This study investigates how to schedule nanosatellite tasks more efficiently using Graph Neural Networks (GNN). 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 precise 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 many optimization problems, including traveling salesman problems, scheduling problems, and facility placement problems. Here, we fully represent MILP instances of the ONTS problem in bipartite graphs. We apply a feature aggregation and message-passing methodology allied to a ReLU activation function to learn using a classic deep learning model, obtaining an optimal set of parameters. Furthermore, we apply Explainable AI (XAI), another emerging field of research, to determine which features -- nodes, constraints -- had the most significant impact on learning performance, shedding light on the inner workings and decision process of such models. We also explored an early fixing approach by obtaining an accuracy above 80\% both in predicting the feasibility of a solution and the probability of a decision variable value being in the optimal solution. Our results point to GNNs as a potentially effective method for scheduling nanosatellite tasks and shed light on the advantages of explainable machine learning models for challenging combinatorial optimization problems.

翻译：本研究探讨如何更高效地利用图神经网络（GNN）调度纳米卫星任务。在离线纳米卫星任务调度（ONTS）问题中，目标是在考虑服务质量（QoS）因素（如优先级、最小和最大激活事件、执行时间框架、周期和执行窗口）以及卫星功率资源约束与能量收集管理复杂性的前提下，找到在轨执行任务的最优调度方案。传统数学公式与精确方法已被用于解决ONTS问题，但其在复杂情况下的适用性有限。本研究考察了GNN在该场景中的应用——此类网络已有效应用于旅行商问题、调度问题及设施选址问题等多种优化场景。我们采用二分图完整表征ONTS问题的混合整数线性规划（MILP）实例，通过特征聚合与消息传递方法，结合ReLU激活函数，利用经典深度学习模型进行学习，获得最优参数集。此外，我们应用可解释人工智能（XAI）这一新兴研究领域，识别对学习性能影响最显著的特征（节点与约束），揭示此类模型的内部运作机制与决策过程。我们还探索了早期固定方法，在预测解的可行性与决策变量值属于最优解的概率时均获得超过80%的准确率。结果表明，GNN是调度纳米卫星任务的潜在有效方法，并为可解释机器学习模型在复杂组合优化问题中的优势提供了新见解。