Motor imagery (MI) analysis from EEG signals constitutes a class of emerging brain-computer interface (BCI) applications that face EEG's predominant complexities arising from the multitude of channels and the vast number of possible features. This study presents a two-step multiobjective set-based integer-coded fuzzy-initialized evolutionary algorithm (MOSIFE) for efficient EEG-based MI signal analysis. The two-step process is a non-dominant wrapper strategy that sequentially identifies the optimal channels and the minimal set of features, thereby reducing MI's combinatorial search complexity. We also employ a reptile-based search algorithm (RSA), a recent metaheuristic for efficient search in multimodal continuous domains, to optimize the classifier's hyper-parameters. The proposed MOSIFE-RSA algorithm is benchmarked against 12 representative algorithms on four standard BCI Competition databases, including IV-I, III-IVa, III-IIIa, and II. The results show that MOSIFE-RSA improves accuracy by 20%, with channel selection contributing as much as 15% and feature selection as much as 5% towards these results. Furthermore, it reduces computational complexity by 81% through channel selection and 16% through feature selection, demonstrating its effectiveness in advancing EEG-based MI signal analysis. This research has practical implications for developing more accurate and efficient brain-computer interface systems.

Filters and wrappers represent two mainstream approaches to feature selection (FS). Although evolutionary wrapper-based FS outperforms filters in addressing real-world classification problems, extending these methods to high-dimensional, many-objective optimization problems with imbalanced data poses substantial challenges. Overcoming computational costs and identifying suitable performance metrics are vital for navigating search operation complexities. Here, we propose using the Jaccard similarity (JS) in a set-based evolutionary many-objective (JSEMO) FS search, addressing both evolutionary FS and imbalanced classifier choice concurrently. This study highlights the mutual influence between these aspects, impacting overall algorithm performance. JSEMO integrates JS into population initialization, reproduction, and elitism steps, enhancing diversity and avoiding duplicate solutions. The set-based variation operator utilizes intersection and union operators for compatibility with binary coding. We also introduce a double-weighted KNN (KNN2W) classifier with four supportive objectives as a many-objective FS problem to handle imbalanced distributions. Compared with 20 methods on 15 benchmark problems, JSEMO produces distinct optimal features, significantly improving overall accuracy, balance accuracy, and g-mean metrics with comparable feature set size and computational cost. The ablation study underscores the positive impact of all JSEMO components, highlighting the set-based variation operation with JS and KNN2W with relevant evaluation metrics as the most influential aspects.