Simple, efficient and robust techniques for automatic multi-objective function parameterisation: Case studies of local and global optimisation using APSIM

Several techniques for automatic parameterisation are explored using the software PEST. We parameterised the biophysical systems model APSIM with measurements from a maize cropping experiment with the objective of finding algorithms that resulted in the least distance between modelled and measured data (φ) in the shortest possible time. APSIM parameters were optimised using a weighted least-squares approach that minimised the value of φ. Optimisation techniques included the Gauss-Marquardt-Levenberg (GML) algorithm, singular value decomposition (SVD), least squares with QR decomposition (LSQR), Tikhonov regularisation, and covariance matrix adaptation-evolution strategy (CMAES). In general, CMAES with log transformed APSIM parameters and larger population size resulted in the lowest φ, but this approach required significantly longer to converge compared with other optimisation algorithms. Regularisation treatments with log transformed parameters also resulted in low φ values when combined with SVD or LSQR; LSQR treatments with no regularisation tended to converge earliest. In addition to an analysis of several PEST algorithms, this study provides a narrative on how methodologies presented here could be generalised and applied to other models.