A capacitated network flow optimization approach for short notice evacuation planning (original) (raw)

Improved Algorithms for the Evacuation Route Planning Problem

Lecture Notes in Computer Science, 2015

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 Single Source Single Sink Evacuation Route Planner (SSEP), whose evacuation time is always at most that of a famous algorithm Capacity Constrained Route Planner (CCRP), 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.

A Critical Survey on the Network Optimization Algorithms for Evacuation Planning Problems

2018

In the last decades, research on emergency traffic management has received high attention from the operations research community and many pioneer researchers have established it as one of the most fertile research areas. We consider the computationally hard flows over time problems from wider perspective including flow/time dependent attributes (dynamic flows), a possibility of flows loss on paths while travelling (lossy network problems), arcs/path reversal capability (contraflow models) and possibilities of eliminating merging and crossing conflicts at intersections (abstract flows). The topics also include the networks for relief distribution, location-allocation of facilities, multi-criterion characteristics and transit based flow models in brief. The issues are highly motivated from the perspective of traffic control and emergency route choice and scheduling. Despite of many directions such as differential equations for fluid flows, measure and function theory, cell transmissio...

Dynamic network flow location models and algorithms for quickest evacuation planning

Journal of Industrial & Management Optimization, 2017

Dynamic network flow problems have wide applications in evacuation planning. From a given subset of arcs in a directed network, choosing the suitable arcs for facility location is very important in the optimization of flows in emergency cases. Because of the decrease in the capacity of an arc by placing a facility in it, there may be a reduction in the maximum flow or increase in the quickest time. In this work, we consider a problem of identifying the optimal facility locations so that the increase in the quickest time is minimum. Introducing the quickest FlowLoc problem, we give strongly polynomial time algorithms to solve the single facility case. Realizing NP-hardness of the multi-facility case, we develop a mixed integer programming formulation of it and give a polynomial time heuristic for its solution. Because of the growing concerns of arc reversals in evacuation planning, we introduce quickest Con-traFlowLoc problem and present exact algorithms to solve single-facility case and a heuristic to solve the multi-facility case, both of which have polynomial time complexity. The solutions thus obtained here are practically important, particularly in evacuation planning, to systematize traffic flow with facility allocation minimizing evacuation time.

A time-extended network model for staged evacuation planning

Safety Science, 2018

Over the past few years, rapid urbanization has stressed an urgent need for the development of comprehensive and efficient contingency plans in urban spaces. Amongst other actions to take, evacuation plans are important solutions to protect people from unforeseen effects of disasters. In this paper, we develop an optimal method to design appropriate evacuation plans. Its objectives include minimizing total clearance time and travel time of each evacuee, avoiding traffic congestions, and balancing traffic loads among different exits. A series of algorithms are developed to determine the departure time, the destination, and the route of each evacuation group. A time-extended network model is presented to support these algorithms. A real-world case is employed to examine the performance of the proposed model. The performance and applicability of the proposed approach when targeting different scales and granularities of evacuation are discussed and analyzed in detail. Results demonstrate that the above four objectives can be closely satisfied, and the approach performs better for evacuations with a large scale and a small granularity. Many research efforts have been devoted to the problem of evacuation, and they can be roughly classified into simulation-oriented and optimization-oriented approaches. Simulation-oriented works aim at figuring out the significant factors or parameters influencing an evacuation process or evaluating the performance of an evacuation plan under different scenarios, policies, or strategies (

Optimal Scheduling of Evacuation Operations

Transportation Research Record, 2006

Evacuations necessitated by extreme events are usually envisioned as taking place with all people evacuating simultaneously; this leads to premature congestion on the surface streets and excessive delays. With the evacuating load onto the network staggered, the onset of congestion may be delayed, and people can evacuate more quickly. In this study, the problem of scheduling evacuation trips between a selected set of origin nodes and (safety) destinations was considered, with the objective of minimizing network clearance time. A modified system-optimal dynamic traffic assignment formulation is proposed; in it the total system evacuation time, as opposed to the total system trip time, is minimized. An iterative heuristic procedure is used to solve this problem: the method of successive averages is used to find the flow assignments for the next iteration; a traffic simulator, DYNASMART-P, is used to propagate the vehicles on their prescribed paths and determine the state of the system. Therefore, the simulator serves as a tool to satisfy the dynamic traffic assignment constraints implicitly while evaluating the objective function. The output of this model will be the departure time, route, and destination choices for each evacuee. The output is then aggregated to produce a time-dependent staging policy for each selected origin.

Experiences with evacuation route planning algorithms

2012

Efficient tools are needed to identify routes and schedules to evacuate affected populations to safety in the event of natural disasters. Hurricane Rita and the recent tsunami revealed limitations of traditional approaches to provide emergency preparedness for evacuees and to predict the effects of evacuation route planning (ERP). Challenges arise during evacuations due to the spread of people over space and time and the multiple paths that can be taken to reach them; key assumptions such as stationary ranking of alternative routes and optimal substructure are violated in such situations. Algorithms for ERP were first developed by researchers in operations research and transportation science. However, these proved to have high computational complexity and did not scale well to large problems. Over the last decade, we developed a different approach, namely the Capacity Constrained Route Planner (CCRP), which generalizes shortest path algorithms by honoring capacity constraints and the spread of people over space and time. The CCRP uses time-aggregated graphs to reduce storage overhead and increase computational efficiency. Experimental evaluation and field use in Twin Cities Homeland Security scenarios demonstrated that CCRP is faster, more scalable, and easier to use than previous techniques. We also propose a novel scalable algorithm that exploits the spatial structure of transportation networks to accelerate routing algorithms for large network datasets. We evaluated our new approach for large-scale networks around downtown Minneapolis and riverside areas. This article summarizes experiences and lessons learned during the last decade in ERP and relates these to Professor Goodchild's contributions.

Optimal egress time calculation and path generation for large evacuation networks

Annals of Operations Research, 2012

Finding the optimal clearance time and deciding the path and schedule of evacuation for large networks have traditionally been computationally intensive. In this paper, we propose a new method for finding the solution for this dynamic network flow problem with considerably lower computation time. Using a three phase solution method, we provide solutions for required clearance time for complete evacuation, minimum number of evacuation paths required for evacuation in least possible time and the starting schedules on those paths. First, a lower bound on the clearance time is calculated using minimum cost dynamic network flow model on a modified network graph representing the transportation network. Next, a solution pool of feasible paths between all O-D pairs is generated. Using the input from the first two models, a flow assignment model is developed to select the best paths from the pool and assign flow and decide schedule for evacuation with lowest clearance time possible. All the proposed models are mixed integer linear programing models and formulation is done for System Optimum (SO) scenario where the emphasis is on complete network evacuation in minimum possible clearance time without any preset priority. We demonstrate that the model can handle large size networks with low computation time. A numerical example illustrates the applicability and effectiveness of the proposed approach for evacuation.

Efficient contraflow algorithms for quickest evacuation planning

Science China Mathematics, 2018

The optimization models and algorithms with their implementations on flow over time problems have been an emerging field of research because of largely increasing human-created and natural disasters worldwide. For an optimal use of transportation network to shift affected people and normalize the disastrous situation as quickly and efficiently as possible, contraflow configuration is one of the highly applicable operations research (OR) models. It increases the outbound road capacities by reversing the direction of arcs towards the safe destinations that not only minimize the congestion and increase the flow but also decrease the evacuation time significantly. In this paper, we sketch the state of quickest flow solutions and solve the quickest contraflow problem with constant transit times on arcs proving that the problem can be solved in strongly polynomial time O(nm 2 (log n) 2), where n and m are number of nodes and number of arcs, respectively in the network. This contraflow solution has the same computational time bound as that of the best min-cost flow solution. Moreover, we also introduce the contraflow approach with load dependent transit times on arcs and present an efficient algorithm to solve the quickest contraflow problem approximately. Supporting the claim, our computational experiments on Kathmandu road network and on randomly generated instances perform very well matching the theoretical results. For sufficiently large number of evacuees, about double flow can be shifted with the same evacuation time and about half time is sufficient to push the given flow value with contraflow reconfiguration.

Global Optimization of Emergency Evacuation Assignments

Interfaces, 2006

Conventional emergency evacuation plans often assign evacuees to fixed routes or destinations based mainly on geographic proximity. Such approaches can be inefficient if the roads are congested, blocked, or otherwise dangerous because of the emergency. By not constraining evacuees to prespecified destinations, a one-destination evacuation approach provides flexibility in the optimization process. We present a framework for the simultaneous optimization of evacuation-traffic distribution and assignment. Based on the one-destination evacuation concept, we can obtain the optimal destination and route assignment by solving a one-destination traffic-assignment problem on a modified network representation. In a county-wide, large-scale evacuation case study, the onedestination model yields substantial improvement over the conventional approach, with the overall evacuation time reduced by more than 60 percent. More importantly, emergency planners can easily implement this framework by instructing evacuees to go to destinations that the one-destination optimization process selects.

Heuristics for Scheduling Evacuation Operations in Case of Natural Disaster

Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems, 2014

In this paper, we consider a large-scale evacuation problem after an important disaster. The evacuation is assumed to be done by means of a fleet of buses, thus leading to schedule the evacuation operations by buses (Bus Evacuation Problem, BEP). We propose time indexed formulations, as well as heuristic algorithms like greedy algorithms and a matheuristic. This matheuristic uses the former formulation to improve the best solution obtained by the greedy heuristics. In computational experiments, we analyse and evaluate the efficiency of the proposed solution algorihms.