Quadcopter swarm flight is of great significance in light displays, exploratory missions, and aerial surveillance. However, trajectory optimization and target assignment are accompanied by challenges such as collision avoidance, stability preservation, and achieving rapid convergence. In this study, a centralized control framework is proposed in which a central decision-making unit is responsible for target allocation, path generation, and enforcing safety constraints for the entire flying swarm. Within this framework, an improved hybrid algorithm based on particle swarm optimization and physics-based learning optimizes the trajectory, target assignment, and coordination of quadcopter swarms. The aim of this method is to enhance convergence speed and search stability by combining the capabilities of the two algorithms. In the proposed structure, the particle swarm optimization algorithm serves as the global exploration component, while the physics-based learning algorithm, leveraging the concepts of energy and momentum, dynamically adjusts particle positions to prevent entrapment in local minima. Simulation results confirm the superiority of the hybrid method over the independent algorithms in terms of convergence speed, accuracy, stability, and computational efficiency.