Sampling Strategies for Exploratory Landscape Analysis of Bi-Objective Problems

Exploratory landscape analysis (ELA) is a popular method for the understanding of complex, often black-box optimization problems. It tries to approximate and describe the surfaces formed by the fitness and other characteristic values associated with problem solutions on top of the multi-dimensional solution spaces. Sampling is the initial step of the ELA pipeline. It is a strategy for selecting a limited number of solutions, i.e., points in the multi-dimensional solution space, for which the fitness function(s) are evaluated. Consequently, the fitness landscape is approximated and its properties are drawn from these fitness values. In this work, the properties and the impact of various sampling strategies on the analysis of the fitness landscape are studied in the context of bi-objective optimization. Extensive computational experiments show that the use of different sampling strategies affects both the value of high-level landscape features and their usability for problem classification. The results also demonstrate that the magnitude and significance of the impact depend on problem dimension and sample size.