A GA-based fuzzy modeling approach for generating TSK models

Abstract

This paper proposes a new genetic-based modeling method for building simple and well-defined TSK models with scatter-type input partitions. Our approach manages all attributes characterizing the structure of a TSK model, simultaneously. Particularly, it determines the number of rules, the input partition, the participating inputs in each rule and the consequent parameters. The model building process is divided into two phases. In phase one, the structure learning task is formulated as a multi-objective optimization problem which is resolved using a novel genetic-based structure learning (GBSL) scheme. Apart from the mean square error (MSE) and the number of rules, three additional criteria are introduced in the fitness function for measuring the quality of the partitions. Optimization of these measures leads to models with representative rules, small overlapping and efficient data cover. In order to obtain models with accurate data fitting and good local performance, the consequent parameters are determined using a local MSE function while the overall model is evaluated on the basis of a global MSE function. The search capabilities of the suggested structure learning scheme are significantly enhanced by including a highly effective local search operator implemented by a micro-genetic algorithm and four problem-specific operators. Finally, a genetic-based parameter learning (GBPL) scheme is suggested in phase two, which performs fine-tuning of the initial models obtained after structure learning. The performance of the proposed modeling approach is evaluated using a static example and a well-known dynamic benchmark problem. Simulation results demonstrate that our models outperform those suggested by other methods with regard to simplicity, model structure, and accuracy.