  In this study, we analyze behaviours of the well-known CMA-ES by extracting
the time-series features on its dynamic strategy parameters. An extensive
experiment was conducted on twelve CMA-ES variants and 24 test problems taken
from the BBOB (Black-Box Optimization Bench-marking) testbed, where we used two
different cutoff times to stop those variants. We utilized the tsfresh package
for extracting the features and performed the feature selection procedure using
the Boruta algorithm, resulting in 32 features to distinguish either CMA-ES
variants or the problems. After measuring the number of predefined targets
reached by those variants, we contrive to predict those measured values on each
test problem using the feature. From our analysis, we saw that the features can
classify the CMA-ES variants, or the function groups decently, and show a
potential for predicting the performance of those variants. We conducted a
hierarchical clustering analysis on the test problems and noticed a drastic
change in the clustering outcome when comparing the longer cutoff time to the
shorter one, indicating a huge change in search behaviour of the algorithm. In
general, we found that with longer time series, the predictive power of the
time series features increase.
