Optimization of Takagi-Sugeno-Kang Fuzzy Model Based on Differential Evolution with Lévy Flight

Xiao Feng, Yongbin Yu, Jingye Cai, Hao Wang, Xiangxiang Wang, Xinyi Han, Jingya Wang

Abstract: In this article, a novel evolutionary algorithm called differential evolution with Lévy flight (DEFL) algorithm was proposed to optimize the Takagi-Sugeno-Kang fuzzy model (TSK fuzzy model) by finding the optimal hyper-parameter combination. DEFL consists of the conventional differential evolution (DE) algorithm as the primary search method and Lévy flight which is adopted to improve the early convergence problem of DE by its more changeable step size. Moreover, an adaptive soft-switch factor is designed to achieve the balance between exploration and exploitation according to the fitness of parent individuals, which can enhance the searching ability of DEFL. To verify the high performance of our proposed DEFL, two simulations are conducted. First, the five test functions: Ackley, Rastrigin, Sphere, Dixon & Price, and Perm are performed to verify the searching ability of DEFL and other three evolutionary algorithms: genetic algorithm (GA), particle swarm optimization (PSO), and DE are adopted for comparison. Then, TSK fuzzy model optimized by DEFL is adopted on eight datasets for classification tasks which are compared with the other nine methods. The first simulation shows that DEFL has the best searching ability compared with other algorithms. The accuracy and ranks of the optimized TSK fuzzy model on eight tasks demonstrate the high performance of the model improved by DEFL.