## 2 The EA-CA Model
### The NS-AS Strategy  
The traditional CA model adopts the AS strategy, i.e., the state of agent is determined by the states of all its neighboring agents. This makes the system more computationally-consumed and difficult to converge, while using the NS strategy can increase the convergence speed of the system and improve the stability of the system [16; 17]. In the NS strategy, neighboring agents are divided into several communication sectors. In order to benefit the system convergence and enhance the system consistency, the neighbor agents with the smallest state difference in each communication sector are selected to construct the backbone network topology. In the network topology, all candidate neighbor agents of agent \(i\) participate in the calculation of the state update for agent \(i\). Thus, the state transition equation is given by  
\[x_{i}(t+1)=x_{i}(t)+u_{i}(t) \tag{7}\]  
where \(u_{i}(t)\) represents the control input. Supposing a neighborhood member \(j\) with the smallest state difference between the communication area and that of the agent \(i\), the agent \(i\) selects the agent \(j\) for collaborative cooperation and adds it to the candidate set. Then, \(u_{i}(t)\) can be written as  
\[u_{i}(t)=\alpha(\sum_{u=1}^{m}\left(x_{\min(i^{m})}(t)-x_{i}(t)\right)\] \[+\sum_{i\in P_{i}(i),i\
eq i\in A_{i}(t)}(x_{ii}(t)-x_{i}(t))) \tag{8}\]  
where \(\alpha\) is the adjustment factor of the model, \(m\) represents the number of communication sector, \(i^{m}\) represents the neighbor agents set of agent \(i\) in the \(u\)th sector, and \(x_{min(i^{m})}(t)\) is the state of the agent with smallest difference from the state of agent \(i\) among its neighboring agents in the \(u\)th sector at time \(t\). In the above, \(P_{i}(t)\) and \(A_{i}(t)\) represent the set of neighborhood members of agent \(i\) and the set of agents from the smallest state difference in each sector, respectively. As the NS strategy only selects the neighbor agent with the smallest difference in each sector to participate in the update calculation, a small sum of state difference is obtained. The step of each update of the agent is small, which causes the system to converge too slowly. Therefore, in order to improve the convergence speed of the system, the system switches to the NS-AS strategy. When the system is fully connected, the number of neighbor agents of agent \(i\) is \(n-1\), and all agents within communication range are select to participate in state evolution. The algorithm process of the NS-AS strategy is shown in Algorithm 1. ```
The NS-AS strategy for \(n\) agents:
1: Initialize the network topology and \(x_{i}(t)\), \(i\in{1,2\ldots N}\)
2: for agent \(i\)=1 to N
3: if the network is not fully connected
4: Adopt the NS stateegy
5: Divide the agents into several communication sectors. 6: Calculate the rotation angle set \(\beta=rotate\_array(min(std(N_{n})))\)
7: for \(j=1\) to \(m\)
8: Selects the neighbor agent \(\min(i^{u})=\)argmin\(||x_{i^{u}}(t)-x_{i}(t)||\), add the agent into candidate set \(u_{i}(t)\), update \(x_{i}(t)\);
9: \(\exists i,ii\in P_{i}(t),ii\
otin A_{i}(t)\), add agent ii into candidate set \(u_{i}(t)\);
10: Acooording to candidate set \(u_{i}(t)\), update \(x_{i}(t)\). 11: end for
12: else
13: Switch to AS strategy
14: Select all agents in the neighborhood, update \(x_{i}(t)\)
15: end for
```  
**Algorithm 1**The NS-AS Strategy Algorithm  
By calculating the standard deviation of the number of agents in each sector, the angle of the rotating sector can be adjusted. In Algorithm 1, \(rotate\_array\) represents the list of rotation angles to be searched, which cannot exceed the angle of each sector. \(N_{n}\) represents the number of agents in each sector and \(N_{c}\) denotes the number of communication sector.