Estimation-based metaheuristic algorithms such as the Simulated Kalman Filter (SKF) and Single-Agent Finite Impulse Response (SAFIRO) have been proposed to solve optimization problems that frequently arise in fields like engineering, economics, and industry. However, these algorithms rely solely on simulated measurements during the search process and operate by generating and updating only a single candidate solution within the search space. This strategy limits their exploration capability, often causing the algorithms to become trapped in local optima rather than discovering the global optimum . This study introduces a new algorithm by using the Cubature Kalman Filter (CKF) framework. The proposed optimization algorithm employs a multi-agent approach with an asynchronous iteration strategy. Each prediction phase implements the Cubature Transformation Technique (CTT), generating multiple candidate solutions that enhance the balance between exploration and exploitation phases. This balanced approach significantly improves the algorithm's capacity to solve optimization problems. The proposed Asynchronous Cubature Kalman Optimizer (ACKO) leverages the inherent characteristics of the Cubature Kalman filter, employing solution prediction with CTT, measurement prediction with CTT, simulated measurement, and solution estimation. ACKO was tested on the CEC 2014 benchmark suite, and its performance was compared with eight well-known metaheuristic algorithms. The Friedman test ranked ACKO as the top-performing algorithm, with SAFIRO, SKF, and others following. The Holm post hoc test, conducted at a significance level of α = 0.05 with 8 degrees of freedom, confirmed that ACKO significantly outperforms the compared algorithms. These findings highlight its strong potential for addressing high-dimensional optimization tasks. For real application, ACKO is used to determine optimum proportional-integral-derivative (PID) controller parameters of an automatic voltage regulator (AVR) system. The proposed method (PID-ACKO) was found efficient and robust in improving the transient response of AVR system compared with the other PID controller tunning methods.
Musa et al. (Fri,) studied this question.