A covariance-based Moth–flame optimization algorithm with Cauchy mutation for solving numerical optimization problems

Abstract

Moth–Flame Optimization (MFO) algorithm, which is inspired by the navigation method of moths, is a nature-inspired optimization algorithm. The MFO is easy to implement and has been used to solve many real-world optimization problems. However, the MFO cannot balance exploration and exploitation well, and the information exchange between individuals is limited, especially in solving some complex numerical problems. To overcome these disadvantages of the MFO in solving the numerical optimization problems, a covariance-based Moth–Flame Optimization algorithm with Cauchy mutation (CCMFO) is proposed in this paper. In the CCMFO, the concept of covariance is used to transform the individuals of the moths and flames from the original space to the eigenspace and update the positions of moths, which can better improve the information exchange ability of the flames and moths in the eigenspace. In addition, Cauchy mutation is utilized to improve the exploration. And the CCMFO is compared with the other 22 algorithms on CEC 2020 test suite. The test results show that the CCMFO is better than other population-based optimization algorithms and MFO variants in search performance, while its performance is statistically similar to CEC competition algorithms. Furthermore, the CCMFO is compared with the other 12 algorithms on CEC 2020 real-world constrained optimization problems, and the results show that the CCMFO can effectively solve real-world constrained optimization problems. Finally, the CCMFO is used to optimize the tracking controller parameters of continuous casting mold vibration displacement. The experimental results based on the experimental platform show that the CCMFO can effectively reduce the difficulty of parameter selection and improve the tracking accuracy.