Decision Space Coverage of Random Walks

Abstract

Fitness landscape analysis is an approach used to mathematically characterize optimization problems. Random walk algorithms are used to sample fitness landscapes in order to perform fitness landscape analysis. Random walk algorithms have an advantage over random samples, in that random walk algorithms keep note of successive points in the walk, along with the relationships between them. It is important that the sample generated by a random walk algorithm is representative of the entire fitness landscape. A representative sample can be said to have good coverage of the decision space of the optimization problem. A new measure of the coverage of random walk algorithms, i.e. the Hausdorff distance, is proposed. The coverage of random walk algorithms found in the literature is investigated using the Hausdorff distance. This study shows that it is not sufficient to consider only the robustness of a random walk algorithm when performing fitness landscape analysis, but that the coverage of decision space should also be considered. This study shows that there is no significant difference in the coverage provided by the random walk algorithms investigated. However, the differences between the coverage of the random walk algorithms is more prominent when the length of the random walks is short, or the dimensionality of the optimization problem is increased.