Quantum-Inspired Evolutionary Optimization for Optimal Re-Orbital Entry Trajectory Planning in Support of In-Orbit Satellite Refueling Missions

Trajectory optimization for reusable launch vehicles is a critical challenge in space mission design, aiming to determine fuel-efficient paths for spacecraft during ascent, hover, and descent phases. Minimizing fuel consumption not only enhances cost-effectiveness but also improves mission sustainability. The optimization process is governed by nonlinear orbital mechanics, gravitational perturbations, atmospheric drag, and operational constraints such as thrust limits and collision avoidance. These factors make the problem highly nonconvex and discontinuous, posing significant difficulties for classical gradient-based approaches, which often fail to identify global optima. In this work, we formulate the trajectory optimization problem for a reusable rocket executing an ascent–hover–descent cycle. The vehicle must ascend to a specified target altitude, maintain a stable hover for a given duration, and then return to the launch site. The primary decision variable is the throttle control profile, which is represented as a vector of throttle settings over a discretized time horizon and governs thrust levels throughout all flight phases. The objective is to minimize total fuel consumption while satisfying all physical and operational constraints. To address the problem’s complexity, we employ the BQPhy platform, which implements Quantum-Inspired Evolutionary Optimization (QIEO). This metaheuristic approach efficiently explores the search space, overcoming the limitations of traditional methods. Comparative analysis with a classical Genetic Algorithm (GA) shows that the QIEO-based method delivers solutions 5–10 times faster while achieving superior fuel-optimal trajectories. The proposed approach highlights the potential of quantum-inspired optimization for high-dimensional, nonlinear aerospace trajectory design problems, offering a promising solution for enhancing the efficiency of reusable spaceflight operations.