Using Landscape Topology to Compare Continuous Metaheuristics: A Framework and Case Study on EDAs and Ridge Structure

Abstract

In this paper we extend a previously proposed randomized landscape generator in combination with a comparative experimental methodology to study the behavior of continuous metaheuristic optimization algorithms. In particular, we generate two-dimensional landscapes with parameterized, linear ridge structure, and perform pairwise comparisons of algorithms to gain insight into what kind of problems are easy and difficult for one algorithm instance relative to another. We apply this methodology to investigate the specific issue of explicit dependency modeling in simple continuous estimation of distribution algorithms. Experimental results reveal specific examples of landscapes (with certain identifiable features) where dependency modeling is useful, harmful, or has little impact on mean algorithm performance. Heat maps are used to compare algorithm performance over a large number of landscape instances and algorithm trials. Finally, we perform a meta-search in the landscape parameter space to find landscapes which maximize the performance between algorithms. The results are related to some previous intuition about the behavior of these algorithms, but at the same time lead to new insights into the relationship between dependency modeling in EDAs and the structure of the problem landscape. The landscape generator and overall methodology are quite general and extendable and can be used to examine specific features of other algorithms.