Knowledge-based function optimization using fuzzy cultural algorithms with evolutionary programming

In this paper, the advantages of a fuzzy representation in problem solving and search is investigated using the framework of Cultural algorithms (CAs), Since all natural languages contain a fuzzy component, the natural question is "Does this fuzzy representation facilitate the problem-solving process within these systems?" In order to investigate this question we use the CA framework of Reynolds [1], CAs are a computational model of cultural evolution derived from and used to express basic anthropological models of culture and its development. A mathematical model of a full fuzzy CA is developed here, In it, the problem solving knowledge is represented using a fuzzy framework. Several theoretical results concerning its properties are presented. The model is then applied to the solution of a set of 12 difficult, benchmark problems in nonlinear real-valued function optimization. The performance of the full fuzzy model is compared with 8 other fuzzy and crisp architectures. The results suggest that a fuzzy approach can produce a statistically significant improvement in search efficiency over nonfuzzy versions for the entire set of functions, We then investigate the class of performance functions for which the full fuzzy system exhibits the greatest improvements over nonfuzzy systems. In general, these are functions which require some preliminary investigation in order to embark on an effective search.