Abstract
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.
Highlights
Metaheuristic optimization methods represent a very interesting alternative for the optimization of complex problems without the mathematical modeling of the problem, and they have been successfully applied in several kinds of application, for example, in control applications [1,2,3], optimizing Artificial Neural Networks [4,5,6], optimizing a controller applied in an complex electromechanical process [7], fuzzy controllers [8,9], etc
There are some works where the dynamic adaptation of metaheuristic parameters is realized through Interval Type-2 Fuzzy systems, for example, in [2,3], and in some works, this adaptation is successfully realized by General Type-2 Fuzzy Systems
Storn and Price in 1994 [34] and is mainly composed of the following operations: initialization of the population structure defined by Equations (11)–(16), initialization by Equation (17), mutation expressed by Equation (18), crossover defined by Equation (19), and selection defined with Equation (20)
Summary
Metaheuristic optimization methods represent a very interesting alternative for the optimization of complex problems without the mathematical modeling of the problem, and they have been successfully applied in several kinds of application, for example, in control applications [1,2,3], optimizing Artificial Neural Networks [4,5,6], optimizing a controller applied in an complex electromechanical process [7], fuzzy controllers [8,9], etc. Dynamic parameter adaptation in metaheuristic methods based on fuzzy logic can improve their optimization performance as can be observed in [10,11,12,13]. This dynamic adaptation based on fuzzy logic significantly increases the computational cost of the optimization process. There are some works where the dynamic adaptation of metaheuristic parameters is realized through Interval Type-2 Fuzzy systems, for example, in [2,3], and in some works, this adaptation is successfully realized by General Type-2 Fuzzy Systems.
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