Abstract-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.
Abstract. In this paper we extend a previously proposed randomized landscape generator in combination with a comparative experimental methodology to study the behaviour of continuous metaheuristic optimization algorithms. In particular, we generate landscapes with parameterised, 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 modelling in simple continuous Estimation of Distribution Algorithms. Experimental results reveal specific examples of landscapes (with certain identifiable features) where dependency modelling is useful, harmful or has little impact on average algorithm performance. The results are related to some previous intuition about the behaviour of these algorithms, but at the same time lead to new insights into the relationship between dependency modelling in EDAs and the structure of the problem landscape. The overall methodology is quite general and could be used to examine specific features of other algorithms.
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.
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