Availability of Perfect Decomposition in Statistical Linkage Learning for Unitation-Based Function Concatenations

Statistical Linkage Learning (SLL) is a part of many state-of-the-art optimizers. The purpose of SLL is to discover variable interdepen-dencies. It has been shown that the effectiveness of SLL-using optimizers is highly dependent on the quality of SLL-based problem decomposition. Thus, understanding what kind of problems are hard or easy to decompose by SLL is important for practice. In this work, we analytically estimate the size of a population sufficient for obtaining a perfect decomposition in case of concatenations of certain unitation-based functions. The experimental study confirms the accuracy of the proposed estimate. Finally, we identify those problem types that may be considered hard for SLL-using optimizers.