Improved surrogate-assisted whale optimization algorithm for fractional chaotic systems ’ parameters identification

Abstract

Accurate identification of the unknown parameters in fractional chaotic systems is crucial for their precise control. However, the evaluation of these systems is relatively expensive in the sense that its numerical process demands considerable time. Thus, it is essential to design a less time-demanding algorithm with high accuracy. Motivated by this, this paper aims to propose an algorithm with high accuracy and quick convergence speed, leading to a smaller computational budget. To achieve this goal, an Improved Surrogate-Assisted Whale Optimization Algorithm, denoted as ISAWOA, is proposed. A surrogate-assisted model is employed to approximate the fitness function, then, both the Lévy flight and the quadratic interpolation techniques are used to improve the exploration and exploitation capacity of the Whale Optimization Algorithm. The simulation results on 20 classical benchmark functions demonstrate that ISAWOA is able to locate an optimal solution with high accuracy and much faster than 14 other algorithms found in the literature. Finally, the proposed algorithm is validated on several representative fractional chaotic systems where ISAWOA is again able to outperform other methods, both in precision and CPU time. The overall test results show that ISAWOA is a promising algorithm with high accuracy, quick convergence, and that it requires a moderate amount of CPU time when dealing with parameter estimation problems on fractional chaotic systems.