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

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.

An adaptive structure on a new local branching algorithm using instantaneous dimensions and convergence speed: a case study for multi-commodity network design problems

“…Furthermore, different variants of the HS algorithm employ novel methods for generating new solution vectors that enhance accuracy and convergence rate. As a result of good performance and convergence in parameter tuning, the HS algorithm and its extensions are widely used as parameter tuning approaches for improving structural optimization and dynamic parameter adaptation [48][49][50][51][52][53].…”

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

“…Previously, 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 control problem [1]. In this work, now 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 in improving the performance of the DE algorithm in the process of optimizing fuzzy controllers.…”

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

“…Previously, 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]. In this work, we are now 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.…”