Towards Exploratory Landscape Analysis for Large-scale Optimization: A Dimensionality Reduction Framework

Abstract: Although exploratory landscape analysis (ELA) has shown its effectiveness in various applications, most previous studies focused only on low- and moderate-dimensional problems. Thus, little is known about the scalability of the ELA approach for large-scale optimization. In this context, first, this paper analyzes the computational cost of features in the flacco package. Our results reveal that two important feature classes (ela_level and ela_meta) cannot be applied to large-scale optimization due to their high computational cost. To improve the scalability of the ELA approach, this paper proposes a dimensionality reduction framework that computes features in a reduced lower-dimensional space than the original solution space. We demonstrate that the proposed framework can drastically reduce the computation time of ela_level and ela_meta for large dimensions. In addition, the proposed framework can make the cell-mapping feature classes scalable for large-scale optimization. Our results also show that features computed by the proposed framework are beneficial for predicting the high-level properties of the 24 large-scale BBOB functions.