Algorithm 2: TASP Algorithm

Begin Initialize the value of all the decision variables to be zero, and the node position of the evacuating person be the start node;   Construct the nodes and links in the 2-D planar graph;   Let the node position of the evacuating person be the start node;   While $\left(t\le \left|T\right|\right)$//looping at each time slot t   Begin Collect the temperature data at each node and the link cost data at each link at time slot $t$; Remove the link L from set L if the link temperature is over the upper limit of human temperature tenability M; //avoiding traverse to a node with temperature more than M on the evacuation path Calculate the shortest path from the start node to every exit node by using Dijkstra’s algorithm; //Step 3 Let $\sigma$= 0; For every exit $e\in E$ Begin If there is the best path to exit $e\in E$ Begin Let ${\lambda }_e=$ the best path cost to exit $e\in E$; $\sigma$= 1; End //if End //For    If ($\sigma$== 0)//cannot find any best path to all the exits    Begin     Report no$\mathrm{feasible} \mathrm{solutions}$;    Break from the While loop;   End //If ($\sigma$== 0)   Else //at least there is the shortest path to exit Let $\tilde{\lambda }=\mathrm{Min} Ar{g}_{e\in E}{\lambda }_e$; //the exit number that has the smallest shortest path cost, evacuation path is the best path to exit $\tilde{\lambda }$ If (the hop distance from the start node to the exit number $\tilde{\lambda }$ on the evacuation path $\le$ $\mathsf{\Lambda }$) //reach the exit Begin  Let $\mathsf{\Omega }$ = $\mathsf{\Omega }$ + (The link cost from the start node to the exit $\tilde{\lambda }$ on the evacuation path);  Report $\mathsf{\Omega }$ and the evacuation path;  $\rho$= 1;  Break from the While loop; End // If (the hop Else // have not reached the exit, then move the start node $\mathsf{\Lambda }$ hop distance closer to exit $\tilde{\lambda }$ on the emergency path Begin Let $\mathsf{\Omega }$ = $\mathsf{\Omega }$ + (All the link cost from the start node to the node with hop distance $\mathsf{\Lambda }$on the evacuation path); Move the start node to the new position with $\mathsf{\Lambda }$ hop distance on the evacuation path; End // Else End;//While loop If ($\rho$== 0)   Report no$\mathrm{feasible} \mathrm{solutions}$; End