scholarly journals Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 194
Author(s):  
Patricia Ochoa ◽  
Oscar Castillo ◽  
Patricia Melin ◽  
José Soria
Keyword(s):  
Differential Evolution ◽  
Fuzzy Systems ◽  
General Type ◽  
Differential Evolution Algorithm ◽  
Dynamic Parameter ◽  
Benchmark Problems ◽  
Parameter Adaptation ◽  
Different Types ◽  
Evolution Algorithm

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.

scholarly journals Differential Evolution With Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

2021 ◽  
Author(s):  
Patricia Ochoa ◽  
Oscar Castillo ◽  
Patricia Melin ◽  
José Soria
Keyword(s):  
Differential Evolution ◽  
Fuzzy Systems ◽  
General Type ◽  
Differential Evolution Algorithm ◽  
Main Idea ◽  
Dynamic Parameter ◽  
Performance Comparison ◽  
Parameter Adaptation ◽  
Fuzzy Controllers

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. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

scholarly journals Cloud Particles Differential Evolution Algorithm: A Novel Optimization Method for Global Numerical Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-36 ◽  
Author(s):  
Wei Li ◽  
Lei Wang ◽  
Quanzhu Yao ◽  
Qiaoyong Jiang ◽  
Lei Yu ◽  
...  
Keyword(s):  
Solid State ◽  
Differential Evolution ◽  
Liquid State ◽  
Differential Evolution Algorithm ◽  
Optimization Method ◽  
Benchmark Problems ◽  
Gaseous State ◽  
Mutation Strategy ◽  
Evolution Algorithm ◽  
Cloud Particles

We propose a new optimization algorithm inspired by the formation and change of the cloud in nature, referred to as Cloud Particles Differential Evolution (CPDE) algorithm. The cloud is assumed to have three states in the proposed algorithm. Gaseous state represents the global exploration. Liquid state represents the intermediate process from the global exploration to the local exploitation. Solid state represents the local exploitation. The best solution found so far acts as a nucleus. In gaseous state, the nucleus leads the population to explore by condensation operation. In liquid state, cloud particles carry out macrolocal exploitation by liquefaction operation. A new mutation strategy called cloud differential mutation is introduced in order to solve a problem that the misleading effect of a nucleus may cause the premature convergence. In solid state, cloud particles carry out microlocal exploitation by solidification operation. The effectiveness of the algorithm is validated upon different benchmark problems. The results have been compared with eight well-known optimization algorithms. The statistical analysis on performance evaluation of the different algorithms on 10 benchmark functions and CEC2013 problems indicates that CPDE attains good performance.

scholarly journals Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Cinthia Peraza ◽  
Fevrier Valdez ◽  
Juan R. Castro ◽  
Oscar Castillo
Keyword(s):  
Fuzzy Systems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Dynamic Parameter ◽  
Harmony Search Algorithm ◽  
Parameter Adaptation ◽  
Error Metrics ◽  
Interval Type ◽  
Following Error

This paper presents a method for dynamic parameter adaptation in the harmony search algorithm (HS) based on fuzzy logic. The adaptation is performed using Type 1 (FHS), interval Type 2 (IT2FHS), and generalized Type 2 (GT2FHS) fuzzy systems as the number of improvisations or iterations advances, achieving a better intensification and diversification. The main contribution of this work is the dynamic parameter adaptation using different types of fuzzy systems in the harmony search algorithm applied to optimization of the membership functions for a benchmark control problem; in this case it is focused on the ball and beam controller. Experiments are presented with the HS, FHS, IT2FHS, and GT2FHS with noise (uniform random number) and without noise for the controller, and the following error metrics are obtained: ITAE, ITSE, IAE, ISE, and RMSE, to validate the efficacy of the proposed methods.

COMPUTING TWO LINCHPINS OF TOPOLOGICAL DEGREE BY A NOVEL DIFFERENTIAL EVOLUTION ALGORITHM

2005 ◽  
Vol 05 (03) ◽  
pp. 335-350 ◽  
Author(s):  
FEI GAO ◽  
HENG-QING TONG
Keyword(s):  
Differential Evolution ◽  
Topological Degree ◽  
Large Scale ◽  
Uniform Design ◽  
Lipschitz Constant ◽  
Differential Evolution Algorithm ◽  
Initial Point ◽  
Benchmark Problems ◽  
Initial Population ◽  
Evolution Algorithm

How to detect the topological degree (TD) of a function is of vital importance in investigating the existence and the number of zero values in the function, which is a topic of major significance in the theory of nonlinear scientific fields. Usually a sufficient refinement of the boundary of the polyhedron decided by Boult and Sikorski algorithm (BS) is needed as prerequisite when the well known method of Stenger and Kearfott is chosen for computing TD. However two linchpins are indispensable to BS, the parameter δ on the boundary of the polyhedron and an estimation of the Lipschitz constant K of the function, whose computations are analytically difficult. In this paper, through an appropriate scheme that transforms the problems of computing δ and K into searching optimums of two non-differentiable functions, a novel differential evolution algorithm (DE) combined with established techniques is proposed as an alternative method to computing δ and K. Firstly it uses uniform design method to generate the initial population in feasible field so as to have the property of large scale convergence, without better approximation of the unknown parameter as iterative initial point. Secondly, it restrains the normal DE's local convergence limitation virtually through deflection and stretching of objective function. The main advantages of the put algorithm are its simplicity and its ability to work by using function values solely. Finally, details of applying the proposed method into computing δ and K are given, and experimental results on two benchmark problems in contrast to the results reported have demonstrated the promising performance of the proposed algorithm in different scenarios.

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