There exist many multi-objective optimization problems (MOPs) containing several inequality and equality constraints in practical applications, which are known as CMOPs. CMOPs pose great challenges for existing multi-objective evolutionary algorithms (MOEAs) since the difficulty in balancing the objective minimization and constraint satisfaction. Without loss of generality, the distribution of the Pareto set for a continuous m-objective CMOP can be regarded as a piecewise continuous manifold of dimension (m − 1). According to this property, a self-organizing map (SOM) approach for constrained multi-objective optimization problems is proposed in this article. In the proposed approach, we adopt the strategy of two population evolution, in which one population is evolved by considering all the constraints and the other population is used to assist in exploring the areas. In the evolutionary stage, each population is assigned a self-organizing map for discovering the population distribution structure in the decision space. After the topological mapping, we utilize the extracted neighborhood relationship information to generate promising offspring solutions. Afterwards, the neuron weight vectors of SOM are updated by the objective vectors of the surviving offsprings. Through the proposed approach, we can make the population efficiently converge to the feasible region with suitable levels of diversity. In the experiments, we compare the proposed method with several state-of-the-art approaches by using 48 benchmark problems. The evaluation results indicate that the overwhelmingly superior performance of the proposed method over the other peer algorithms on most of the tested problems. The source code is available at https://github.com/hccccc92918/CMOSMA.

Though the accuracy and robustness of optical flow has been dramatically enhanced over the past few years, the issue of edge-blurring near the image and motion boundaries has remained a challenge in flow field estimation. In this paper, we propose a refined total variation with L1 norm (TV-L1) optical flow estimation approach using joint filtering, named JOF. First, we divide the image into three categorized regions: mutual-structure regions, inconsistent structure regions and smooth regions. The mutual-structure guided filter for optical flow estimation is constructed by extracting the mutual- structure regions of the flow field. Second, the refined TV-L1 optical flow model is proposed by incorporating the non-local term and mutual-structure guided filter objective function into the classical TV-L1 energy function. Furthermore, the novel TV-L1 optical flow objective function is minimized using a joint filtering program composed of a weighted median filter and a mutual-structure guided filter to optimize the estimated flow field during the coarse-to-fine optical flow computation scheme. Finally, we compare the proposed JOF method with several state-of-the-art approaches including variational and deep learning based optical flow models using the Middlebury, MPI-Sintel and UCF101 test databases. The evaluation results indicate that the proposed method has high accuracy and good robustness for flow field computation, especially owns the significant benefit of edge-preserving.

Although multiobjective particle swarm optimizers (MOPSOs) have performed well on multiobjective optimization problems (MOPs) in recent years, there are still several noticeable challenges. For example, the traditional particle swarm optimizers are incapable of correctly discriminating between the personal and global best particles in MOPs, possibly leading to the MOPSOs lacking sufficient selection pressure toward the true Pareto front (PF). In addition, some particles will be far from the PF after updating, this may lead to invalid search and weaken the convergence efficiency. To address the abovementioned issues, we propose a competitive swarm optimizer with probabilistic criteria for many-objective optimization problems (MaOPs). First, we exploit a probability estimation method to select the leaders via the probability space, which ensures the search direction to be correct. Second, we design a novel competition mechanism that uses winner pool instead of the global and personal best particles to guide the entire population toward the true PF. Third, we construct an environment selection scheme with the mixed probability criterion to maintain population diversity. Finally, we present a swarm update strategy to ensure that the next generation particles are valid and the invalid search is avoided. We employ various benchmark problems with 3–15 objectives to conduct a comprehensive comparison between the presented method and several state-of-the-art approaches. The comparison results demonstrate that the proposed method performs well in terms of searching efficiency and population diversity, and especially shows promising potential for large-scale multiobjective optimization problems.

In recent years, the integration of brain–computer interface technology and neural networks in the field of music generation has garnered widespread attention. These studies aimed to extract individual-specific emotional and state information from electroencephalogram (EEG) signals to generate unique musical compositions. While existing research has focused primarily on brain regions associated with emotions, this study extends this research to brain regions related to musical composition. To this end, a novel neural network model incorporating attention mechanisms and steady-state activation mapping (SSAM) was proposed. In this model, the self-attention module enhances task-related information in the current state matrix, while the extended attention module captures the importance of state matrices over different time frames. Additionally, a convolutional neural network layer is used to capture spatial information. Finally, the ECA module integrates the frequency information learned by the model in each of the four frequency bands, mapping these by learning their complementary frequency information into the final attention representation. Evaluations conducted on a dataset specifically constructed for this study revealed that the model surpassed representative models in the emotion recognition field, with recognition rate improvements of 1.47% and 3.83% for two different music states. Analysis of the attention matrix indicates that the left frontal lobe and occipital lobe are the most critical brain regions in distinguishing between ‘recall and creation’ states, while FP1, FPZ, O1, OZ, and O2 are the electrodes most related to this state. In our study of the correlations and significances between these areas and other electrodes, we found that individuals with musical training exhibit more extensive functional connectivity across multiple brain regions. This discovery not only deepens our understanding of how musical training can enhance the brain’s ability to work in coordination but also provides crucial guidance for the advancement of brain–computer music generation technologies, particularly in the selection of key brain areas and electrode configurations. We hope our research can guide the work of EEG-based music generation to create better and more personalized music.

Because of the high cost of experimental data acquisition, the limited size of the sample set available when conducting tissue structure ultrasound evaluation can cause the evaluation model to have low accuracy. To address such a small-sample problem, the sample set size can be expanded by using virtual samples. In this study, an ultrasound evaluation method for the primary α phase grain size based on the generation of virtual samples by a generative adversarial network (GAN) was developed. TC25 titanium alloy forgings were treated as the research object. Virtual samples were generated by the GAN with a fully connected network of different sizes used as the generator and discriminator. A virtual sample screening mechanism was constructed to obtain the virtual sample set, taking the optimization rate as the validity criterion. Moreover, an ultrasound evaluation optimization problem was constructed with accuracy as the target. It was solved by using support vector machine regression to obtain the final ultrasound evaluation model. A benchmark function was adopted to verify the effectiveness of the method, and a series of experiments and comparison experiments were performed on the ultrasound evaluation model using test samples. The results show that the learning accuracy of the original small samples can be increased by effective virtual samples. The ultrasound evaluation model built based on the proposed method has a higher accuracy and better stability than other models.

Existing self-supervised monocular depth estimation methods usually explore increasingly large networks to achieve accurate estimation results. However, larger networks are more difficult to train and require more storage space. To balance the network size and the computational accuracy, we propose in this article a compact lightweight network for monocular depth estimation, named LW-Net. First, we construct a compact network by designing an iterative decoder with shared weights and a lightweight pyramid encoder. The proposed network includes significantly fewer parameters than most of the existing monocular depth estimation networks. Second, we exploit a self-supervised training strategy by combining the proposed LW-Net model with a pose network, and we then use a hybrid loss function to train the decoder and encoder separately. The proposed training strategy results in the LW-Net model achieving a better performance in terms of estimation accuracy than other methods. Finally, we respectively run the proposed LW-Net model on the KITTI and Make3D datasets to conduct a comprehensive comparison with several state-of-the-art methods. The experimental results demonstrate that our method performs the best in terms of computational accuracy while utilizing the fewest parameters. Specifically, the model parameters of our method are reduced by 46.6%, the time cost is decreased by 7.69%, and the frame rate is increased by 5.19% compared with the existing state-of-the-art method.