Genetic Algorithms perform crossovers effectively when linkage sets — sets of variables tightly linked to form building blocks — are identified. Several methods have been proposed to detect the linkage sets. Perturbation methods (PMs) investigate fitness differences by perturbations of gene values and Estimation of distribution algorithms (EDAs) estimate the distribution of promising strings. In this paper, we propose a novel approach combining both of them, which detects dependencies of variables by estimating the distribution of strings clustered according to fitness differences. The proposed algorithm, called the Dependency Detection for Distribution Derived from fitness Differences (D 5 ), can detect dependencies of a class of functions that are difficult for EDAs, and requires less computational cost than PMs.

This paper presents the linkage identification by non-monotonicity detection (LIMD) procedure and its extension for overlapping functions by introducing the tightness detection (TD) procedure. The LIMD identifies linkage groups directly by performing order-2 simultaneous perturbations on a pair of loci to detect monotonicity/non-monotonicity of fitness changes. The LIMD can identify linkage groups with at most order of k when it is applied to O (2 k ) strings. The TD procedure calculates tightness of linkage between a pair of loci based on the linkage groups obtained by the LIMD. By removing loci with weak tightness from linkage groups, correct linkage groups are obtained for overlapping functions, which were considered difficult for linkage identification procedures.