Analyzing the Interdependence Between Some Certain Gene Loci by Epistasis Measures in Fitness Landscapes of Schemata

GA hardness and interdependence between genes in the chromosome are important questions in the study of genetic algorithms(GA). Traditional methods, which are used to measure the interaction between genes, can only reflect the extent of epistasis between all genes in the chromosome. Therefore, the definition of the fitness landscape of schemata is proposed in this paper, and epistasis measures on this landscape of schemata are used to analyze the degree of interdependence between some certain gene loci in study. Some information between these sites can be reflected by some characters of the fitness landscape of schemata which are composed of these fixed sites. The stronger the interaction between these sites, the larger the variation of the fitness of schemata whose fixed sites correspond to those sites in study, and the more rugged the fitness landscape of these schemata. According to the degree of interaction between these given gene loci, building blocks of GA can be analyzed and determined, and further genetic operators and the structure of GA can be designed and adjusted to improve the performance of GA. At last, a lot of experiments including NK models are done, and results of empirical analysis show that this method is effective.