An enhanced Equilibrium Optimizer for solving complex optimization problems

Equilibrium Optimizer (EO), despite its acceptable performance in several complex problems, suffers from low exploitation ability with unbalanced exploration, stagnation in local optima and poor convergence rate. To enhance the performance of the EO, the authors infused the intelligence of quasi-opposite numbers and chaotic-maps into the EO and proposed a QuasiOppositional Chaotic Equilibrium Optimizer (QOCEO) that consists of Quasi-Opposition based learning for improving the scalability, Chaotic Time Parameter for ensuring a proper balance between exploration and exploitation, and Chaotic Local Search for reducing the local stagnation. The performance of QOCEO and several contemporary metaheuristics have been evaluated on 96 benchmark functions (including classical benchmark, CEC-2017, CEC-2019, CEC-2020 and CEC2022) and six constrained engineering optimization problems employing several statistical tests. The average rank Friedman test confirms that for all 96 benchmark functions, QOCEO outperforms CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA, SPS_L_SHADE_EIG, SHADE by 88%, 83%, 49%, 35%, 27%, 18% and 5%, respectively. Comparing the results of Bonferroni-Dunn and Holm's tests, QOCEO outperforms PSO, GWO, EO, HGSO, SSA, and GSA for classical benchmark functions with 30, 100, 300, and 500 dimensions. Further, QOCEO outperform CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA for all 96 benchmark functions and statistically similar to SPS_L_SHADE_EIG, SHADE and EBOwithCMAR.