Strategic evacuation planning with pedestrian guidance and bus routing: a mixed integer programming model and heuristic solution

This paper presents a mathematical model to plan emergencies in a densely populated urban zone where a certain numbers of pedestrians depend on transit for evacuation. The proposed model features an integrated operational framework, which simultaneously guides evacuees through urban streets and crosswalks (referred to as “the pedestrian network”) to designated pickup points (e.g., bus stops), and routes a fleet of buses at different depots to those pick‐up points and transports evacuees to their destinations or safe places. In this level, the buses are routed through the so‐called “vehicular network.” An integrated mixed integer linear program that can effectively take into account the interactions between the aforementioned two networks is formulated to find the maximal evacuation efficiency in two networks. Because the large instances of the proposed model are mathematically difficult to solve to optimality, a two‐stage heuristic is developed to solve larger instances of the model. Results from hundreds of numerical examples analysis indicate that proposed heuristic works well in providing (near) optimal or feasibly good solutions for medium‐scale to large‐scale instances that may arise in real transit‐based evacuation situations in a much shorter amount of computational time compared with cplex (can find optimal/feasible solutions for only five instances within 3 hours of running). Copyright © 2016 John Wiley & Sons, Ltd.     

A conflict-based path-generation heuristic for evacuation planning

Evacuation planning and scheduling is a critical aspect of disaster management and national security applications. This paper proposes a conflict-based path-generation approach for evacuation planning. Its key idea is to decompose the evacuation planning problem into a master and a subproblem. The subproblem generates new evacuation paths for each evacuated area, while the master problem optimizes the flow of evacuees and produce an evacuation plan. Each new path is generated to remedy conflicts in the evacuation flows and adds new columns and a new row in the master problem. The algorithm is applied to a set of large-scale evacuation scenarios ranging from the Hawkesbury-Nepean flood plain (West Sydney, Australia) which require evacuating in the order of 70,000 persons, to the New Orleans metropolitan area and its 1,000,000 residents. Experiments illustrate the scalability of the approach which is able to produce evacuation for scenarios with more than 1200 nodes, while a direct Mixed Integer Programming formulation becomes intractable for instances with more than 5 nodes. With this approach, realistic evacuations scenarios can be solved near-optimally in reasonable time, supporting both evacuation planning in strategic, tactical, and operational environments.     

Large-scale evacuation network optimization: a bi-level control method with uncertain arterial demand

To improve the efficiency of large-scale evacuations, a network aggregation method and a bi-level optimization control method are proposed in this paper. The network aggregation method indicates the uncertain evacuation demand on the arterial sub-network and balances accuracy and efficiency by refining local road sub-networks. The bi-level optimization control method is developed to reconfigure the aggregated network from both supply and demand sides with contraflow and conflict elimination. The main purpose of this control method is to make the arterial sub-network to be served without congestion and interruption. Then, a corresponding bi-objective network flow model is presented in a static manner for an oversaturated network, and a Genetic Algorithm-based solution method is used to solve the evacuation problem. The numerical results from optimizing a city-scale evacuation network for a super typhoon justify the validity and usefulness of the network aggregation and optimization control methods.     

Model and a solution algorithm for the dynamic resource allocation problem for large-scale transportation network evacuation

Allocating movable resources dynamically enables evacuation management agencies to improve evacuation system performance in both the spatial and temporal dimensions. This study proposes a mixed integer linear program (MILP) model to address the dynamic resource allocation problem for transportation evacuation planning on large-scale networks. The proposed model is built on the earliest arrival flow formulation that significantly reduces problem size. A set of binary variables, specifically, the beginning and the ending time of resource allocation at a location, enable a strong formulation with tight constraints. A solution algorithm is developed to solve for an optimal solution on large-scale network applications by adopting Benders decomposition. In this algorithm, the MILP model is decomposed into two sub-problems. The first sub-problem, called the restricted master problem, identifies a feasible dynamic resource allocation plan. The second sub-problem, called the auxiliary problem, models dynamic traffic assignment in the evacuation network given a resource allocation plan. A numerical study is performed on the Dallas–Fort Worth network. The results show that the Benders decomposition algorithm can solve an optimal solution efficiently on a large-scale network.     

Optimizing one‐way traffic network reconfiguration and lane‐based non‐diversion routing for evacuation

Unfortunately, situations such as flood, hurricanes, chemical accidents, and other events occur frequently more and more. To improve the efficiency and practicality of evacuation management plan, an integrated optimization model of one‐way traffic network reconfiguration and lane‐based non‐diversion routing with crossing elimination at intersection for evacuation is constructed in this paper. It is an integrated model aiming at minimizing the network clearance time based on Cell Transmission Model. A hybrid algorithm with modified genetic algorithm and tabu search method is devised for approximating optimal problem solutions. To verify the effectiveness of the proposed model and solving method, two cases are illustrated in this paper. Through the first example, it can be seen that the proposed model and algorithm can effectively solve the integrated problems, and compared with the objective value of the original network, the network clearance time of the final solution reduces by 47.4%. The calculation results for the realistic topology and size network of Ningbo in China, which locates on the east coast of the Pacific Ocean, justify the practical value of the model and solution method, and solutions under different settings of reduction amount of merging cell capacity embody obvious differences. Copyright © 2015 John Wiley & Sons, Ltd.     

Leveraging social networks for efficient hurricane evacuation

One of the important factors affecting evacuation performance is the departure time choices made by evacuees. Simultaneous departures of evacuees can lead to overloading of road networks causing congestion. We are especially interested in cases when evacuees subject to little or no risk of exposure evacuate along with evacuees subject to higher risk of threat (also known as shadow evacuation). One of the reasons for correlated evacuee departures is higher perceived risk of threat spread through social contacts. In this work, we study an evacuation scenario consisting of a high risk region and a surrounding low risk area. We propose a probabilistic evacuee departure time model incorporating both evacuee individual characteristics and the underlying evacuee social network. We find that the performance of an evacuation process can be improved by forcing a small subset of evacuees (inhibitors) in the low risk area to delay their departure. The performance of an evacuation is measured by both average travel time of the population and total evacuation time of the high risk evacuees. We derive closed form expressions for average travel time for ER random network. A detailed experimental analysis of various inhibitor selection strategies and their effectiveness on different social network topologies and risk distribution is performed. Results indicate that significant improvement in evacuation performance can be achieved in scenarios where evacuee social networks have short average path lengths and topologically influential evacuees do not belong to the high risk regions. Additionally, communities with stronger ties improve evacuation performance.     

A dynamic evacuation model for pedestrian–vehicle mixed-flow networks

In urban emergency evacuation, a potentially large number of evacuees may depend either on transit or other modes, or need to walk a long distance, to access their passenger cars. In the process of approaching the designated pick-up points or parking areas for evacuation, the massive number of pedestrians may cause tremendous burden to vehicles in the roadway network. Responsible agencies often need to contend with congestion incurred by massive vehicles emanating from parking garages, evacuation buses generated from bus stops, and the conflicts between evacuees and vehicles at intersections. Hence, an effective plan for such evacuation needs to concurrently address both the multi-modal traffic route assignment and the optimization of network signal controls for mixed traffic flows. This paper presents an integrated model to produce the optimal distribution of vehicle and pedestrian flows, and the responsive network signal plan for massive mixed pedestrian–vehicle flows within the evacuation zone. The proposed model features its effectiveness in accounting for multiple types of evacuation vehicles, the interdependent relations between pedestrian and vehicle flows via some conversion locations, and the inevitable conflicts between intersection turning vehicle and pedestrian flows. An illustrating example concerning an evacuation around the M&T stadium area has been presented, and the results indicate the promising properties of our proposed model, especially on reflecting the complex interactions between vehicle and pedestrian flows and the favorable use of high-occupancy vehicles for evacuation operations.     

Behavior-consistent information-based network traffic control for evacuation operations

The evacuation operations problem aims to avoid or mitigate the potential loss of life in a region threatened or affected by a disaster. It is shaped to a large extent by the evolution of evacuation traffic resulting from the demand–supply interactions of the associated transportation network. Information-based control is a strategic tool for evacuation traffic operations as it can enable greater access to the affected population and more effective response. However, comparatively few studies have focused on the implementation of information-based control in evacuation operations. This study develops a control module for evacuation operations centered on addressing the demand–supply interactions by using behavior-consistent information strategies. These strategies incorporate the likely responses of evacuees to the information provided in the determination of route guidance information. The control module works as an iterative computational process involving an evacuee route choice model and a control model of information strategies to determine the route guidance information to direct evacuation traffic so as to approach a desired network traffic flow pattern. The problem is formulated as a fuzzy logic based optimization framework to explicitly incorporate practical concerns related to information dissemination characteristics and social equity in evacuation operations. Numerical experiments highlight the importance of accounting for the demand–supply interactions, as the use of behavior-consistent information strategies can lead evacuee route choices to approach the operator-desired proportions corresponding to the desired traffic pattern. The results also indicate that while a behavior-consistent information strategy can be effective, gaps with the desired route proportions can exist due to the discrete nature of the linguistic messages and the real-world difficulty in accurately modeling evacuees’ actual route choice behavior.     

Evacuation Modelling in the United States: Does the Demand Model Choice Matter?

Abstract

This paper reviews the literature on the evacuation demand problem, with an emphasis on the impact of various modelling approaches on network‐wide evacuation performance measures. First, a number of important factors that affect evacuee behaviour are summarized. Evacuation software packages and tools are also investigated in terms of the demand generation model they use. The most widely used models are then selected for performing sensitivity analysis. Next, a cell‐transmission‐based system optimal dynamic traffic assignment (SO‐DTA) model is employed to assess the effects of the demand model choice on the clearance time and average travel time. It is concluded that evacuation demand models should be selected with care, and policy makers should make sure the selected demand curve can replicate real‐life conditions with relatively high fidelity for the study region to be able to develop reliable and realistic evacuation plans.     

Optimization of periodic crew schedules with application of column generation method

We present an alternative approach to the problem of periodic crew scheduling. We introduce the concept of frames which leads us to a modeling approach which suits well the current practice of the majority of European railway operators. It results in a model facilitating column generation techniques resulting in a Dantzig-Wolfe type decomposition, and thus suitable for a parallel implementation in a high-performance computing environment. We exploit the properties of network flow models to avoid several additional integer constraints. We compare two approaches to solve the problem. The first approach consists of solving the original problem by single model. The second approach is our step-by-step column generation. The comparison is based on our implementation which we describe in detail along with its application to certain benchmark instances. The benchmarks originate in real or close-to-realistic problems from railway systems in Slovakia and Hungary. The case studies demonstrate that our model is well-suited for real-life applications.     

Optimal control strategies with an extended cell transmission model for massive vehicular‐pedestrian mixed flows in the evacuation zone

This paper presents an integrated model to design routing and signal plans for massive mixed pedestrian‐vehicle flows within the evacuation zone. The proposed model, with its embedded formulations for pedestrians and vehicles in the same evacuation network, can effectively take their potential conflicts into account and generate the optimal routing strategies to guide evacuees toward either the pickup locations or their parking areas during an evacuation. The proposed model, enhancing the cell transmission model with the notion of sub‐cells, mainly captures the complex movements in the vehicle‐pedestrian flows and can concurrently optimizes both the signals for pedestrian‐vehicle flows and the movement paths for evacuees. An illustrating example concerning the evacuation around the M&T Bank Stadium area has been used to demonstrate the application potential of the proposed model. Copyright © 2013 John Wiley & Sons, Ltd.     

Online calibration of an integrated framework for information‐based evacuation operations

This study seeks to online calibrate the parameters of aggregate evacuee behavior models used in a behavior‐consistent information‐based control module for determining information strategies for real‐time evacuation operations. It enables the deployment of an operational framework for mass evacuation that integrates three aspects underlying an evacuation operation: demand (evacuee behavior), supply (network management), and disaster characteristics. To attain behavior‐consistency, the control module factors evacuees' likely responses to the disseminated information in determining information‐based control strategies. Hence, the ability of the behavior models to predict evacuees' likely responses is critical to the effectiveness of traffic routing by information strategies. The mixed logit structure is used for the aggregate behavior models to accommodate the behavioral heterogeneity across the population. An online calibration problem is proposed to calibrate the random parameters in the behavior models by using the least square estimator to minimize the gap between the predicted network flows and unfolding traffic dynamics. Background traffic, an important but rarely studied issue for modeling evacuation traffic, is also accounted for in the proposed problem. Numerical experiments are conducted to illustrate the importance of the calibration problem for addressing the system consistency issues and integrating the demand, supply, and disaster characteristics for more efficient evacuation operations. Copyright © 2016 John Wiley & Sons, Ltd.     

A network flow model for lane-based evacuation routing

Most traffic delays in regional evacuations occur at intersections. Lane-based routing is one strategy for reducing these delays. This paper presents a network flow model for identifying optimal lane-based evacuation routing plans in a complex road network. The model is an integer extension of the minimum-cost flow problem. It can be used to generate routing plans that trade total vehicle travel-distance against merging, while preventing traffic crossing-conflicts at intersections. A mixed-integer programming solver is used to derive optimal routing plans for a sample network. Manual capacity analysis and microscopic traffic simulation are used to compare the relative efficiency of the plans. An application is presented for Salt Lake City, Utah.     

Estimating road network accessibility during a hurricane evacuation: A case study of hurricane Irma in Florida

Understanding the spatio-temporal road network accessibility during a hurricane evacuation—the level of ease of residents in an area in reaching evacuation destination sites through the road network—is a critical component of emergency management. While many studies have attempted to measure road accessibility (either in the scope of evacuation or beyond), few have considered both dynamic evacuation demand and characteristics of a hurricane. This study proposes a methodological framework to achieve this goal. In an interval of every six hours, the method first estimates the evacuation demand in terms of number of vehicles per household in each county subdivision (sub-county) by considering the hurricane’s wind radius and track. The closest facility analysis is then employed to model evacuees’ route choices towards the predefined evacuation destinations. The potential crowdedness index (PCI), a metric capturing the level of crowdedness of each road segment, is then computed by coupling the estimated evacuation demand and route choices. Finally, the road accessibility of each sub-county is measured by calculating the reciprocal of the sum of PCI values of corresponding roads connecting evacuees from the sub-county to the designated destinations. The method is applied to the entire state of Florida during Hurricane Irma in September 2017. Results show that I-75 and I-95 northbound have a high level of congestion, and sub-counties along the northbound I-95 suffer from the worst road accessibility. In addition, this research performs a sensitivity analysis for examining the impacts of different choices of behavioral response curves on accessibility results.     

Variable guidance for pedestrian evacuation considering congestion,hazard, and compliance behavior

A methodology for optimizing variable pedestrian evacuation guidance in buildings with convex polygonal interior spaces is proposed. The optimization of variable guidance is a bi-level problem. The calculation of variable guidance based on the prediction of congestion and hazards is the upper-level problem. The prediction of congestion provided the variable guidance is the lower-level problem. A local search procedure is developed to solve the problem. The proposed methodology has three major contributions. First, a logistic regression model for guidance compliance behavior is calibrated using a virtual reality experiment and the critical factors for the behavior are identified. Second, the guidance compliance and following behaviors are considered in the lower-level problem. Third, benchmarks are calculated to evaluate the performance of optimized variable guidance, including the lower bound of the maximum evacuation time and the maximum evacuation time under a fixed guidance. Finally, the proposed methodology is validated with numerical examples. Results show that the method has the potential to reduce evacuation time in emergencies.     

Mapping evacuation risk on transportation networks using a spatial optimization model

The focus of this paper is on the development of a methodology to identify network and demographic characteristics on real transportation networks which may lead to significant problems in evacuation during some extreme event, like a wildfire or hazardous material spill. We present an optimization model, called the critical cluster model, that can be used to identify small areas or neighborhoods which have high ratios of population to exit capacity. Although this model in its simplest form is a nonlinear, constrained optimization problem, a special integer-linear programming equivalent can be formulated. Special contiguity constraints are needed to keep identified clusters spatially connected. We present details on how this model can be solved optimally as well as discuss computational experience for several example transportation networks. We describe how this model can be integrated within a GIS system to produce maps of evacuation risk or vulnerability. This model is now being utilized in several research projects, in Europe and the US.     

Potential-based dynamic pedestrian flow assignment

This study proposes a potential-based dynamic pedestrian flow assignment model to optimize the evacuation time needed for all pedestrians to leave an indoor or outdoor area with internal obstacles and multiple exits, e.g., railway station, air terminal, plaza, and park. In the model, the dynamic loading of pedestrian flows on a two-dimensional space is formulated by a cell transmission model, the movement of crowds is driven by space potential, and the optimization of evacuation time is solved by a proportional swapping process. In this way, the proposed model can be applied to not only efficiently optimize the evacuation process of a crowd with large scale but also recognize local congestion dynamics during crowd evacuation. Finally, a set of numerical examples are presented to show the proposed model’s effectiveness for optimizing crowd evacuation process and its application to design a class of variable guide sign systems.     

Transportation service procurement problem with transit time

In this work, we investigate transit time in transportation service procurement, which is conducted by shippers using auctions to purchase transportation service from carriers in the planning stage. Besides cost, we find that many shippers are most concerned with transit time in practice; shorter transit time indicates better transportation service. To minimize both the total cost and transit time, the problem faced by shippers is the biobjective transportation service procurement problem with transit time. To solve the problem, we introduce a biobjective integer programming model that can also accommodate some important business constraints. A biobjective branch-and-bound algorithm that finds all extreme supported nondominated solutions is developed. To speed up the algorithm, two fast feasibility checks, a network flow model for particular subproblems, and lower bounds from relaxation are proposed. In addition, a sophisticated heuristic is introduced to meet shipper’s requirements in some situations. Computational experiments on evaluating the performance of the algorithms are conducted on a set of test instances that are generated from practical data.     

Ant colony optimization for the real-time train routing selection problem

This paper deals with the real-time problem of scheduling and routing trains in a railway network. In the related literature, this problem is usually solved starting from a subset of routing alternatives and computing the near-optimal solution of the simplified routing problem. We study how to select the best subset of routing alternatives for each train among all possible alternatives. The real-time train routing selection problem is formulated as an integer linear programming formulation and solved via an algorithm inspired by the ant colonies’ behavior. The real-time railway traffic management problem takes as input the best subset of routing alternatives and is solved as a mixed-integer linear program. The proposed methodology is tested on two practical case studies of the French railway infrastructure: the Lille terminal station area and the Rouen line. The computational experiments are based on several practical disturbed scenarios. Our methodology allows the improvement of the state of the art in terms of the minimization of train consecutive delays. The improvement is around 22% for the Rouen instances and around 56% for the Lille instances.     

The representation and implementation of time-dependent inundation in large-scale microscopic evacuation simulations

Multi-agent simulation has increasingly been used for transportation simulation in recent years. With current techniques, it is possible to simulate systems consisting of several million agents. Such multi-agent simulations have been applied to whole cities and even large regions. In this paper it is demonstrated how to adapt an existing multi-agent transportation simulation framework to large-scale pedestrian evacuation simulation. The underlying flow model simulates the traffic-based on a simple queue model where only free speed, bottleneck capacities, and space constraints are taken into account. The queue simulation, albeit simple, captures the most important aspects of evacuations such as the congestion effects of bottlenecks and the time needed to evacuate the endangered area. In the case of an evacuation simulation the network has time-dependent attributes. For instance, large-scale inundations or conflagrations do not cover all the endangered area at once.These time-dependent attributes are modeled as network change events. Network change events are modifying link parameters at predefined points in time. The simulation framework is demonstrated through a case study for the Indonesian city of Padang, which faces a high risk of being inundated by a tsunami.