# Multi-Objective Edge Node Deployment Method Based on Improved Heuristic Algorithms for Smart Mines
## 3 System Model and Problem Description
### System Model
#### 3.1.1 Fixed Device Model  
We use the loading device as a case study and simulate the loading task on the production line platform in the subsequent experimental section. The loading task requires that, when the bucket is transported around the loading device via the hoist, the loading device must receive information about the bucket (e.g., position, load status, etc.) and transmit its own position and orientation to the bucket to ensure coordinated operation between the two. In the event that the bucket becomes stuck, an immediate warning signal must be sent to surrounding equipment to prevent hazardous operations. This task is subject to strict time constraints to minimize the risk of disaster. Ideally, edge nodes for fixed devices should be deployed during the construction phase of smart mines. However, the current shift towards intelligent mining is predominantly realized by upgrading traditional mining operations to facilitate intelligent control systems. A significant portion of the mining and transportation equipment has already been installed, and both power lines and network cables have been fully deployed. This pre-existing infrastructure limits the flexibility of potential edge node placement locations, thereby introducing challenges in the deployment process. To reduce the complexity of this problem, the following assumptions are proposed:  
* Large-scale fixed equipment and intelligent terminals have already been deployed. * Communication delays between edge nodes and intelligent terminals are consistent. * Task requests from intelligent terminals vary periodically. Considering the aforementioned constraints, the system model for edge node placement in the mining production line is illustrated in Figure 1.  
In an already constructed mining line, this paper selects several potential locations for deploying edge nodes, based on the traditional expertise of scholars. In this paper, we denote the set of edge nodes as \(SE\), \(SE=\{se_{1},se_{2},\ldots,se_{SM}\}\), where \(SM\) represents the number of edge nodes. The CPU frequency of each node is denoted by \(SFR=\{sfre_{1},sfre_{2},\ldots,sfre_{SM}\}\). The set of potential candidate locations is represented by \(SP=\{sp_{1},sp_{2},\ldots,sp_{SX}\}\), where \(SX\) is the number of potential candidate locations and satisfies \(SX<SN\). Each candidate location \(sp_{i}\) is characterized by its coordinates \(sp_{i}=(x_{i},y_{i})\) \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline SN & Number of fixed equipment \\ SD & Fixed equipment collection \\ SX & Number of potential candidate locations for fixed equipment \\ SP & A collection of potential candidate locations for fixed equipment \\ SM & Number of edge nodes for fixed equipment \\ SE & Fixed device edge node collection \\ MN & Number of mobile devices \\ MD & Mobile device collection \\ MM & Number of edge nodes for mobile devices \\ ME & Collection of edge nodes for mobile devices \\ \(C^{all}\) & Edge node deployment cost \\ \(\beta_{1}\) & Delay weight coefficient \\ \(\beta_{2}\) & Placement cost weight coefficient \\ \(T_{ij}^{trans}\) & The transmission time of a task \\ \(T_{ij}^{time}\) & The execution time of a task \\ \(T_{ij}^{time}\) & The queuing time of a task \\ \(T_{max}\) & Maximum task delay \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notations. The communication between the edge nodes and the fixed devices is carried out by wired or wireless means [23]. Fixed devices send real-time task requests to the edge nodes during operation, with the requests changing periodically. In this paper, \(SD=\{sd_{1},sd_{2},\ldots,sd_{SN}\}\) represents the set of fixed devices, where \(SN\) corresponds to the total number of devices, and \((x_{i},y_{i})\) encapsulates the location status information for each fixed device, \(sd_{i}\). The task requests of the devices are represented by the set \(ST=\{st_{1},st_{2},\ldots,st_{SN}\}\), where each request is described as \(st_{i}=\{sdin_{i},sy_{i},sdout_{i}\}\).