We present a general survey on the base and the combinatorial classification methods for EEG signals (sensory motor rhythm and event-related potentials) as well as their optimization methods through the evolutionary algorithms. In addition, experimental and statistical significance tests are carried out to study the applicability and effectiveness of the reviewed methods.

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 estimationbased 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.

Hybrid multi-objective evolutionary algorithms have recently become a hot topic in the domain of metaheuristics. Introducing new algorithms that inherit other algorithms' operators and structures can improve the performance of the algorithm. Here, we proposed a hybrid multi-objective algorithm based on the operators of the genetic algorithm (GA) and teaching learning-based optimization (TLBO) and the structures of reference point-based (from NSGA-III) and R2 indicators methods. The new algorithm (R2-HMTLBO) improves diversity and convergence by using NSGA-III and R2-based TLBO, respectively. Also, to enhance the algorithm performance, an elite archive is proposed. The proposed multi-objective algorithm is evaluated on 19 benchmark test problems and compared to four state-of-the-art algorithms. IGD metric is applied for comparison, and the results reveal that the proposed R2-HMTLBO outperforms MOEA/D, MOMBI-II, and MOEA/IGD-NS significantly in 16/19 tests, 14/19 tests and 13/19 tests, respectively. Furthermore, R2-HMTLBO obtained considerably better results compared to all other algorithms in 4 test problems, although it does not outperform NSGA-III on a number of tests. CCS CONCEPTS• Theory of computation → Bio-inspired optimization; Evolutionary algorithms.

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