Continuous Hopfield Network (CHN) is a recurrent neural network model widely used in various fields such as optimization, operations research, image restoration, economics, and electronic circuit design. Inspired by biological neural networks, CHNs operate by minimizing an energy function, which results in stable states called attractors. The penalty parameters, integrated into the energy function, and the hyperparameters, which significantly influence the convergence of the network, are at the heart of CHN performance. In this study, we explore hyperparameter selection methods, particularly focusing on metaheuristics such as genetic algorithms, ant colony optimization, and particle swarm optimization. Our research evaluates the effectiveness of these methods in optimizing CHN hyperparameters using Graph Coloring Problem instances as a reference. Through a series of experiments, we aim to provide insight into the strengths of metaheuristic approaches for CHN hyperparameter optimization, thereby improving the practical applicability and performance of Hopfield networks.