A novel equilibrium optimizer based on levy flight and iterative cosine operator for engineering optimization problems

Equilibrium optimizer (EO) is a novel optimization algorithm with high exploration and exploitation capabilities. The capabilities of EO are impacted by the generation rate, exponential term, and equilibrium pool, wherein the initial two depend on the turnover rate. The performance of the EO on different optimization functions can be improved by updating these factors. This paper designs a modified equilibrium optimizer (MEO) by incorporating three changes in the EO: (i) replacement of the equilibrium pool with an iterative cosine operator (ICO) that gradually reduces diversification to intensification as the iterations progress; (ii) implementation of levy flight to update the concentration of particle that improves exploration capabilities; and (iii) the random vector with uniform distribution of turnover rate is replaced by heavy-tailed non-uniform levy distribution to improve exploration capability of the algorithm. Here, the other parameters on which MEO depends are selected by performing the sensitivity analysis. The capabilities of MEO have been analysed by comparing it with 19 algorithms, including the EO algorithm, 12 state-of-art algorithms, and 6 hybrid/improved algorithms on 62 functions, that is, 23 benchmark functions, 10 CEC-06-2019, 29 CEC-2017 functions. The non-parametric Friedman test and Kruskal-Wallis test validate that MEO outperforms the other algorithms due to its balanced exploration and exploitation abilities. MEO robustness has been validated by the diversity analysis along with the scalability test. MEO is also evaluated on five practical engineering problems to showcase its significance.