansen, N., Muller, S.D. and Koumoutsakos, P., 2003. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput, 9, 159-195.


SCEUA_P implements the SCE (“shuffled complex evolution”) algorithm described by Duan (1991) and Duan et al (1992; 1993; 1994); UA stands for “University of Arizona”. Like the CMA-ES method, the SCE method does not require computation of derivatives of model outputs with respect to adjustable parameters. Hence it can operate successfully even where the relationship between model parameters and model outputs is discontinuous, or is contaminated by model-generated numerical noise. It can also perform well where the objective function features local optima on either a large or small scale (or both) in parameter space.

Like CMAES_P, SCEUA_P can be used interchangeably with PEST. It also has parallelisation functionality, this existing at the level of “complexes”. Thus complexes can evolve on different nodes or computers, with PEST assimilating the results of those different evolutionary processes.


Duan, Q., 1991. A global optimization strategy for efficient and effective calibration of hydrologic models. PhD thesis, Department of Hydrology and Water Resources, University of Arizona, Tuscon, 1991.

Duan, Q., Soorooshian, S. and Gupta, V., 1992. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resourc. Res. 28 (4), 1015-1031.

Duan, Q., Gupta, V.K. and Sorooshian, S., 1993. A Shuffled Complex Evolution approach for effective and efficient global minimization. Journal of Optimization Theory and its Applications, 76 (3), 501-521.

Duan, Q., Sorooshian, S. and Gupta, V.K., 1994. Optimal use of the SCE-UA global optimization method for calibrating watershed models. Journal of Hydrology, 158 265-284.

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