Abstract
This article mainly focuses on the utilization of shadowed type-2 fuzzy systems used to achieve the goal of dynamically adapting the parameters of two already known algorithms in the literature: the harmony search and the differential evolution algorithms. It has already been established that type-2 fuzzy logic enhances the performance of metaheuristics by enabling parameter adaptation; however, the utilization of fuzzy logic results in an increased execution time. For this reason, in this article, the shadowed type-2 fuzzy approach is put forward as a way of reducing execution time, while maintaining the good results that the complete type-2 fuzzy model produces. The harmony search and differential evolution algorithms with shadowed type-2 parameter adaptations were applied to the problem of optimally designing fuzzy controllers. The simulations were performed with the controllers working in an ideal situation, and then with a real situation under different noise levels in order to reach a conclusion regarding the performance of each of the algorithms that were applied.
Highlights
Two algorithms based on two different approaches are considered: the harmony search (HS) and the differential evolution (DE) algorithms, which have already been compared in previous studies using different types of fuzzy systems and for different problems, both for control and mathematical functions
Some of the studies that have considered these two algorithms together are the following: the first discussed the optimal design of fuzzy systems using differential evolution and harmony search algorithms with dynamic parameter adaptations [1]
Feedback control problems are very popular for testing the performance of an algorithm; this article uses a control case that is widely used in proportional integral (PI) and proportional integral derivative (PID) controllers, and the implementation in this work was carried out in a type-1 fuzzy controller, with the goal of validating the performance of the two proposed methods
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Mathematics 2021, 9, 2439 unconstrained problems is shown in [42], the optimal design of fuzzy controllers based on a DE algorithm with parameter adaptation utilizing fuzzy systems (of the type-2 and type-1 form) is presented in [43], and the accelerated DE algorithm with novel proposed operators for multi-damage detection in plate structures is described in [44] It has already been established in previous works that type-2 fuzzy enhancements can help augment performance in metaheuristics by enabling dynamic parameter adaptation during execution.
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