This paper introduces genetic algorithms (GA) as a complete entity, in which knowledge of this emerging technology can be integrated together to form the framework of a design tool for industrial engineers. An attempt has also been made to explain "why'' and "when" GA should be used as an optimization tool.

odeling is a common but important technique for signal characterization. With the advent of computational power, many problems that were considered to be unsolvable in the past can now be tackled with ease. Successful applications in this area include the time-delay estimation modeled as a finite impulse response (FIR) filter [ 11 for sonar and radar systems; speech coding using linear predictive coding [2-41; wavelets for speech and image coding and recognition [5-81; fractals for image compression and recognition systems [9-111; and delayed-X filter [12-141 for active noise control [ 151, to name but a few.An efficient model for signal processing is not easy to come by and is often obtained with the aid of an optimization scheme. The accuracy of the model is generally governed by a set of variables or parameters that is optimized in the 22 IEEE SIGNAL PROCESSING MAGAZINE

A new approach for generating-scroll attractors is introduced. It is demonstrated that-scroll attractors can be generated using a simple sine or cosine function. A guideline is given so that a different number of scrolls can be designed easily by modifying two variables in the function. An electronic circuit is also designed for the implementation and the observation of a 9-scroll attractor is reported for the first time.

This paper introduces an optimal fuzzy proportional-integral-derivative (PID) controller. The fuzzy PID controller is a discrete-time version of the conventional PID controller, which preserves the same linear structure of the proportional, integral, and derivative parts but has constant coefficient yet self-tuned control gains. Fuzzy logic is employed only for the design; the resulting controller does not need to execute any fuzzy rule base, and is actually a conventional PID controller with analytic formulas. The main improvement is in endowing the classical controller with a certain adaptive control capability. The constant PID control gains are optimized by using the multiobjective generic algorithm (MOGA), thereby yielding an optimal fuzzy PID controller. Computer simulations are shown to demonstrate its improvement over the fuzzy PID controller without MOGA optimization. Index Terms-Fuzzy control, genetic algorithm, optimization, proportional-integral-derivative controller.Manuscript received February 26, 2001. Abstract published on the Internet

11A new scheme based on multi-objective hierarchical genetic algorithm (MOHGA) is proposed to extract interpretable rule-based knowledge from data. The approach is derived from the use of multiple objective genetic 13 algorithm (MOGA), where the genes of the chromosome are arranged into control genes and parameter genes. These genes are in a hierarchical form so that the control genes can manipulate the parameter genes in a more 15 effective manner. The effectiveness of this chromosome formulation enables the fuzzy sets and rules to be optimally reduced. Some important concepts about the interpretability are introduced and the fitness function in the MOGA 17 will consider both the accuracy and interpretability of the fuzzy model. In order to remove the redundancy of the rule base proactively, we further apply an interpretability-driven simplification method to newborn individuals. In 19 our approach, we first apply the fuzzy clustering to generate an initial rule-based model. Then the multi-objective hierarchical genetic algorithm and the recursive least square method are used to obtain the optimized fuzzy models. 21The accuracy and the interpretability of fuzzy models derived by this approach are studied and presented in this paper. We compare our work with other methods reported in the literature on four examples: a synthetic nonlinear 23 dynamic system, a nonlinear static system, the Lorenz system and the Mackey-Glass system. Simulation results show that the proposed approach is effective and practical in knowledge extraction. 25