  This study investigates how to schedule nanosatellite tasks more efficiently
using Graph Neural Networks (GNNs). In the Offline Nanosatellite Task
Scheduling (ONTS) problem, the goal is to find the optimal schedule for tasks
to be carried out in orbit while taking into account Quality-of-Service (QoS)
considerations such as priority, minimum and maximum activation events,
execution time-frames, periods, and execution windows, as well as constraints
on the satellite's power resources and the complexity of energy harvesting and
management. The ONTS problem has been approached using conventional
mathematical formulations and exact methods, but their applicability to
challenging cases of the problem is limited. This study examines the use of
GNNs in this context, which has been effectively applied to optimization
problems such as the traveling salesman, scheduling, and facility placement
problems. More specifically, we investigate whether GNNs can learn the complex
structure of the ONTS problem with respect to feasibility and optimality of
candidate solutions. Furthermore, we evaluate using GNN-based heuristic
solutions to provide better solutions (w.r.t. the objective value) to the ONTS
problem and reduce the optimization cost. Our experiments show that GNNs are
not only able to learn feasibility and optimality for instances of the ONTS
problem, but they can generalize to harder instances than those seen during
training. Furthermore, the GNN-based heuristics improved the expected objective
value of the best solution found under the time limit in 45%, and reduced the
expected time to find a feasible solution in 35%, when compared to the SCIP
(Solving Constraint Integer Programs) solver in its off-the-shelf configuration
