The complexity of Deep Neural Networks (DNNs) has driven advancements in Neural Architecture Search (NAS), Hyperparameter Optimization (HPO), and Learning Rule Optimization (LRO). This study reviews heuristic methodologies, focusing on Evolutionary Algorithms (EAs) and Swarm Intelligence (SI). We analyze Genetic Algorithms (GAs), Particle Swarm Optimization (PSO), and Multi-Objective Optimization (MOO), emphasizing the Biased Random Key Genetic Algorithm (BRKGA). BRKGA encodes neural architectures and hyperparameters as continuous vectors, enhancing search efficiency in NAS and HPO. We evaluate BRKGA on Feedforward Neural Networks (FNNs), Convolutional Neural Networks (CNNs), and Graph Neural Networks (GNNs), demonstrating their effectiveness in tuning learning rates, dropout rates, and batch sizes. Additionally, we explore its role in LRO, optimizing adaptive weight updates and gradient modulation. Experiments on benchmark datasets show that BRKGA consistently yields promising architectures and hyperparameter configurations, balancing accuracy, efficiency, and adaptability. Our findings highlight BRKGA as a viable alternative for NAS, HPO, and LRO, particularly in complex search spaces where structured exploration is essential. Finally, challenges in heuristic-driven NAS, HPO, and AutoML are examined, along with future research directions in scalable optimization, adaptive learning mechanisms, and neuromorphic computing.