Emergency evacuation is the process of movement of people away from the threat or actual occurrence of hazards such as natural disasters, terrorist attacks, fires and bombs. In this paper, we focus on evacuation from a building, but the ideas can be applied to city and region evacuation. We define the problem and show how it can be modeled using graphs. The resulting optimization problem can be formulated as an integer linear program. Though this can be solved exactly, this approach does not scale well for graphs with thousands of nodes and several hundred thousands of edges. This is impractical for large graphs. We study a special case of this problem, where there is only a single source and a single sink. For this case, we give an improved algorithm , whose evacuation time is always at most that of a famous algorithm , and whose running time is strictly less than that of CCRP. We prove this mathematically and give supporting results by extensive experiments. We also study randomized behavior model of people and give some interesting results.
@cite_10: Given a large city represented by nodes and arcs, with a subset of these nodes having people required to be evacuated in a disaster situation, and a subset of destination nodes where the people may be taken for safety, the evacuation route planner finds routes in this network to evacuate the people in minimum possible time. Evacuation route planning in pre-known disasters such as hurricanes is of utmost importance for civic authorities. Computing such evacuation routes in a large graph with road infrastructure constraints such as road capacities and travelling times can be challenging. The Capacity Constrained Route Planner (CCRP) is a well studied heuristic algorithm proposed by Lu, George and Shekhar for solving this problem. It uses shortest path computations as a basis for finding and scheduling possible evacuation paths in the graph. However, the algorithm fails to scale to very large graphs. Other algorithms based on CCRP like CCRP++ and Incremental Data Structure based CCRP have been proposed to scale them to larger graphs. In this paper, we analyze these algorithms from performance perspective and suggest a faster algorithm by extending the CCRP algorithm that avoids recomputing partial paths. We have carried out experiments on various graph structures which show a vast improvement in runtime without impacting the optimality of CCRP results. For instance, for the city of Oldenburg with 382285 people, 6105 nodes and 7034 edges, our algorithm produced an evacuation plan in 2.6 seconds as compared to 123.8 seconds by CCRP and 9.3 seconds by CCRP++.
The solutions produced by CCRP++ and QPER do not follow semantics of CCRP, i.e., the solution quality is not better than that of CCRP. Recently Gupta and Sarda @cite_10 have given an algorithm called CCRP*, where evacuation plan is same as that of CCRP and it runs faster in practice. Instead of running Dijkstra's algorithm from scratch in each iteration, they resume it from the previous iteration.