Hybrid Direct–Indirect Optimization of Low-Thrust Earth–Mars Transfer Trajectories Using Vectorized Particle Swarm Algorithms

This study addresses the optimization of low-thrust Earth–Mars orbital transfer trajectories under complex dynamical constraints. To overcome the limitations of conventional direct or indirect methods, a hybrid optimization framework integrates direct trajectory initialization, vectorized particle swarm optimization (VPSO), and co-state-based indirect refinement. The three-dimensional transfer model systematically incorporates propulsion constraints, co-state variable initialization, and multi-algorithm synergy, with direct methods generating initial guesses for subsequent VPSO-enhanced global exploration and indirect precision optimization. Numerical experiments confirm the framework’s convergence properties and computational stability under varying mission parameters. Compared to standalone optimization approaches, the hybrid strategy demonstrates superior solution quality in escaping local optima while maintaining computational efficiency.