Multi-Agent cubature Kalman optimizer: A novel metaheuristic algorithm for solving numerical optimization problems

Optimization problems arise in diverse fields such as engineering, economics, and industry. Metaheuristic algorithms, including the Simulated Kalman Filter (SKF), have been developed to solve these problems. SKF, inspired by the Kalman Filter (KF) in control engineering, requires three parameters (initial error covariance $P\left(0\right)$, measurement noise $Q$, and process noise $R$). However, studies have yet to focus on tuning these parameters. Furthermore, no significant improvement is shown by the parameter-less SKF (with randomized $P\left(0\right)$, $Q$, and $R$). Randomly choosing values between 0 and 1 may lead to too small values. As an estimator, KF raises concerns with excessively small $Q$ and $R$ values, which can introduce numerical stability issues and result in unreliable outcomes. Tuning parameters for SKF is a challenging and time-consuming task. The Multi-Agent Cubature Kalman Filter (MACKO), inspired by the Cubature Kalman filter (CKF), was introduced in this work. The nature of the Cubature Kalman filter (CKF) allows the use of small values for parameters $P\left(0\right)$, $Q$, and $R$. In the MACKO algorithm, Cubature Transformation Techniques (CTT) are employed. CTT can use small values for parameters $P\left(0\right)$, $Q$, and $R$, so CKF was developed to overcome KF and other estimation algorithms. Moreover, in CTT, the term local neighborhoods is used to propagate the cubature point in local search, where the radius, $\delta$, of local search is updated in every iteration to balance between the exploration and exploitation processes. MACKO is evaluated on the CEC 2014 benchmark suite with 30 optimization problems, and its performance is compared with nine existing metaheuristic algorithms. Simulation results demonstrate that MACKO is superior, outperforming the benchmark algorithms, as indicated by Friedman's test with a 5 % significance level.