Fast flow algorithm prioritizing the most time-consuming source point by using a multi-source evacuation model

In many public spaces (e.g. colleges and shopping malls), people are frequently distributed discretely, and thus, single-source evacuation, which means there’s only one point of origin, is not always a feasible solution. Hence, this paper discusses a multi-source evacuation model and algorithm, which are intended to evacuate all the people that are trapped within the minimum possible time. This study presents a fast flow algorithm to prioritize the most time-consuming source point under the constraint of route and exit capacity to reduce the evacuation time. This fast flow algorithm overcomes the deficiencies in the existing global optimization fast flow algorithm and capacity constrained route planner (CCRP) algorithm. For the fast flow algorithm, the first step is to determine the optimal solution to single-source evacuation and use the evacuation time of the most time-consuming source and exit gate set as the initial solution. The second step is to determine a multi-source evacuation solution by updating the lower limit of the current evacuation time and the exit gate set continually. The final step is to verify the effectiveness and feasibility of the algorithm through comparison.