Fig. 1: Comparison of the performance of four different implementations of the CMA-ES.
From: Evolutionary computing and machine learning for discovering of low-energy defect configurations
For each of the four implementations 50 independent runs of the algorithm were performed. a The distribution of total energies of the 50 final solutions with respect to the global minimum. b The distribution of the number of fitness evaluations necessary before such converged solutions are reached. Labels: (a) Original CMA-ES. (b) Initialization of the covariance matrix as per equation (4), without using a hard cutoff. (c) Initialization of the covariance matrix as per equation (4), using a hard cutoff. (d) The final version of the algorithm, as proposed in this work including gradients in the update of the distribution mean. In each violin plot, the white dot represents the median of the distribution, the bold black bar the interquartile range and the thin black lines represents the range of data points comprising the interquartile range extended by a factor of 1.5.
