A Multi-Objective Sine Cosine Algorithm Based on a Competitive Mechanism and Its Application in Engineering Design Problems

There are a lot of multi-objective optimization problems (MOPs) in the real world, and many multi-objective evolutionary algorithms (MOEAs) have been presented to solve MOPs. However, obtaining non-dominated solutions that trade off convergence and diversity remains a major challenge for a MOEA. To solve this problem, this paper designs an efficient multi-objective sine cosine algorithm based on a competitive mechanism (CMOSCA). In the CMOSCA, the ranking relies on non-dominated sorting, and the crowding distance rank is utilized to choose the outstanding agents, which are employed to guide the evolution of the SCA. Furthermore, a competitive mechanism stemming from the shift-based density estimation approach is adopted to devise a new position updating operator for creating offspring agents. In each competition, two agents are randomly selected from the outstanding agents, and the winner of the competition is integrated into the position update scheme of the SCA. The performance of our proposed CMOSCA was first verified on three benchmark suites (i.e., DTLZ, WFG, and ZDT) with diversity characteristics and compared with several MOEAs. The experimental results indicated that the CMOSCA can obtain a Pareto-optimal front with better convergence and diversity. Finally, the CMOSCA was applied to deal with several engineering design problems taken from the literature, and the statistical results demonstrated that the CMOSCA is an efficient and effective approach for engineering design problems.

Adaptive binary multi-objective harmony search algorithm for channel selection and cross-subject generalization in motor imagery-based BCI

OBJECTIVE

Multi-channel EEG data containing redundant information and noise may result in low classification accuracy and high computational complexity, which limits the practicality of motor imagery-based BCI systems. Therefore, channel selection can improve BCI performance and contribute to user convenience. Additionally, cross-subject generalization is a key topic in the channel selection of motor imagery-based BCI.

APPROACH

In this study, an adaptive binary multi-objective harmony search (ABMOHS) algorithm is proposed to select the optimal set of channels. Furthermore, a new adaptive crosssubject generalization model (ACGM) is proposed. Three public motor imagery datasets were used to validate the effectiveness of the proposed method.

MAIN RESULTS

The Wilcoxon signed-rank test was performed on the test accuracies, and the results indicated that the ABMOHS method significantly outperformed all channels (p<0.001), the C3-Cz-C4 channels (p<0.001), and 20 channels (p<0.001) in the sensorimotor cortex. The ABMOHS algorithm based on Fisher's linear discriminant analysis (FLDA) and support vector machine (SVM) classifiers greatly reduces the number of selected channels, especially for larger channel sizes (Dataset 2), and obtains a comparative classification performance. Although there was no significant difference in test classification performance between ABMOHS and non-dominated sorting genetic algorithm II (NSGA-II) when FLDA and SVM were used, ABMOHS required less computational time than NSGA-II. Furthermore, the number of channels obtained by ABMOHS algorithm were significantly smaller than those obtained by CSP-Rank and correlation-based channel selection algorithm (CCS). Additionally, the generalization of ACGM to untrained subjects shows that the mean test classification accuracy of ACGM created by a small sample of trained subjects is significantly better than that of Special-16 and Special-32.

SIGNIFICANCE

The proposed method can reduce the calibration time in the training phase and improve the practicability of MI-BCI.