Hybrid Optimization Technique for Finding Efficient Earth–Moon Transfer Trajectories

The Lunar Gateway is a planned small space station that will orbit the Moon and serve as a central hub for NASA’s Artemis program to return humans to the lunar surface and to prepare for Mars missions. This work presents a hybrid optimization strategy for designing minimum-fuel transfers from an Earth orbit to a Lunar Near-Rectilinear Halo Orbit. The corresponding optimal control problem—crucial for missions to NASA’s Lunar Gateway—is characterized by a high-dimensional, non-convex solution space due to the multi-body gravitational environment. To tackle this challenge, a two-stage hybrid optimization scheme is employed. The first stage uses a Genetic Algorithm heuristic as a global search strategy, to identify promising feasible trajectory solutions. Subsequently, the initial solution guess (or guesses) produced by GA are improved by a local optimizer based on a Sequential Quadratic Programming method: from a suitable initial guess, SQP rapidly converges to a high-precision feasible solution. The proposed methodology is applied to a representative cargo mission case study, demonstrating its efficiency. Our numerical results confirm that the hybrid optimization strategy can reliably generate mission-grade quality trajectories that satisfy stringent constraints while minimizing propellant consumption. Our analysis validates the combined GA-SQP optimization approach as a robust and efficient tool for space mission design in the cislunar environment.