Abstract
This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.
Highlights
IntroductionThe utilization of new strategies to improve the functioning of certain processes is something very common today, and under this concept we have the differential evolution (DE) algorithm, which is used in multiple disciplines to perform optimization
A study was carried out using the differential evolution algorithm and the concept of shadowed type 2 fuzzy systems applied to benchmark functions and a specific control problem [1]
The null and alternative hypotheses that we propose for the statistical test are the following: Ho: The results of the GT2FDE methodology without noise and with noise are higher than the methodology ST2FDE without noise and with noise
Summary
The utilization of new strategies to improve the functioning of certain processes is something very common today, and under this concept we have the differential evolution (DE) algorithm, which is used in multiple disciplines to perform optimization. The main approach for this work is the adaptation of a parameter of the DE algorithm using two variants of fuzzy logic, which are shadowed and general type 2 fuzzy systems. A study was carried out using the differential evolution algorithm and the concept of shadowed type 2 fuzzy systems applied to benchmark functions and a specific control problem [1]. We are aiming at comparing the two concepts of shadowed and general type 2 fuzzy systems in order to find out which method is better for improving the performance of the DE algorithm in the process of optimizing fuzzy controllers
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