A new Approach for Dynamic Stochastic Fractal Search with Fuzzy Logic for Parameter Adaptation

Metaheuristic algorithms are widely used as optimization methods, due to their global exploration and exploitation characteristics, which obtain better results than a simple heuristic. The Stochastic Fractal Search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic-stochastic diffusion property, an improved Dynamic Stochastic Fractal Search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuzzy logic in the adaptation of the diffusion parameter in a dynamic fashion. This parameter is in charge of creating new fractal particles, and the diversity and iteration are the input information used in the fuzzy system to control the values of diffusion.

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A New Approach for Dynamic Stochastic Fractal Search with Fuzzy Logic for Parameter Adaptation

Fractal and Fractional ◽

10.3390/fractalfract5020033 ◽

2021 ◽

Vol 5 (2) ◽

pp. 33

Author(s):

Marylu L. Lagunes ◽

Oscar Castillo ◽

Fevrier Valdez ◽

Jose Soria ◽

Patricia Melin

Keyword(s):

Fuzzy Logic ◽

Fuzzy Inference ◽

Dynamic Parameter ◽

Mathematical Concept ◽

Parameter Adaptation ◽

Inference Models ◽

Fractal Particles ◽

Novel Method ◽

Dynamic Stochastic ◽

Stochastic Fractal Search

Stochastic fractal search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic stochastic diffusion property, an improved dynamic stochastic fractal search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid, and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuzzy logic in the adaptation of the diffusion parameter in a dynamic fashion. This parameter is in charge of creating new fractal particles, and the diversity and iteration are the input information used in the fuzzy system to control the values of diffusion.

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Shadowed Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Harmony Search and Differential Evolution Algorithms

Algorithms ◽

10.3390/a12010017 ◽

2019 ◽

Vol 12 (1) ◽

pp. 17 ◽

Cited By ~ 19

Author(s):

Oscar Castillo ◽

Patricia Melin ◽

Fevrier Valdez ◽

Jose Soria ◽

Emanuel Ontiveros-Robles ◽

...

Keyword(s):

Differential Evolution ◽

Fuzzy Inference ◽

Harmony Search ◽

Dynamic Parameter ◽

Optimization Methods ◽

Dynamic Adaptation ◽

Fuzzy Inference Systems ◽

Parameter Adaptation ◽

Inference Systems

Nowadays, dynamic parameter adaptation has been shown to provide a significant improvement in several metaheuristic optimization methods, and one of the main ways to realize this dynamic adaptation is the implementation of Fuzzy Inference Systems. The main reason for this is because Fuzzy Inference Systems can be designed based on human knowledge, and this can provide an intelligent dynamic adaptation of parameters in metaheuristics. In addition, with the coming forth of Type-2 Fuzzy Logic, the capability of uncertainty handling offers an attractive improvement for dynamic parameter adaptation in metaheuristic methods, and, in fact, the use of Interval Type-2 Fuzzy Inference Systems (IT2 FIS) has been shown to provide better results with respect to Type-1 Fuzzy Inference Systems (T1 FIS) in recent works. Based on the performance improvement exhibited by IT2 FIS, the present paper aims to implement the Shadowed Type-2 Fuzzy Inference System (ST2 FIS) for further improvements in dynamic parameter adaptation in Harmony Search and Differential Evolution optimization methods. The ST2 FIS is an approximation of General Type-2 Fuzzy Inference Systems (GT2 FIS), and is based on the principles of Shadowed Fuzzy Sets. The main reason for using ST2 FIS and not GT2 FIS is because the computational cost of GT2 FIS represents a time limitation in this application. The paper presents a comparison of the conventional methods with static parameters and the dynamic parameter adaptation based on ST2 FIS, and the approaches are compared in solving mathematical functions and in controller optimization.

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