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We analyse fitness landscapes of evolutionary feature selection to obtain information about feature importance in supervised machine learning. Local optima networks (LONs) are a compact representation of a landscape, and can potentially be adapted for use in explainable artificial intelligence (XAI). This work examines their applicability for discerning feature importance in supervised machine learning datasets. We visualise aspects of feature selection LONs for a breast cancer prediction dataset as case study, and this process reveals information about the composition of feature sets for the underlying ML models. The estimations of feature importance obtained from LONs are compared with the coefficients extracted from logistic regression models (interpretable AI), and also against feature importances obtained through an established XAI technique: SHAP (explainable AI). We find that the features present in the …