Optimization Algorithms for Calibrating Cropping Systems Simulation Models - A Case Study with Simplex-derived Methods Integrated in the WARM Simulation Environment

Calibration is the process of adjusting parameters values to obtain a good fit between model outputs and observations. The objective is to later apply the model to conditions similar to those characterizing the data used for the calibration. Even if calibration is a standard in model application, it is a high risk procedure. The purpose of calibration is to determine the values of unknown variables or parameters on the basis of their effects; the underlying risk of calibration is to degrading a mechanistic model to a totally empirical model very similar to a regression model, but without the statistical support to the conclusion drawing from the latter type of model. A reliable calibration process includes four steps. Step 1 is to define a criterion to evaluate the performance of a model in terms of an objective function; step 2 is to select the variables (or parameters) that will be calibrated; step 3 is to select an appropriate algorithm for minimisation (or maximisation) of the objective function; step 4 is the test of calibration results against new data sets. This paper focuses on step 3, and in particular on discussing, testing, and comparing two optimization algorithms derived from the simplex method: a bounded version of the Downhill Simplex (BS) and a modified version of the Evolutionary Shuffled Simplex (ESS). The two algorithms, selected because they do not use derivatives (crop models are strongly not-linear), were tested using two standard benchmark functions for optimization methods: the Rosenbrock and the Rastrigin functions. Results show that, even if BS requires few model evaluations, in some cases it is not able to find a global minimum in a multidimensional complex hyperspace. In this case, a more performing algorithm (such as ESS) should be used. The two algorithms have been introduced in the WARM simulation environment, allowing WARM to run automatic calibrations using both methods. Some results are presented.