An Integer Programming Approach to Observation Scheduling for Space Domain Awareness

Satellites underpin all economic, military, and scientific activity in space. Ground-based telescope observations provide much of the tracking information that enables collision avoidance and space traffic management, but recent growth in the size and dynamism of the satellite population divides the available observing capacity between multiple competing observation objectives. The task of selecting an optimal assignment of telescope observing capacity to observation objectives is NP-hard and involves domain-specific considerations such as sequence-dependent transition times, observability constraints, occlusion avoidance, and astrodynamic limitations. These features conspire to prevent direct and efficient application of traditional scheduling approaches over long time horizons.This work maps the task of scheduling ground-based sensor observations to an unrelated parallel machine scheduling problem with sequence-dependent transition times, restricted time windows, and a fixed time horizon. We contribute an integer programming model of the task, complete with inequality formulations of domain-specific constraints, and a decomposition algorithm that discovers reward-optimal schedules. Using the open-source CBC solver, the integer programming model can reliably be solved for problem instances with up to 6 sensors and 40 targets for a 4 minute time horizon within an equal runtime limit. To address more challenging problem instances, we propose a decomposition algorithm that supports early termination and returns suboptimal schedules along with an associated optimality gap for instances with up to 6 sensors and 200 targets over a 15 minute time horizon.