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

翻译：本研究探讨如何利用图神经网络（GNNs）更高效地调度纳卫星任务。在离线纳卫星任务调度（ONTS）问题中，目标是找到在轨执行任务的最优调度方案，同时考虑服务质量（QoS）因素，如优先级、最小与最大激活次数、执行时间框架、周期和执行窗口，以及卫星电力资源约束和能量收集与管理的复杂性。传统上，ONTS问题通过常规数学建模和精确方法求解，但其在复杂案例中的适用性有限。本研究考察了GNNs在此场景中的应用——该技术已成功应用于旅行商问题、调度问题及设施布局问题等优化任务。具体而言，我们探究GNNs能否学习ONTS问题中候选解可行性与最优性的复杂结构。此外，我们评估了基于GNN的启发式求解方法在ONTS问题中提供更优解（就目标值而言）并降低优化成本的能力。实验表明，GNNs不仅能学习ONTS问题实例的可行性与最优性，还能泛化至比训练时更复杂的实例。与默认配置下的SCIP（约束整数规划求解器）相比，基于GNN的启发式方法在时间限制内将最优解的期望目标值提升了45%，并将找到可行解的期望时间缩短了35%。