Optimal Design of Fuzzy Systems Using Differential Evolution and Harmony Search Algorithms with Dynamic Parameter Adaptation

Abstract

This paper presents a study of two popular metaheuristics, namely differential evolution (DE) and harmony search (HS), including a proposal for the dynamic modification of parameters of each algorithm. The methods are applied to two cases, finding the optimal design of a fuzzy logic system (FLS) applied to the optimal design of a fuzzy controller and to the optimization of mathematical functions. A fuzzy logic controller (FLC) of the Takagi-Sugeno type is used to find the optimal design in the membership functions (MFs) for the stabilization problem of an autonomous mobile robot following a trajectory. A comparative study of the results for two modified metaheuristic algorithms is presented through analysis of results and statistical tests. Results show that, statistically speaking, optimal fuzzy harmony search (OFHS) is better in comparison to optimal fuzzy differential evaluation (OFDE) for the two presented study cases.