R2-HMEWO: Hybrid multi-objective evolutionary algorithm based on the Equilibrium Optimizer and Whale Optimization Algorithm

Multi-objective evolutionary algorithms can be categorized into three basic groups: domination-based, decomposition-based, and indicator-based algorithms. Hybrid multi-objective evolutionary algorithms, which combine algorithms from these groups, are gaining increased popularity in recent years. This is because hybrid algorithms can compensate for the drawbacks of the basic algorithms by adding different operators and structures that complement each other. This paper introduces a hybrid-multi objective evolutionary algorithm (R2-HMEWO) that applies hybridization in the form of structure and operators. R2-HMEWO is based on the whale optimization algorithm (WOA) and equilibrium optimizer (EO). Elite individuals of WOA and EO are selected from a repository based on the R2-indicator and shifted density estimation-based method. In order to improve solutions' diversity, a reference points method is devised to select next-generation individuals. The proposed multi-objective algorithm is evaluated on 19 benchmark test problems (ZDT, DTLZ, and CEC009) and compared with six state-of-the-art (SOTA) algorithms (NSGA-III, NSGA-II, MOEA/D, MOMBI-II, MOEA/IGD-NS, and dMOPSO). Based on the inverted generational distance (IGD) metric (mean of 25 independent runs), R2-HMEWO outperformed other algorithms on 14 out of 19 test problems and revealed a highly competitive performance on the other test problems. Also, R2-HMEWO performed statistically significant better than MOEA/D and dMOPSO in 15/19 and 14/19 test problems, respectively (p < 0.05), and reached significant performance in 4 test problems (from ZDT and CEC09) compared to other algorithms.