# Multi-Objective Real-Time Planning of Evacuation Routes for Underground Mine Fires
## 3 Sensor-Based Network Weight Update Methodology
### Network Weight Update Algorithm  
When a fire occurs underground, as the fire smoke spreads, the passability and efficiency of the downwind side of the roadway decreases as the smoke stream encroaches. In this case, the weights on the edges of the graph increase with the concentration of the smoke stream in the roadway or decrease as the smoke stream is expelled. The roadway network is represented as a directed graph \(G=(V,E)\), where \(V\) denotes the set of all points in the graph and \(E\) denotes the set of all pairs of points in the graph, i.e., the set of edges. For any edge \((i,j)\in E\), there is an equivalent length \(w_{ij}\). The path is a finite set of nodes, denoted by \(P\), then \(P=\left(v_{0},v_{1},\ldots,v_{p}\right)\). For any road \(P\), the sum of equivalent lengths is denoted as \(W\).  
Equivalent length is a measure of roadway passability. Parameters related to roadway passability during catastrophic periods are mainly obtained in real time through real-time monitoring by underground monitoring and surveillance systems, in addition to reporting by underground personnel. The monitoring and control system monitors various toxic and hazardous gases underground through sensors such as carbon monoxide, nitrogen dioxide, and smoke. The arrangement of sensors is the key to disaster monitoring, and the arrangement method is based on the type of mine and the characteristics of the disaster. Coal mines mainly arrange carbon monoxide sensors to monitor fire in the return-airway and the downwind side of the belt conveyor, the observation point of spontaneous combustion, and the firewall of the closed fire zone [32]. In addition to carbon monoxide and smoke sensors on the downwind side of the belt conveyor, metal mines are encouraged to arrange carbon monoxide or nitrogen dioxide sensors for blasting smoke in the middle of production, in the sectional inlet and return airways, and in the return airway of the excavation roadway.  
However, due to cost considerations, it is impossible to deploy sensors in every roadway downhole, so the smoke flow arrival times of all sensor downstream nodes are derived based on [PERSON]'s algorithm, and a network of roadway passability is generated. The specific implementation of the algorithm is shown in Figure 1.  
The specific steps of the algorithm are described as follows:  
Step 1: Obtain the position of all sensors and initialize them to the non-alarm state. Add all sensors to the non-alarm set and initialize the roadway network weights;  
Step 2: Determine whether to interrupt sensor monitoring. If not, refresh the sensor data and execute the next step; if yes, jump to step 7.  
Step 3: Determine whether there is a sensor alarm, if yes, execute the next step; if no, jump to step 2;  
Step 4: Move the alarming sensor out of the non-alarm set and add it to the alarm set;  
Step 5: Use the Dijkstra algorithm to traverse the downstream nodes of each alarm sensor and calculate the arrival time of the downstream node smoke flow. If the node is downstream of multiple alarm sensors, take the first arrival time of the smoke flow;Step 6: Recalculate the equivalent length of the roadway and output the network weight, jump to step 2;  
Step 7: Complete the time-varying network weight solution.  
Update the network weights.