Abstract
Fuzzy systems have become a good solution to the problem of fixed parameters in metaheuristic algorithms, proving their efficiency when performing dynamic parameter adaptations using type-1 and type-2 fuzzy logic. However, the computational cost of type-2 fuzzy systems when using the continuous enhanced Karnik–Mendel (CKM) algorithm for type-reduction, when applied to control and optimization, is too high. Therefore, it is proposed to use an approximation to the CKM algorithm in the type-2 fuzzy system for adjusting the pitch adjustment rate (PArate) parameter in the original harmony search algorithm (HS). The main contribution of this article is to verify that the implementation of the proposed methodology achieves results that are equivalent to the interval type-2 fuzzy system with the CKM algorithm, but in less computing time and also allowing an efficient dynamic parameter adaptation. It is noteworthy that this method is relatively new in the area of metaheuristics algorithms so there is a current interest to work with this methodology. The proposed method was used in optimizing the antecedents and consequents for an interval type-2 fuzzy controller of direct current motor. Experimental results without noise and then with uniform random noise numbers (Gaussian noise) in the controller were obtained to verify that the implementation is efficient when compared to conventional and other existing methods.
Highlights
Published: 1 April 2021Currently, in state of the art science, there exists a plethora of algorithms for solving real world problems, and some of them are classified as bio-inspired algorithms, which replicate the way in which nature deals with optimization problems
Interval type-2 fuzzy logic has the ability to deal with uncertainty; its main advantages are that it achieves the stabilization and improvement of results on complex problems, Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
This article has presented the implementation of the new approximate continuous enhanced Karnik–Mendel (NACEKM) method in the parameter adaptation of the original harmony search (HS) algorithm
Summary
In state of the art science, there exists a plethora of algorithms for solving real world problems, and some of them are classified as bio-inspired algorithms, which replicate the way in which nature deals with optimization problems Examples of these algorithms are shown in [1,2,3,4,5]: metaheuristics that are derived from hybrid algorithms, mechanisms, and statistics, as we find in [6,7,8], applied to neural networks as in [9,10,11]; and type-2/3 fuzzy systems applied in various applications, such as in [12,13] among others. Type-2 [17,18,19] fuzzy logic for parameter adaptation, and they have been implemented with relative success in various control problems and benchmark mathematical functions, as shown in [20,21].
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