Effects of function translation and dimensionality reduction on landscape analysis

Exploratory Landscape Analysis (ELA) measures have been shown to predict algorithm performance; hence, they are being applied on critical tasks such as automatic algorithm selection and problem generation. This paper provides a cautionary examination on their use in black-box continuous optimization. We explore the effect that translations have on the measures, when the cost function is defined within a bound-constrained region. Furthermore, we examine the robustness of the neighborhood structure after dimensionality reduction. The results demonstrate that a measure may transition abruptly due a translation. Therefore, we should not generalize the measures of an instance nor report average values of a measure as belonging to the generating function. Moreover, dimensionality reduction could alter the neighborhood structure, such that the regions corresponding to significantly different functions overlap.