Optimization algorithms
Due to the many parameters of advanced constitutive models, their calibration is a major challenge. To address this, we have implemented interfaces to a variety of optimization algorithms from different libraries:
Choosing which algorithm is the most appropriate is not easy to predict. A simple - but costly - method is “try and compare” - which we have done below. For all the above algorithms, the parameters of the hypoplastic constitutive model for the BMU sand were calibrated. The calibration was repeated 5 times. The final values of the cost function as well as the required computation times are shown below, where the dot corresponds to the mean value and the bars correspond to the bandwidth (from minimum to maximum) of all simualtions with this algorithm.
The comparison of computation times between DE from MEALPY and DE from SciPy is not quite fair, because SciPy uses a different termination criterion. While MEALPY requires that the cost function does not change within 50 iterations, SciPy requires that the change of the cost function falls below a certain tolerance ($TOL=0.01$). If the development of the cost function for the DE in MEALPY (here) is examined more closely, it becomes apparent that this criterion would already have been met earlier.