Linkage identification for real-valued loci by fitness difference classification

In order to enhance efficiency of genetic algorithms, it is important to identify a linkage set, i.e. a set of loci tightly linked to construct a building block. In this paper, we propose a novel linkage identification method for real-valued strings called the real-valued dependency detection for distribution derived from df (rD⁵). It can detect linkage sets with quasilinear fitness evaluations. The rD⁵ is designed based on the D⁵ which has been proposed for binary strings. It detects dependencies of loci by estimating the distribution of strings classified according to fitness differences. The rD⁵ and the LINC-R which is one of linkage identification methods proposed elsewhere, provide approximate equivalent information about a function to be solved, however, the rD⁵ performs smaller number of fitness evaluations than the LINC-R for larger functions. Although estimation of distribution algorithms (EDAs) also estimate distribution of strings, it is difficult for EDAs to solve a function composed of exponentially scaled subfunctions. The proposed method, by contrast, can be applied to the function in the similar way to as to a function composed of uniformly scaled subfunctions which is easy for EDAs. We perform experiments to compare the proposed method with the LINC-R and to examine the scaling effect stability of the rD⁵. We also investigate two parameters, that define the amount of perturbation (mutation) and that define the quantization level.