A Comprehensive Analysis of the Invariance of Exploratory Landscape Analysis Features to Function Transformations

Exploratory Landscape Analysis is a powerful technique that allows us to gain an understanding of a problem landscape solely by sampling the problem space. It has been successfully used in a number of applications, for example for the task of automatic algorithm selection. However, recent work has shown that Exploratory Landscape Analysis contains some specific weaknesses that its users should be aware of. As the technique is sample based, it has been shown to be sensitive to the choice of sampling strategy. Additionally, many landscape features are not invariant to transformations of the underlying samples which should have no effect on algorithm performance, specifically shifting and scaling. The analysis of the effect of shifting and scaling has so far only been demonstrated on a single problem set and dimensionality. In this paper, we perform a comprehensive analysis of the invariance of Exploratory Landscape Analysis features to these two transformations, by considering different sampling strate-gies, sampling sizes, problem dimensionalities, and benchmark problem sets to determine their individual and combined effect. We show that these factors have very limited influence on the features' invariance when they are considered either individually or combined.