## 3 Method
### Architecture of the Proposed Neural Network  
The architecture of the proposed neural network is depicted in Figure 2, which is an end-to-end framework with an encoder-decoder structure. The neural network is composed of five components: a static embedding layer, a static encoder, a dynamic embedding layer, a dynamic encoder and a decoder. In addition, a local attention mechanism is proposed to improve the generation of solutions. In the general SAOSSP, given a set of tasks \(T=\{t_{i}|i=1,\cdots,|T|\}\), the neural network is used as the policy network to extract features from inputs and generate a permutation of the executable tasks and a corresponding observation action sequence in an auto-regression way, both of which compose the solution of the problem. The inputs of this problem comprise two parts: task information and satellite state information. Task information is static and consists of time window information and requirement information. For the task \(t_{i}\), its time window information is denoted by a set \(WX_{i}=\left\{wx_{i}^{k}=\left[c_{i}^{k},est_{i}^{k},lst_{i}^{k},px_{i}^{k},pn_ {i}^{k},r_{i}^{k}\right]\middle|k=1,\cdots,|W_{i}|\right\}\), and its requirement information is denoted by a vector \(R_{i}=[d_{i},p_{i}]\). Satellite state information is dynamic and changes every time a task is executed. After the AOS executes the task \(t_{i}\) through the observation action \(a_{i}^{k}\), its state information is denoted as a vector \(s_{n}=[c_{i}^{k},get_{i}^{k},pq_{i}^{k},ra_{i}^{k},mr_{i},er_{i}]\), where \(n\) is the step number and the observation end time \(get_{i}^{k}\) is also the start time of the free state. The output permutation of the executable tasks is denoted as \(\{i_{n}|n=1,\cdots,N\}\), where \(i_{n}\) is the task index and \(N\) is the length of output permutation. Accordingly, the observation action sequence of the AOS is \(A=\{a_{i_{n}}^{k_{n}}|n=1,\cdots,N\}\). Obviously, the elements of \(s_{n}\) can be obtained in \(a_{i_{n}}^{k_{n}}\). To better utilize the above input information, the designed neural network must be able to process both static and dynamic information simultaneously. Therefore, the proposed neural network adopts a static embedding layer and a static encoder to handle the static inputs and a dynamic embedding layer and a dynamic encoder to deal with the dynamic inputs on the basis of the basic encoder-decoder structure. The above inputs have been normalized before they are formally inputted. Formally, the set of inputs is denoted as \(X=\{tx^{i}|i=1,\cdots,|T|\}\). Each input \(tx^{i}\) is denoted as a sequence of tuples \(\{tx_{n}^{i}=(sx^{i},dx_{n}^{i})|n=0,\cdots,N\}\), where \(sx^{i}=(WX_{i},R_{i})\) is the static element, and \(dx_{n}^{i}=s_{n}\) is the dynamic one at the decoding step \(n\). In addition, \(X_{n}\) denotes the state set of all inputs at the decoding step \(n\), and \(X_{0}\) is the initial state of the inputs. \(Y=\{ty_{n}|n=0,\cdots,N\}\) is the final permutation, where \(ty_{0}\) is an initial virtual tuple composed of the virtual static elements and the initial satellite state vector. \(Y_{n}=\{ty_{0},\cdots,ty_{n}\}\) is the decoded permutation up to the step \(n\). At every decoding step \(n(n=0,\cdots,N)\), the neural network generates the probability distribution of inputs in \(X_{n}\) at first. Then, \(ty_{n}\) points to an available input  
Figure 2: Architecture of the proposed neural network. For task \(t_{i},se_{i}\) is its static embedding form, and \(sc_{i}\) is its static encoding form. At step \(n\), \(de_{n}\) is the dynamic embedding form mapped by \(s_{n}\), and \(dc_{n}\) is its dynamic encoding form. \(c_{n}\) is the output of the dynamic encoder. \(h_{n}\) is the hidden state of the LSTM cell in the decoder.