Knowledge-based function optimization using fuzzy cultural algorithms withevolutionary 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 questi on is "Does this fuzzy representation facilitate the problem-solving proces s within these systems?" In order to investigate this question we use the C A framework of Reynolds [1], CAs are a computational model of cultural evol ution derived from and used to express basic anthropological models of cult ure and its development. A mathematical model of a full fuzzy CA is developed here, In it, the probl em solving knowledge is represented using a fuzzy framework. Several theore tical results concerning its properties are presented. The model is then ap plied to the solution of a set of 12 difficult, benchmark problems in nonli near real-valued function optimization. The performance of the full fuzzy m odel is compared with 8 other fuzzy and crisp architectures. The results su ggest that a fuzzy approach can produce a statistically significant improve ment in search efficiency over nonfuzzy versions for the entire set of func tions, 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 investigat ion in order to embark on an effective search.