Explorative Data Analysis of Time Series based AlgorithmFeatures of CMA-ES Variants

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

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