Sampling Techniques and Distance Metrics in High Dimensional Continuous Landscape Analysis: Limitations and Improvements

In metaheuristic optimization, understanding the relationship between problems and algorithms is important but nontrivial. There has been a growing interest in the literature on techniques for analyzing problems and algorithm performance; however, the validity of the assumptions and implementation choices behind many techniques is often not closely examined. In this paper, we review some interesting theoretical properties regarding sampling techniques and distance metrics in continuous spaces. In particular, we examine the effect of using Euclidean distance in conjunction with uniform random sampling on the behavior of the Dispersion metric. We show that the current methodology employed for the estimation of dispersion has important flaws, and we propose and evaluate modifications to improve the methodology. The modifications are simple and do not add significant complexity or computational effort to the methodology.