The synergy between multideme genetic algorithms and fuzzy systems

In this article, a real-coded genetic algorithm (GA) is proposed capable of simultaneously optimizing the structure of a system (number of inputs, membership functions and rules) and tuning the parameters that define the fuzzy system. A multideme GA system is used in which various fuzzy systems with different numbers of input variables and with different structures are jointly optimized. Communication between the different demes is established by the migration of individuals presenting a difference in the dimensionality of the input space of a particular variable. We also propose coding by means of multidimensional matrices of the fuzzy rules such that the neighborhood properties are not destroyed by forcing it into a linear chromosome. The effectiveness of the proposed approach is verified and is compared with other fuzzy, and neuro-fuzzy approaches in terms of the root mean squared error (RMSE). I. GENETIC ALGORITHMS AND FUZZY SYSTEM Since the introduction of the basic methods of fuzzy reasoning by Zadeh and the success of their first application to fuzzy control, fuzzy logic has been widely studied [5][7] and [11]. However, certain important problems still remain, including: 1) the selection of the fuzzy rule base; 2) the subjective definitions of the membership functions; 3) the selection of the variables of the system. The design of a fuzzy system involves the structure of the rules of the system, and the membership function parameters. GAs have the potential to be used to evolve both the fuzzy rules and the corresponding fuzzy set parameters [9]. Some of the work of fuzzy systems and GAs concentrates exclusively on tuning of membership functions [6] or on the selecting an optimal set of fuzzy rules [8], while others attempt to derive rules and membership functions together [2]. To obtain optimal rule sets and optimal sets of membership functions, it is preferable that both are acquired simultaneously [4]. To optimize the whole fuzzy system simultaneously, two structures will be used: one to encode the membership functions and the other for the fuzzy rules. A. Membership function coding The membership functions are encoded within an "incomplete" matrix in which each row represents one of the variables of the system, and where the columns encode the parameters of the membership functions (Fig.1). Because each of the input variables of the system has a different number of membership functions, the chromosome structure used to store the membership functions is not a "complete" matrix, as each of the m rows has a different number of columns nm. As we have selected a triangular partition (TP), the only parameter that needs to be stored is the centre of the function [12]. ESANN'2001 proceedings European Symposium on Artificial Neural Networks Bruges (Belgium), 25-27 April 2001, D-Facto public., ISBN 2-930307-01-3, pp. 199-204