EVOLUTIONARY ALGORITHMS FOR FUZZY LOGIC: A BRIEF OVERVIEW

Evolutionary algorithms are direct, global optimization algorithms gleaned from the model of organic evolution. The most important representatives, genetic algorithms and evolution strategies, are brieey introduced and compared in this paper, and their major diierences are clariied. Furthermore, the paper summarizes the application possibilities of evolutionary algorithms in the design of fuzzy logic controllers. The optimization of fuzzy membership functions turns out to be a promising and successful application domain for evolutionary algorithms, while the automatic learning of fuzzy control rules by means of fuzzy classiier systems is still in an early stage of research. Evolutionary algorithms are a class of direct, prob-abilistic search and optimization methods based on the model of organic evolution (where they also borrow most of the terminology from). The algorithms exploit the collective learning process within a population of individuals, and each of the individuals represents a search point in the space of potential solutions to a given problem. The start population (which is often randomly initialized) evolves towards increasingly better regions of the search space by means of randomized processes of selection , mutation, and recombination. The selection operator favours individuals of higher tness (quality in terms of the objective function f : M ! IR which characterizes the optimization problem) to reproduce more often than individuals of lower t-ness. Recombination allows for the exchange of information (partial solutions) between individuals, and mutation introduces innovation into the population. Using this high level of abstraction, we can formulate a general basic algorithm which subsumes the existing evolutionary algorithms. In the following , t denotes a generation (iteration) counter and P(t) 2 I is a population of individuals at generation t. I denotes the space of individuals and is not necessarily identical to the optimization problem's search space M because individuals may carry additional information. P 0 (t) 2 I and P 00 (t) 2 I are used to indicate intermediate populations of size (= is possible). Furthermore, we use Q 2 fP(t); ;g to denote a set of individuals which might be taken into account by selection in addition to the intermediate population P 00 (t). The resulting evolutionary algorithm consists of a simple loop of recombination, mutation, tness evaluation, and selection which is iterated until a speciic termination criterion is fulllled: Algorithm 1 (Basic evolutionary algorithm) t := 0; initialize P(t) 2 I ; evaluate P(t); while not terminate(P (t)) do recombine: P 0 …