High-Speed Interval Type-2 Fuzzy System for Dynamic Crossover Parameter Adaptation in Differential Evolution and Its Application to Controller Optimization

Abstract

The main contribution in this paper is the use of a new type-reduction method to improve the processing speed of Type-2 fuzzy systems for dynamic parameter adaptation in the Differential Evolution algorithm. The proposed type-reduction is an approximation to the Continuous Karnik–Mendel (CEK) method, which is the equivalent to using a traditional Interval Type-2 fuzzy system, but with lower computational cost. The motivation of this work is to verify that the proposed methodology is equivalent in performance to an Interval Type-2 fuzzy system. The first type-reduction method was proposed by Karnik and Mendel (KM), and then was followed by its enhanced version called EKM, and the continuous versions were called CKM and CEKM. In addition, there were variations of these and also other types of variations that eliminate the type-reduction process reducing the computational cost to a Type-1 defuzzification. The concept of approximation to the Continuous Karnik–Mendel (CEK) method is new in the area of metaheuristic algorithms and this is why it is in our interest to work with this methodology. We propose to use this methodology to achieve a dynamic crossover (CR) parameter adaptation in the Differential Evolution algorithm, and the objective is to use the type-reduction process and also provide a continuous solution to the defuzzification. This proposed methodology is applied to a set of mathematical functions and a control problem, for verifying the efficiency of the proposed methodology compared to the original algorithm and other existing methods in the literature.