Route-Phasing-Split-Encoded Genetic Algorithm for Multi-Satellite On-Orbit Servicing Mission Planning

This article addresses multi-servicer on-orbit servicing mission planning in geosynchronous Earth orbit, where routing decisions are tightly coupled with time-dependent orbital phasing and strict propellant and mission-duration constraints. We propose a Route-Phasing-Split Genetic Algorithm (RPS-GA) that simultaneously optimizes target sequencing, discrete phasing rotation decisions (i.e., the number of phasing revolutions/waiting cycles), and route partitioning across multiple servicing spacecrafts (SSCs). An RPS triplet chromosome encodes route order, phasing rotations, and route splits in a unified structure, enabling split-aware recombination without disrupting feasible multi-servicer route blocks. Feasibility is enforced through a constraint-aware fitness function that ranks feasible solutions based on total $\Delta V$, while penalizing propellant and mission duration violations, using aggregate and imbalance penalties. This formulation discourages the concentration of violations on a single servicing spacecraft (SSC). Once a feasible best solution is identified, it is preserved as feasible in subsequent generations, thereby enhancing convergence stability. The framework incorporates split-aware crossover, mutation and a regret-based Large Neighborhood Search for local intensification. Experiments on representative GEO servicing scenarios demonstrate that RPS-GA produces feasible multi-servicer plans with substantially improved fuel efficiency, reducing total $\Delta V$ by $24.5\%$, (from $1956.36 \ m/s$ to $1476.32\ m/s$) compared with a state-of-the-art LNS-AGA baseline.