Abstract: Very Low Earth Orbit (VLEO) satellites offer inherent advantages for high-resolution earth observation and low-latency communication. However, the exponential increase in atmospheric density at these altitudes creates severe aerodynamic drag and atomic oxygen erosion, critically limiting orbital lifetimes. Air-Breathing Electric Propulsion (ABEP) emerges as a disruptive solution theoretically enabling ultra-long orbital lifecycles by utilizing atmospheric molecules as propellant. The operational efficacy of ABEP systems relies heavily on the synergistic design of the air intake and the satellite's aerodynamic configuration. Addressing the prohibitive computational costs and multi-parameter coupling in rarefied flow simulations, this paper proposes an efficient multi-objective optimization framework. First, a parametric geometric model comprising a parabolic intake, a cylindrical satellite body, and solar arrays is established. To overcome the high time costs of Direct Simulation Monte Carlo (DSMC), the framework introduces an improved Automatic Kernel Construction Gaussian Process Regression (AKC-GPR) method. By replacing traditional greedy search with a beam search strategy, this approach significantly enhances global search capabilities, accurately fitting high-fidelity data ( R^2> 0.92 ) with small sample sizes. Subsequently, a comprehensive multi-objective optimization is conducted by coupling this surrogate model with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Sensitivity analysis reveals that the intake outlet radius and flow path length are dominant factors, supporting a "short body, long channel, large contraction ratio" design philosophy. Compared to the baseline, the optimized configuration achieves a 40.55% reduction in aerodynamic drag, while simultaneously increasing intake collection efficiency by 24.74% and the compression ratio by 31.11%. In-orbit validation confirms that the thrust-to-drag ratio improves from a critical 0.98 to 1.69, successfully surpassing the thrust-drag balance threshold. Furthermore, orbital dynamics analysis validates the feasibility of stable operations in a 176 km circular orbit and elliptical missions with a perigee as low as 146 km. These findings provide a robust theoretical basis and a reproducible engineering design workflow for future long-endurance VLEO platforms.