The Effect of Sampling Methods on the Invariance to Function Transformations When Using Exploratory Landscape Analysis

Exploratory Landscape Analysis is a methodology for transforming the samples of an optimization problem into numerical descriptors called landscape features. Since Exploratory Landscape Analysis is sample based, recent studies have shown that the choice of the method used to collect the problem samples can have an effect on the calculation of landscape features.In our recent work, we have shown that certain landscape features are not invariant to even simple function transformations such as shifting or scaling. However, the analysis in our previous work was conducted using only Latin Hypercube Sampling. Since we are now aware that the choice of sampling method can affect the calculation of landscape features, this paper expands upon our earlier work by using a variety of different sampling methods. We show that different sampling methods do indeed have an effect on the invariance of landscape features, and present a list of landscape features that are invariant under all of our chosen sampling methods.