Accurate and robust brain tumor segmentation remains a critical challenge in medical image analysis due to high inter-patient variability, complex tumor morphology, and modality-specific noise in MRI scans. This study proposes PSO-GA-U-Net, a novel hybrid deep learning framework that integrates Particle Swarm Optimization (PSO) and Genetic Algorithms (GA) to optimize the U-Net architecture for enhanced segmentation performance and generalization. PSO dynamically tunes the learning rate to accommodate modality-specific variations, while GA adaptively regulates dropout to improve feature diversity and reduce overfitting. The model is evaluated on three benchmark datasets---FBTS, BraTS 2021, and BraTS 2018---using five-fold cross-validation. PSO-GA-U-Net achieves Dice Similarity Coefficients (DSC) of 0.9587, 0.9406, and 0.9480, and Jaccard Index (JI) scores of 0.9209, 0.8881, and 0.9024, respectively, consistently outperforming state-of-the-art models in both overlap accuracy and boundary delineation. Statistical tests confirm that these improvements are significant across folds ($p< 0.05$). Visual heatmaps further illustrate the model's ability to preserve structural integrity across tumor types and modalities. These results indicate that metaheuristic-guided deep learning offers a promising and clinically applicable solution for automatic tumor segmentation in radiological workflows.