Using exploratory landscape analysis to visualize single-objective problems

Abstract

Selecting the relevant algorithm for a given problem is a crucial first step for achieving good optimization algorithm performance. Exploratory Landscape Analysis can help with this problem by calculating landscape features that numerically describe individual problems. To understand the problem space in single-objective numerical optimization, we recently presented a preliminary study of how Exploratory Landscape Analysis can be used to visualize different optimization benchmark problems, with the ultimate goal of visualizing problems that are similar to one another close together. In this paper, we examine how the selection of landscape features affects such a visualization, and show that proper preprocessing of landscape features is crucial for producing a good visualization. In particular, we show that only a subset of landscape features is invariant to simple transforms such as translation and scaling. Further, we examine how such an approach can be used to visually compare problems from different optimization benchmark sets.