Innovative Applications of O.R.Bi-objective safe and resilient urban evacuation planning☆
Introduction
Urban evacuation planning has become an important topic due to the growing frequency and intensity of natural and man-made disasters. For example, the number of natural disasters has increased from less than 60 in 1975 to 385 disasters in 2010. In all, more than 200 million people were affected by natural disasters that same year and nearly 300,000 people lost their lives (Guha-Sapir, Vos, Below, & Ponserre, 2011). The reasons for this negative trend are varied: Environmental problems such as global warming cause bush fires or floods. Poor planning of buildings or cities increases the consequences of hurricanes or earthquakes. Moreover, humans themselves are intentionally (e.g., terrorist attacks) or unintentionally (e.g., chemical disasters) responsible for a multitude of disasters. The Federal Emergency Management Agency of the United States (2008) reports annually 45–75 disasters in recent years that require state and federal assistance and may lead to an evacuation. Therefore, reasonably planned evacuations are important in order to ensure a complication-free evacuation process and to secure the health (and the lives) of the evacuees.
In general, evacuation is a process whereby people under threat are relocated from a hazardous area to safer places. Planning an evacuation involves many different aspects: considering human behaviour, warning and informing people, demand modelling, zoning hazardous areas, defining safe zones and/or shelters, route selecting, traffic assignment and more. For an overview we refer to Murray-Tuite and Wolshon (2013).
In this paper, we focus on route selection and traffic assignment for an urban evacuation scenario. In general, in evacuation planning the objective is to minimize the evacuation time, the travelled distance or the total exposed hazard for all evacuees. This paper presents a completely new approach to evacuation planning by introducing a resilient aspect that designs the evacuation plan more moderately against potential effects of capacity drops in street networks. The motivation for introducing this resilient aspect is the following: Streets can be (partially) blocked (= capacity drop). This blockage may be due to either the effects of the disaster itself (e.g., fallen trees or destroyed streets) or the behaviour effects of the evacuees (e.g., traffic accidents or driving with reduced speed, due to the insecure situation). We define an evacuation plan as more resilient, the less a capacity drop effects the performance of the evacuation process. This aspect of resilience is implemented by utilizing the available capacities of street sections in a more balanced manner. By considering the utilization of street networks in a more balanced way, we suppose two improvements: First, the consequences of a blocked street will be reduced and second, the capacity of the preferred main evacuation routes will not be utilized up to the capacity limit. Resilient evacuation plans are more conservative, which is why a higher total hazard is accepted than the minimum hazard level. Nevertheless, we think it would be an unrealistic to consider the identical street network for a unique evacuation situation as for daily traffic. Thus, the resilient evacuation planning concept can potentially outperform the safe evacuation planning concept if the street network suffers a capacity drop.
When applying this concept of resilience to evacuation planning, it is necessary to consider not only the fastest or the safest routes. Therefore, we also consider further routes, which we divide into reasonable and unreasonable routes. For a better illustration let us consider the network in Fig. 1. We assume one vehicle intends to drive from its starting position to the exit and three possible evacuation routes. The shortest path is represented by the solid line. The dashed route is obviously not the shortest path, but it could be a viable alternative if the shortest path is (partially) blocked or the hazard is significant on the shortest path. Therefore, this path represents a reasonable route. However, the dotted line represents an unreasonable route. Although this route utilizes street sections that no other path utilizes, the route includes an (undesired) sub-tour. Such a route cannot be a reasonable evacuation route and must be prohibited in an optimal evacuation plan.
The contribution of this paper lies in the consideration of resilience regarding evacuation planning. The literature provides various (so-called) reliable, stochastic and robust approaches (see Section 2.2) that directly consider uncertainties in their evacuation planning models. Although we agree that capacity drops are caused randomly, we do not explicitly take these uncertainties into account. Owing to the uniqueness and rarity of these events and resultant missing historical data, it is impossible to estimate a probability distribution function for an arbitrary urban street network. Our deterministic approach indirectly considers the uncertainty of street capacities in the model by taking into account two conflicting objective functions. Evacuees are assigned to evacuation routes that are safe and resilient. Therefore, we introduce a bi-objective Resilient Path-Based Cell-Transmission-Based Evacuation Planning Model (RPCTEPM) that on the one hand, minimizes the total exposed hazard for the evacuees (safe aspect) and on the other hand, utilizes the network capacities in a more balanced way (resilient aspect). This network capacity utilization approach represents our idea of resilience. To the best of our knowledge, there is no approach that considers uncertainties in such a manner. The routing and assignment process is separated in order to guarantee reasonable evacuation routes. First, the evacuation routes are determined, whereupon the evacuees are assigned to these routes with the help of a new path-based evacuation model. The key challenge is to generate the evacuation paths. The main problem is that the utilization of cells is not a given parameter and hence it is not possible to determine the utilization of an evacuation path in a stand-alone way. Therefore, a new Path Generation Algorithm (PGA) is developed to meet the special requirements of the evacuation paths. In order to deal with the two objective functions, the ϵ-Constraint Method (Chankong & Haimes, 1983) is applied. Finally, we evaluate our new concept of resilience in a computational study. Therefore, we develop a special test procedure to demonstrate the benefit of our new approach. The results not only show that the resilient approach can improve the evacuation process in case of capacity drops, but also indicate that the benefit depends on the considered evacuation scenario and the capacity drop level.
The remainder of this paper is structured as follows: Section 2 gives a brief literature review on cell-based evacuation planning models and resilience with regard to evacuation models. Section 3 introduces the basic evacuation model of this paper. In Section 4 the new aspect of resilience regarding evacuation planning is presented. In the next Section 5 we present the PGA that generates the paths for the proposed path-based evacuation model. Finally, we evaluate our concept of resilient evacuation planning in Section 6 and outline the results in Section 7.
Section snippets
Literature overview
In Section 2.1 we give an outline of the essential works of evacuation planning that also consider the CTM. The literature provides no definition of resilience in the evacuation context. Thus in Section 2.2 we give a brief overview of resilience in the context of transportation systems. We then go on to present a summary of the existing evacuation models that consider uncertainties directly or indirectly with the help of conflicting objective functions.
General assumptions
This section presents the basic assumptions, that are considered for the following evacuation models. Although we are aware that some other parameters are also affected by uncertainties (e.g., the number of evacuees or the distribution of the hazard), we consider only capacity uncertainties.
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A noticed (e.g., flood or hurricane) or a no-noticed, but predictable evacuation scenario (e.g., chemical spill in a factory) is considered so that time is not a restricting factor. On the one hand, time is
Resilient evacuation planning for urban areas
In this section we extend the CTEPM to the aspect of resilience. First, in Section 4.1 we present the implementation of resilience in the CTEPM. This implementation leads to two problems: Unreasonable evacuation routes and two objective functions. In Section 4.2 we explain and define unreasonable evacuation routes. These unreasonable evacuation routes will be prohibited by considering a path-based formulation where only reasonable evacuation paths are generated. In Section 4.3 we overcome the
Path-generation-algorithm
In this section the PGA is presented that generates the required path set P. This algorithm is needed because the path set P has a significant impact on the solution of the RPCTEPM. The issue is that the cell utilization is not known in advance. Moreover, it is a result of the model. Therefore, it is not possible to rate or evaluate the paths in a standalone manner before the model is solved. Furthermore, we cannot just consider all feasible or reasonable paths because the number of paths
Computational study
In this section we test the new concept of resilience evacuation planning. The test bed is presented in Section 6.1. We then explain the test procedure in Section 6.2, which evaluates the consequences of capacity drops regarding both the evacuation concepts. We go on to present the relevant results in Section 6.3.
The models and algorithms are implemented in AMPL and solved by the commercial solver CPLEX (version 12.6.1). All studies are conducted on a computer using an Intel(R) Core(TM)
Conclusion and outlook
This paper introduces a new approach to resilience evacuation planning. The fundamental idea is to utilize the network capacities in a more balanced manner to reduce the consequences of potential capacity drops. This aspect of network utilization leads to the problem of unreasonable routes. Hence, we determine only reasonable evacuation routes in advance so that the optimization model only assigns vehicles to those routes. We thus present a new path-based evacuation model and a path algorithm
Acknowledgement
We would like to express our gratitude to the two anonymous referees for their helpful comments on this paper.
This work was financially supported by the Stiftung Zukunft NRW.
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