A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics

Abstract

Fuzzy dynamic adaptation of parameters in meta-heuristic algorithms has recently been shown to provide an improvement in efficiency with respect to meta-heuristic algorithms with static parameters. However, executing a fuzzy inference in each iteration represents an increase in the computational cost, and this is even more critical in the case of using Type-2 Fuzzy Logic systems. On the other hand, fuzzy dynamic adaptation with Type-2 Fuzzy Logic has shown better performance when compared with respect to Type-1 Fuzzy Logic in diverse areas of application; therefore, the goal of this paper is aimed at reducing the computational cost of Type-2 Fuzzy Logic processing for dynamic adaptation of parameters in meta-heuristic algorithms. To reduce the computational cost of processing the Interval Type-2 Fuzzy system for dynamic adaptation of metaheuristic parameters, the use of an approximation to the Continuous Karnik–Mendel method (CEKM) is proposed. The proposed approach provides an analytical approximation to the CEKM method, in this way reducing the computational cost of evaluating the Interval Type-2 Fuzzy System. The performance of the proposed approach was tested with five benchmark functions and with one benchmark control problem. The proposed approach was tested with two different meta-heuristic algorithms, the Differential Evolution algorithm (DE) and the Harmony Search algorithm (HS), in both cases achieving a reduction in the computational cost, while maintaining the performance with respect to the Type-2 Dynamic adaptation of parameters with the conventional type reduction methods.