## 3 Method
### Local Attention Mechanism  
The decoding process of the neural network is dynamic, and every time, one task is selected through an attention mechanism according to the static encoding information and the current dynamic encoding information, which utilizes auto-regression. The attention mechanism is adopted to calculate the probability distribution of candidate tasks, and that with the highest probability is selected. In this process, the selection order of tasks represents their execution order. Notably, the unreasonable sorting order can form a low-quality solution. In the previous research [30; 31; 32], a global attention mechanism is adopted to calculate the probability distribution of all unselected tasks and make neural networks focus on the essential parts of global task information. However, as the scale of the problem expands, the length of the task sequence also becomes longer, making it more difficult for the global attention mechanism to find out the best candidate task quickly and accurately at every decoding step. In the early training process, the neural network has not formed the optimal decision policy, which is highly likely to generate unreasonable sorting orders. Once the task that should have been executed last is selected first, others will lose the opportunity to be executed. For example, Figure 3 shows several VTWs of five tasks in the four orbits. The orbit \(o_{2}\) is not considered since no VTW exists in this orbit. As shown in Figure 4a, the global attention mechanism is applied to this example, and all the unselected tasks are included in the candidate range at every decoding step. If \(t_{4}\) is selected to be executed in the VTW \(w_{4}^{1}\), the tasks without later VTWs will have no chance to be completed, and \(t_{1}\) and \(t_{2}\) will be abandoned, which could have been executed in the previous orbits. Owing to the tendency to generate unseasonable sorting orders, it is hard for the global attention mechanism to generate great solutions in the training process, making it difficult for the neural network to learn excellent experiences and further influencing the training effect. Figure 3: VTWs of five tasks in the four orbits. To avoid these deficiencies, we propose a local attention mechanism that reduces the range of candidate tasks and focuses on the local task information. An ideal scheduling solution can fully utilize orbit resources and arrange as many feasible tasks as possible in an orbit without causing conflicts. Thus, the range of candidate tasks is limited to the current several orbital cycles at every decoding step, and the local attention mechanism only considers the unselected tasks that satisfy the condition of having VTWs in this local range. The local attention is set to only consider the unselected tasks with VTWs in the current orbit or the next one at every decoding step. As illustrated in Figure 4b, the local attention is employed for the above example. Only \(t_{1}\), \(t_{2}\), \(t_{3}\), and \(t_{5}\), which have VTWs in \(o_{1}\) or \(o_{3}\), are taken into account at the first decoding step. If no unselected tasks have VTWs in the current orbit, those with VTWs in the following two orbits will be considered. If there is only one orbit left, the local attention will only need to focus on the left tasks in this orbit. In this way, the scheduling solutions can be significantly improved. For one thing, it is easier to find the best candidate task within a local range. For another, the observation time of the next task can be arranged close to that of the previous one, preventing some tasks from losing their observation opportunities. In the proposed local attention mechanism, only the conditional probabilities of partial tasks need to be calculated. Let \(LS_{n}\) be the set of encoded static elements of tasks meeting the above condition at the decoding step \(n\), and \(|LS_{n}|\) is the number of these tasks.