Transportation Research Part C 31 (2013) 112–130 Contents lists available at SciVerse ScienceDirect Transportation Research Part C journal homepage: www.elsevier.com/locate/trc A space–time efficiency model for optimizing intra-intersection vehicle–pedestrian evacuation movements Zhixiang Fang a,b,⇑, Qiuping Li a,⇑, Qingquan Li a,b, Lee D. Han c, Shih-Lung Shaw a,d a State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China Engineering Research Center for Spatio-Temporal Data Smart Acquisition and Application, Ministry of Education of China, 129 Luoyu Road, Wuhan 430079, PR China c Department of Civil & Environmental Engineering, The University of Tennessee, 112 Perkins Hall, Knoxville, TN 37996-2010, USA d Department of Geography, University of Tennessee, Knoxville, TN 37996-0925, USA b a r t i c l e i n f o Article history: Received 29 September 2012 Received in revised form 11 March 2013 Accepted 11 March 2013 Keywords: Space-time use efficiency Measure of effectiveness Mixed vehicle and pedestrian turning movements Evacuation plan a b s t r a c t The effectiveness of an evacuation plan is a central concern of emergency management agencies. Methodologies for assessing and optimizing the space–time use efficiency of an evacuation plan have yet to be studied satisfactorily. To this end, this paper proposes an assessment metric and uses it for the optimization of evacuation plans. First, we define a space–time use efficiency metric on the basis of trajectories on road segments and intersections. The metric measures the usage of an evacuation network by supporting a trajectory-based analysis of the competing behaviors of vehicles and pedestrians in a hybrid pedestrian-vehicle simulation. Secondly, we present a two-tier hybrid multi-objective optimization algorithm to plan vehicle and pedestrian turning movement directions in an integrated road and building-interior network for the purpose of making decisions about evacuation plans. This algorithm has three objectives: (i) minimizing average evacuation time, (ii) minimizing the overall length traveled, and (iii) maximizing space–time use efficiency in the evacuation network. The stadium at the Wuhan Sports Centre in China and its adjacent road network were chosen as the study environment. A total of 23,362 evacuees and 1362 vehicles were assumed for the evacuation experiments. The analysis results suggest that intra-intersection evacuation flows can significantly influence the space–time use efficiency of a evacuation plan. The proposed space–time use efficiency evaluation approach provides a practical method of measuring the effectiveness of evacuation plans. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The efficiency and effectiveness of evacuation operations are becoming critical in evacuation planning because of the increasing frequency of natural and man-made disasters. Previous research has investigated a wide range of measures of effectiveness (MOEs) for evacuation operations. Among these, the total evacuation, or clearance, time has been used most often (Løvås, 1995; Urbanik, 2000; Stepanov and Smith, 2009; Yuan et al., 2009; Tavares and Galea, 2009; Lämmel et al., 2010; Kobes et al., 2010; Golmohammadi and Shimshak, 2011; Bretschneider and Kimms, 2012). In addition to the ⇑ Corresponding authors. Address: Transportation Research Center, Wuhan University, P.O. Box C307, Road Luoyu #129, Wuhan University, Wuhan 430079, PR China. Tel.: +86 27 68779889; fax: +86 27 68778043 (Z. Fang). E-mail addresses: zxfang@whu.edu.cn (Z. Fang), leeqiuping@whu.edu.cn (Q. Li), qqli@whu.edu.cn (Q. Li), lhan@utk.edu (L.D. Han), sshaw@utk.edu (S.-L. Shaw). 0968-090X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trc.2013.03.004 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 113 evacuation time, the overall travel time (Han et al., 2007; Li et al., 2011), the cumulative exposure time (Han et al., 2007), a time-based measure of risk and evacuation exposure (Han et al., 2007; Yuan and Han, 2009), the quantity of vehicles (Li et al., 2011), and other quantities also have been proposed for evaluating evacuation plans. Efficient use of evacuation routes (space) and evacuation duration (time) is a major challenge in evacuation planning and management. Recently, Fang et al. (2011a) proposed and demonstrated a space–time use efficiency index that measured accumulated small interval areas between parallel space–time paths on each link as a surrogate for usage efficiency of space–time resources during the evacuation of a stadium, based on a first-in-first-out queue discipline. Nevertheless, these MOEs could be improved further to represent and assess the efficiency of the turning movements in space and time of vehicle and pedestrian flow directions in an evacuation plan. Representation and assessment are among the greater challenges faced by emergency management agencies in their attempt to generate efficient evacuation plans. The authors address two issues in this paper. One introduces a space–time efficiency assessment approach to evaluate the turning movements of vehicle and pedestrian evacuation routes, and the other describes the use of this approach for vehicle and pedestrian turning directions in an integrated evacuation network, which includes a road network and a building interior. To this end, vehicular and pedestrian flows are simulated as the output of the evacuation routes. The planned turning movements can be used to control evacuation flows in an evacuation operation. Simulated space–time results demonstrate an improvement in the space–time use of the road network and of the interior links in the building during an evacuation. This kind of approach may help the decision maker identify space–time bottlenecks in evacuation operations. The planned vehicle and pedestrian movements also may help emergency management agencies to develop feasible evacuation strategies. This paper makes two significant contributions. One is the formulation of a space–time use efficiency metric on the basis of trajectories on road segments and intersections. This efficiency metric is an enhancement of the space–time efficiency index proposed by Fang et al. (2011a) in two realistic aspects, namely, incorporating three-dimensional trajectories of vehicles and pedestrians and relaxing the approximate FIFO (first in, first out) rule (Lämmel et al., 2010) in the case of mixed vehicle and pedestrian flows in intersections. This new metric uses a space–time cube concept to evaluate the space–time use efficiency in intersections as well as space–time paths on links. These enhancements enable the representation of space–time occupancy and interactions between pedestrians and vehicles in intersection areas, which cannot be evaluated by the previously published index (Fang, Li et al., 2011). The second contribution is the proposition of a two-tiered hybrid optimization algorithm for strategizing vehicle and pedestrian turning movements in an integrated road and building-interior network. This algorithm integrates genetic algorithm (GA) and ant colony optimization (ACO) to solve multi-objective optimization problems with the evaluation of simulated results for each potential solution, which cannot be solved by either algorithm independently. In this paper, the implementation of this hybrid algorithm is limited to deterministic input parameters. Considerations related to uncertainties and incompliance to evacuation operations are the realm of future research. This paper is organized into seven sections. Section 2 of this paper reviews previous work related to MOEs for evacuation operations, and space–time organization in such operations. Section 3 defines a space–time use efficiency metric based on trajectories on road segments and intersections. Section 4 introduces a multi-objective optimization algorithm and proposes a hybrid algorithm to optimize vehicle and pedestrian turning movements during an evacuation operation in an integrated road and building-interior network. Section 5 analyzes the results of computational experiments. Section 6 discusses two interesting questions about the patterns of control at intersections in the calculated solutions. Finally, Section 7 draws conclusions and discusses directions for future research. 2. Related work A wide range of MOEs for evacuation operations has been investigated in the literature. Zografos and Androutsopoulos (2008) used the total evacuation time to determine evacuation paths from the impacted area to designated shelters. Yuan and Han (2009) used various MOEs including evacuation (or clearance) time, individual travel times and exposure times, time-based measures of risk and evacuation exposure, time–space-based measures of risk and evacuation exposure, and the average travel time and delay of evacuees. Stepanov and Smith (2009) used the total travel distance, traffic congestion, and blocking probabilities as MOEs. A four-tier MOE framework (Han et al., 2006; Han et al., 2007) was developed to support investigations of evacuation processes. This framework is capable of considering different factors in the case of ties and providing assessments of different evacuation scenarios. A space–time use efficiency index (Fang et al., 2011a) was proposed for evaluating the utilization of the space and time resources of a stadium during an evacuation, which is constrained by a waiting time model of pedestrians. However, there is room for improvement in the way these MOEs represent the efficiency of the space–time usage of vehicle and pedestrian flow directions and turning movements in an evacuation plan. To that end, this paper proposes an approach based on space–time use efficiency to evaluate an MOE in the case of an integrated evacuation network that consists of roads, intersections, and building interiors. The authors aim to fill a gap in the evaluation of the space–time use of vehicle and pedestrian movements in an evacuation plan. Several studies have been conducted that should lead to more effective evacuation operations. One avenue of research focuses on evacuation simulations that employ methodologies including cellular automata models, lattice gas models, social force models, fluid-dynamic models, agent-based models, and game-theoretic models. Approaches based on experiments 114 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 with animals (Zheng et al., 2009) have been developed to investigate the evacuation performance of buildings and transportation networks. These approaches use an experimental scenario-driven methodology (Xie et al., 2010) that involves different movement rules, interaction behaviors, transportation networks and their scales. Several studies investigated traffic jams by simulating the panic behavior of pedestrians (Helbing et al., 2000; Helbing et al., 2002), by using a movement model (Cepolina, 2009; Seyfried et al., 2009), by taking waiting times in crowded areas into account (Chow, 2007; Chow and Ng, 2008), and by taking time-dependent network attributes into account (Lämmel et al., 2010). This avenue of research is a commonly used practical approach for evaluating the effectiveness of evacuation operations, owing to the impossible challenge of staging an identical evacuation scenario repeatedly in the real world. The second avenue of research focuses on the optimization of evacuation routes. For example, Stepanov and Smith (2009) presented an integer-programming-based methodology for designing optimal routing policies that can cope with congestion and time delays on road links. Pursals and Garzón (2009) formulated the building evacuation problem in a way that incorporates the evacuation routes. Abdelgawad et al. (2010) proposed a multimodal optimization framework that combines the use of vehicular traffic and mass transit for emergency evacuation. This framework supports a multi-objective optimization approach that can investigate three objectives such as minimizing in-vehicle travel time, minimizing at-origin waiting time, and minimizing fleet cost in the case of mass transit evacuation. The framework models the use of public transit shuttle buses during an evacuation as a delivery vehicle routing problem. Kimms and Maassen (2011) simulated an evacuation plan to find out which roads should be used in what direction when a large number of vehicles need to be routed in an evacuation network. Some studies have considered the evacuation routes for evacuees (Chalmet et al., 1982; Kaufman et al., 1998; Opasanon, 2004; Andreas and Smith, 2009; So and Daganzo, 2010). These studies seldom consider the space and time organization and the efficient use of vehicle and pedestrian evacuation flows. The third avenue of research focuses on space and time organization in cases of emergency evacuation. Chow (2007) and Chow and Ng (2008) introduced a waiting-time index to analyze the waiting times (Predtechenskii and Milinskii, 1969; Fruin, 1971; Smith, 1982; Owen et al., 1996; Gwynne et al., 1998; Kholshevnikov and Samoshin, 2010) in crowded areas in a fire evacuation scenario. Seyfried et al. (2009) analyzed pedestrian flow and congestion bottlenecks based on evacuees’ trajectories. Lämmel et al. (2010) adapted a traffic queue model to capture congestion bottlenecks and the evacuation time in networks with time-dependent attributes. Murray-Tuite and Wolshon (2013) reviewed some popular evacuation time reducing strategies including contraflow operation, crossing elimination, special signal timing in the optimization of evacuation plans. Karoonsoontawong and Lin (2011) formulated a time-varying lane-based capacity reversibility model for traffic management. However, these efforts seldom have incorporated space–time use efficiency into considerations of conflicts between vehicle and pedestrian evacuation flows. The avoidance of such conflicts in evacuation planning while minimizing the evacuation time is still an open research topic (Bretschneider and Kimms, 2012). To this end, this paper proposes a space–time use efficiency approach to provide an assessment of space and time use for planning the turning movements and flow directions of both vehicles and pedestrians. The fourth avenue of research discusses the emergency evacuation under uncertainty and incompliance owing to the unpredictability of human behavior. Yuan et al. (2007) used dynamic assignment to optimize their all-compliance scenarios for each evacuation zone and noted that non-compliance may sometimes yield acceptable efficiency if evacuation zones are too big to allow flexibility. Yao et al. (2009) and Yazici (2010) used dynamic traffic assignment formulation with probabilistic demand and capacity constraints to generate evacuation time performance measures. This formulation is based on a cell transmission model (Daganzo, 1994). In addition, Xie et al. (2011a) presented Monte Carlo simulation approach to quantify the impact of uncertain parameters (i.e. the standard deviation of pre-movement time, percentage of adults, occupant density, effective width in a certain evacuation scenario) on evacuation time in commercial buildings. Wu et al. (2011) also used Monte Carlo simulation approach to evaluate the uncertainty and risk of a fire collection evacuation model. Liu et al. (2011) determined the effective distance of emergency evacuation signs with incompliance of evacuees. These studies need a space–time MOE to assess the efficient use of vehicle and pedestrian evacuation flows under uncertainty and incompliance. This paper presents a space–time use efficiency approach to assess space and time resource use. The approach can be further expanded to assess evacuation efficiency under uncertainty and incompliance. 3. Space–time use efficiency In this section, we define the space–time use efficiency metric on the basis of trajectories on road segments and intersections. This definition is an expanded version of the space–time use efficiency index of Fang, Li et al. (2011), where the trajectories of vehicles and pedestrians are incorporated and the approximate FIFO rule (Lämmel et al., 2010) is relaxed. These extensions lead to a more realistic assessment for evaluating space–time use efficiency in an evacuation plan. Definition 1. Let STCube(ni, nj, nt) denote a space–time cube in the time geography of Hägerstrand (1970). The edge length of the cube in space is D0s , and the period covered by the cube in the time dimension is D0t (see Fig. 1a). D0s and D0t are defined by the user. ni, nj, nt are the numbers used to identify the space–time cube. If a space–time trajectory passes through a space– time cube, this cube is called a used space–time cube; otherwise, it is called an unused space–time cube. Fig. 1 illustrates used (red and blue) and unused (empty) space–time cubes. 115 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Fig. 1. Used and unused space–time cubes. Definition 2. Let IUE(mi, t[t+Dt]) denote the space–time use efficiency of a road intersection mi in a time period t[t+Dt]. Dt is an incremental time interval used to define a evacuation period. The intersection mi can be divided into nx  ny space–time cubes using the parameters D0s and D0t . The numbers nx and ny; are the maximum values of the numbers used to identify space–time cubes in the space. nt denotes the maximum number in the time dimension, so that nt ¼ dDt=D0t e. In this definition, a space–time cube can be used only by one object at a time (e.g. vehicle or pedestrian) (see Fig. 1d). Therefore, in a time period [t, t + Dt], the space–time use efficiency of a road intersection mi is defined as IUE ðmi ; t½t;tþDt Þ ¼   P    Pnx 1 Pny 1 Pnt 1  nx 1 Pny 1 Pnt 1  i¼0 i¼0 k¼0 f STCube ni ;nj ;t ½kD0 ;ðkþ1ÞD0  k¼0 fwait STCube ni ; nj ; t ½kD0 ;ðkþ1ÞD0  j¼0 j¼0 t t t t ð1Þ nx  ny  nt f ðSTCubeðni ; nj ; t½kDt;ðkþ1ÞDt ÞÞ ¼  1 used 0 ð2Þ unused   where the function f equals 1 if STCube ni ; nj ; t½kD0 ;ðkþ1ÞD0  is a used space–time cube; otherwise, f = 0. The function fwait t t equals 1 if the cube STCubeðni ; nj ; t½kD0 ;ðkþ1ÞD0  Þ represents the waiting status of the moving object at the location (ni, nj). t t For example, nx,ny and nt in Fig. 1 have the value of 8. The values of the space–time use efficiency of the intersections in Fig. 1b and c are (15  2)/(8  8  8) in a concerned pedestrian’s period of 8  D0t and16/(8  8  2) in a concerned vehicle’s period of 2  D0t ;respectively. Definition 3. Let IUE(Rd(r), t[t,t+Dt]) denote the space–time use efficiency of the road r in the time period [t, t + Dt]. It is defined as 0 IUE ðRdðrÞ; t ½t;tþDt Þ ¼ @ X P ri 2P r 1, 0 ðlpri =V max ÞA X t ðlpri =v tr Þ i2P r ! ð3Þ  r is the collection of space–time paths on this road in this time period, Vmax is where Pri is the space–time path on the road r, P 0 the maximum travel speed of a moving object when there is free flow on this road, lpri is the travel distance in the time period [t, t + Dt] when the travel speed of the moving object is Vmax, v t r is the average travel speed of moving objects in the time t period [t, t + Dt], and lpri is the actual travel distance in this time period. For example, in Fig. 2, the space–time use efficiency 0 t 0 t of the road r in the time period [t, t + Dt] is derived from the two space–time paths Pri and Prj by using Eq. (3). If li , li ; lj ; lj are 20, 16, 21 and 17 m, Dt = 6s, v tr ¼ 3 m=s and Vmax = 5 m/s, then IUE(Rd(r), t[t,t+Dt]) = (20/5 + 21/5)/(16/3 + 17/3) in Fig. 2. Definition 4. LetIUE(net, t[s,e]) denote the space–time use efficiency of an evacuation network in the time period [ts, te]. For an evacuation plan P, which consists of all roads and intersections in an evacuation network Net, the space–time use efficiency is defined as
IUE net; t½s;e ¼ ar ¼  P r2Net Pt e t¼t s e ar  IUE RdðrÞ; t½t;tþDt þ mi 2Net tt¼t b  IUE ðmi ; t ½t;tþDt Þ s mi P Pt e Pt e P r2Net t¼t s ar þ r2Net t¼t s bmi O no object has passed along road r 1 else
P P ð4Þ ð5Þ 116 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Fig. 2. Space–time paths on a road. bmi ¼  O no object has passed along road mi 1 else ð6Þ Eqs. (4)–(6) will be used to evaluate the space–time use efficiency of an evacuation plan P in an evacuation network in the following section. This network integrates a road network and the interior travel space of a building into a single network. This space–time use efficiency measure has three basic properties: i. This metric is nonnegative and between 0 and 1. A high value indicates that the space resource is used more efficiently. ii. It is a posteriori metric, which reflects only a process-based efficiency characteristic of pedestrians’ and vehicles’ trajectories. iii. It is a space- and time-dependent metric, which represents the space–time use efficiency in any specific time interval. This property helps demonstrate that the time window of a link or intersection is under-or over-used. Subsequently, this metric enables the identification of the time-dependent bottlenecks. The 3D trajectories used in the proposed metric represent the space–time occupancy of evacuees. These trajectories help pinpoint within a roadway or an intersection conflict and congestion locations, which are usually otherwise unidentified at this level of details by the traditional assessment indexes like traffic volume and density. The traffic volume and density derived from 3D trajectories are more realistic and detailed than traditional approaches. In addition, the using of 3D trajectories affords more realistic representation of different modes of transportation (e.g., pedestrian as well as vehicular traffic in this paper) and the interactions between these modes. A price for introducing this added dimension of time in the proposed metric is the increase in the computational complexity and time. To lessen this increased computational burden, a concept of space–time cube was introduced to represent the common trajectory approximate area in space over time, which simplifies the computation of 3D trajectories. This proposed metric is different from existing MOEs, including the one presented by Fang et al. (2011a), in several ways. i. It is different from traffic density, which is typically described as the number of vehicles per unit length or area of the roadway. The proposed metric reflects the characteristic of space–time occupancy within either a specific space area or time interval. ii. It is different from passing rate (Daganzo, 2005), which reflects the intuitive dynamics of a relaxation process in kinematic wave propagates and is easily measured from two dimensional (space and time) trajectory data. The proposed metric involves three-dimensional (X, Y, T) trajectories of both pedestrians and vehicle flows without the need to adhere to kinematic wave propagation rules, especially in the middle of intersections. iii. It is different from the flow rate of the queueing model in a cell (representing freeway segments) of many cell transmission based models (Daganzo, 2005). Instead, this metric relaxes their approximate FIFO rules to include pedestrian and vehicle mixed flows in evacuation networks. iv. It is different from the typical dynamic traffic assignment (DTA) models. For example, the 3D trajectory approach not only illustrates in detail the results of individual trip-making decisions, particularly the path choices within a road or an intersection, but also addresses the representation mechanism of different modes and the interactions among these modes in an intuitive manner, which is yet to be accomplished by typical DTA models. Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 117 4. A multi-objective optimization problem and its hybrid algorithm This section introduces a multi-objective optimization problem of vehicle and pedestrian turning movement decisions in an evacuation plan. Next, this section introduces a hybrid optimization algorithm to assign vehicle and pedestrian turning movement directions for an evacuation scenario in an integrated road and building-interior network. 4.1. Multi-objective optimization problem Most previous works (Kalafatas and Peeta, 2009; Daganzo and So, 2011; Xie et al., 2011b; Xie and Turnquist, 2011) formulate the evacuation network design problems as a lane-based network optimization with some strategies of lane reversal and crossing elimination under the network flow theory. To assess evacuation efficiency, this paper formulates an evacuation plan with simulated trajectories of vehicles and pedestrians by using the following three objectives: minF T ¼ M ði;jÞ2Path X m X ðT m ij þ m¼1 min F L ¼ M ði;jÞ2Path X m X ! =M ð7Þ ! m ðLm ij þ Li Þ =M m¼1 max F I ¼ Tm i Þ te X IUE ðnet; t½t;tþDt Þ ð8Þ t¼ts subject to: ts P 0; t e 6 T c ð9Þ Lm ij 6 Lij ð10Þ Lij Lij 2 P ð11Þ Li j 2 P; Li 2 P ð12Þ where M is the total number of vehicles and pedestrians in the evacuation plan; Pathm is the evacuation path (or route) of the m m m mth evacuee;T m ij is the travel time on link (i, j) of Pathm;T i is the travel time in intersection i on Pathm; T ij and T i are derived from the space–time path of the mth evacuee, which includes the movement time and the waiting time in the unified evacm uation network; and Lm ij and Li are the travel distances on link (i, j) and in intersection i on Pathm, respectively. Tc is the total clearance time of an evacuation plan. Lij is the length of link (i, j). Eqs. (7) and (8) define the objectives of the minimum average evacuation time and the minimum average length of evacuation route. Eq. (9) defines the objective of the maximum space–time use efficiency of the evacuation network. The minimum average evacuation time is a common and critical index for evacuation. The minimum average length of evacuation route evaluates the travel efforts of evacuees in an evacuation plan. The maximum space–time use efficiency reflects the space and time resource use efficiency in the evacuation process, which helps identify the improvement room of an evacuation plan. Eq. (10) restricts the time interval to be between 0 and the total clearance time. Eq. (11) requires that the trajectory length of pedestrian or vehicle on each link to not exceed the length of the link. Eq. (12) guarantees the configuration of links and intersections to be in the evacuation plan P. 4.2. Overview of hybrid algorithm Fig. 3 gives an overview of the hybrid optimization algorithm for evacuation (HOAE), which is implemented in a two-tier framework. The upper tier optimizes the configuration of turning movement directions in the evacuation network intersections, while the lower tier optimizes the routings of vehicles and pedestrians under the configuration of evacuation network. The optimized routing results in the lower tier supporting the efficiency evaluation of the evacuation plan in the upper tier. The upper tier is based on the non-dominated sorting genetic algorithm NSGA-II (Deb et al., 2002; Murugan et al., 2009; Chaudhuri and Deb, 2010) and is designed to optimize the turning movement directions of the intersections in the evacuation network constrained by the three objectives: the least average evacuation time, the least average length of the evacuation route, and the maximum space–time use efficiency of the evacuation network. NSGA-II is a well-known algorithm for multi-objective optimization, which provides a uniformly spread Pareto-optimal front archive (Saadatseresht et al., 2009; Hájek et al., 2010) by adapting a fast Pareto-compliant ranking method and favoring non-dominated solutions. Details of this algorithm have been published elsewhere (Deb et al., 2002; Chang et al., 2008). The upper tier in Fig. 3 contains the six main steps, where steps 1 and 3–6 are the basic steps of the NSGA-II algorithm, and step 2 is an added step. The lower tier contains two main steps. This tier uses the FIFO queue model to model pedestrian and vehicle movements on road, while using the cellular automata model to simulate the movement of vehicles and pedestrians with the help of a route choice strategy obtained from an ant colony optimization (ACO) algorithm. This simulation does not include traffic 118 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Fig. 3. Overview of the hybrid optimization algorithm. controlling at the intersections. Although various control types could be applied based on the demand if desirable (Han et al., 2008). ACO algorithms have some advantages in solving combinatorial optimization problems because of the strong exploration ability of ants (Li et al., 2009). Blum has presented an overall introduction to ACO algorithms and a summary of recent trends (2005). The first step defines the basic movement rules for a moving object (a vehicle or pedestrian) in order to describe its interaction with other objects in the evacuation network. Constrained by these movement rules, the second step uses the ACO algorithm to optimize the routes of the moving objects constrained by an integrated objective, namely, the least total length(Unit: metersecond) of pedestrians and vehicles’ space–time paths modeled by time geography theory of Hägerstrand (1970). The optimized evacuation routes of vehicles and pedestrians then can be used to measure the performance of an evacuation plan in the upper tier. 4.3. Main steps of the algorithm This section describes only the most important parts of the modifications that we made to the original genetic algorithm and ant colony optimization algorithm; we shall not repeat the basic descriptions of these two algorithms. 4.3.1. Step 1 By acknowledging the influence of conflict points (Cova and Johnson, 2003; Wang et al., 2009; Xie and Turnquist, 2011; Xie et al., 2011b; Bretschneider and Kimms, 2012) on vehicle–pedestrian mixed traffic flows at intersections, our algorithm divides the turning movements of vehicles and pedestrians into 12 combinations in the case of an intersection of type 1 (as defined in Fig. 4) and three combinations in the case of an intersection of type 2. This division was done to reduce conflicts between moving objects (i.e., vehicles and pedestrians) within the intersections. In Fig. 4, there are 16vehicle-vehicle traffic conflict points and 24 vehicle and pedestrian conflict points in the type 1 intersection. The cases (1)–(12) in the figure are the candidate combinations of turning movement directions that can be used if we choose to control the turning movements of vehicles and pedestrians. Each turning movement direction can apply to guide both vehicles and pedestrians at intersections. In the algorithm, a gene in the genetic algorithm’s chromosome represents one of the combinations of turning movement directions listed in this figure. Similarly, there are three vehicle-vehicle traffic conflict points and 12 vehicle–pedestrian conflict points in the type 2 intersection. Three turning movement direction combinations (i.e., 1–3) are considered for the purpose of controlling the turning movements in this type of intersection. A chromosome in the algorithm represents an overall combination of turning movement directions in all intersections in the evacuation network. Let n denote the number of Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 119 Fig. 4. Turning movement direction combinations in two typical types of road intersections. intersections in the evacuation network that need to be controlled. Let m denote the number of intersections of type 1, and n - m the number of intersections of type 2. The chromosome of the genetic algorithm is represented as g i ¼ fk0 ; . . . ; km1 jkm ; . . . ; kn1 g;  j < m; 0 6 kj 6 3 m 6 j 6 n; 0 6 kj 6 12 ð13Þ where kj represents the combination of turning movements in the intersection i. If kj = 0, a turning movement control strategy is not adopted at intersection i. All genes in the chromosome are initialized to random numbers between 0 and 12. The chromosome defines the current turning combination of movement directions in the evacuation network. 4.3.2. Step 2 This step simulates the movements of vehicles and pedestrians in the evacuation network and optimizes evacuation routes for them under the constraint of the current turning movement direction combination. Generally, the movements of vehicles and pedestrians are constrained by two different environments, for example those in a road and in an intersection (Fig. 5). This study simulated movements according to the basic assumption that vehicles and Fig. 5. Movement environments in a road and an intersection. 120 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 pedestrians move in exclusive lanes on a road (see Fig. 5a). This assumption prevents potential interference between vehicles and pedestrians on roads during the process of evacuation. Based on this assumption, we directly formulated the simulated travel speeds of vehicles (Stepanov and Smith, 2009) and pedestrians (Lämmel et al., 2008) on a road in a time period Dt as v ðt þ DtÞ ¼ ( minðV max ; 1=Dtr Þ if mode ¼ 0 V max ðC r þ 1  Nr Þ=C r if mode ¼ 1 ð14Þ where mode = 0 means the case of a pedestrian, and 1 a vehicle. Dti is the pedestrian density on the road r in this time period. The calculation of the pedestrian density can be found in the literature (Fang et al., 2011a). The pedestrian speed in Eq. (14) was directly from a speed-density relationship (Lämmel et al., 2008). The pedestrian speed was tested to show that dynamic produced by their queue model is not too far away from Weidmann’s (1993) fundamental diagram. The detailed calibration of queue model in pedestrian evacuation was explained in Lämmel et al. (2008). Cr is the capacity (vehicle number) of vehicles on the road, and Nr is the current number of vehicles on the road. In addition, the pedestrians and vehicles are constrained to be in FIFO queues (Lämmel et al., 2010) on the corresponding lanes of the road. However, the moving objects on the road do not obey the FIFO rule as a whole, because pedestrians may move into the road earlier, and leave the road later than the vehicles. To simulate the interactions between vehicles and pedestrians, this study simulated the movements of pedestrians and vehicles by using a similar mechanism involving cellular automata (Gerhardt et al., 1990). Each intersection was divided into orthogonal grid cells with a size of 0.5 m  0.5 m (see Fig. 5b). The defined cell size meets evacuation requirement in China. It can be defined differently according to user’s evacuation requirements in practice. Each pedestrian could use a grid cell at any time, whereas a vehicle used 2 m  5 m at a time, that is, a square with 4  10 cells. At any time, a grid cell in an intersection could be used by one moving object (i.e. a vehicle or a pedestrian) only. When two moving objects were competing for a grid cell, this cell was assigned to one of them on the basis of a first-come-first-served interaction rule. This rule simulates the three conflicts between pedestrians, between vehicles, and between pedestrians and vehicles (Zhang and Chang, 2011) in an intersection and at a time interval. Specifically, the moving object with the least travel time to this cell will use this cell, and other moving objects will wait until the clearance of this cell or competing for other cells with a shortest path in all unused cells. This approach is different from Zhang and Chang (2011)’s competition factor in floor field of intersection. The moving speed of pedestrians (Lämmel et al., 2008) and vehicles in the grid cells of the intersection was defined as v ðt þ DtÞ ¼ ( minðV max 1=Dtr Þ if pedestrians v 0t v ehicles if ð15Þ where v 0t is the speed of a vehicle entering the intersection. When pedestrians and vehicles do not move between cells, their speeds of are 0. To optimize the evacuation routes for vehicles and pedestrians, this study divided the whole evacuation process into k stages (see Fig. 6), and calculated the routes by using the ACO algorithm. For example, a pedestrian may be in a stadium; this person needs to walk to a parking place (the first stage) and then drive his or her car to the exit of the road network (the second stage). Each vehicle or pedestrian should move towards one of the network exits in each transition from one stage to the next. The evacuation routes for vehicles and pedestrians were calculated under the assumption of a unified evacuation network with a virtual origin and a virtual destination (Fig. 6). This idea is derived directly from the global optimization of emergency evacuation assignments based on a ‘one-destination network’ (Yuan et al., 2006). This approach uses the virtual origin and destination to simplify the calculation of evacuation routings of vehicles and pedestrians in a unified evacuation network rather than the pedestrians’-only routings in a hierarchical directed network of Fang et al. (2011b). This virtual origin and destination approach improves the calculation speed of the approach in Fang et al. (2011b) by eliminating its repeated checking of destinations. This unified evacuation network can facilitate the planning of routes between multiple origins and multiple destinations by using a shortest-path algorithm, for example, the well-known Dijkstra algorithm Fig. 6. The virtual origin and destination in a unified evacuation network. Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 121 (Dijkstra, 1959) or the A shortest-path algorithm (Hart et al., 1968). The evacuation network can be converted to a directed network G(V, A), where V is the node set in this network, and A is the set of directed edges that can be passed along by vehicles or pedestrians. Let Des Set = {Des1, . . ., Desn|Desi e V} denote the set of exits of all stages in Fig. 6, where Desn is the set of exits of the nth stage. In stage m, a vehicle or pedestrian located at node i has to choose a node j as the next node with a probability defined by ! 8 . X > b < ðsa ðtÞ  gb ðtÞÞ a siw ðtÞ  giw ðtÞ ; ði; wÞ 2 A and Stagej P Stagei ij ij Pm ij ðtÞ ¼ w2V > : 0; else   gij ðtÞ ¼ 1= dismin jd  ð1=fj ðt; DtÞÞ  ð1=fði;jÞ ðt; DtÞÞ ; d 2 Desk ð16Þ ð17Þ where sij(t) is the level of pheromone at the link (i, j) at time t; gij(t), defined by Eq. (17), is the optimization function used to min provide heuristic information; and a and b are parameters used to control the influences of sij(t) and gij(t), respectively. disjd is the minimum distance between the current node j and the exits of Desk. Stagei and Stagej represent the stages of the nodes i and j in this unified evacuation network. The vehicle or pedestrian will choose the node with the highest probability as the next node. fj(t, Dt) is the space–time efficiency of the node (i.e. intersection) j. f(i,j)(t, Dt) is the space–time efficiency of the link (i, j). The algorithm uses two pheromone-updating approaches. After calculating the evacuation path for an incremental travel time Dt, the ACO algorithm updates the pheromone level of each link in the unified evacuation network according to sij ðt þ 1Þ ¼  ð1  uÞ  sij ðtÞ þ u  s0 ; if sij ðtÞ; v ij ðtÞ > v ðtÞ else ð18Þ  ðtÞ is the where u is the rate of pheromone evaporation (u e [0, 1]), vij(t) is the travel speed on the link (i, j) at time t, and v average speed on the evacuation network at t. This pheromone-updating approach suggests that vehicles and pedestrians should choose links with high travel speeds, and is used in a process of local search. The second pheromone-updating approach is designed to update the pheromone from the nth-generation solution to the (n + 1)th-generation solution in the ACO algorithm: sij ðn þ 1Þ ¼ ð1  qÞ  sij ðnÞ þ q  M X Ds m ij ð19Þ m¼1 Ds m ij ¼ 8 > > > > < Q= > > 0; > > : ! ! X STPLmij =Numij ; if STPLm 6 STPL and ði; jÞ 2 pathm m else ð20Þ where sij ðnÞ is the level of pheromone on the link (i, j) in the nth generation; q is the rate of pheromone evaporation m ðq 2 ½0; 1Þ; STP Lm ij is the length of m’s space–time path on the link (i, j); STP_L is the total length of the vehicle or pedestrian m’s space–time path; STPL represents the average space–time path length in the current solution, in which each vehicle or pedestrian has a space–time path in the network; Numij is the number of vehicles and pedestrians on the link (i, j); and Q is a constant parameter. This updating approach suggests that vehicles and pedestrians should choose links with a high space– time efficiency. In addition to the probability function defined by Eq. (16) and the two pheromone-updating approaches above, the study extended the HMERP (hierarchical multi-objective evacuation routing problem) algorithm (Fang et al., 2011b) to solve for the space–time paths in the unified evacuation network by integrating the approach of virtual origin and destination. 4.3.3. Steps 3–6 Step 3 evaluates the objectives (see Eqs. (7)–(9)) of the simulated evacuation plan by sorting the populations by order of Pareto dominance. Combining the parent and offspring populations from the previous steps produces a population set. This population set is sorted according to the non-domination rule. To preserve the diversity of populations, the algorithm measures the similarity between populations of each subgroup on the Pareto front, and then uses a binary tournament selection operator to choose a representative of each subgroup based on crowded comparison. A clear presentation of the pseudocode and an explanation of these functions can be found in the literature (Deb et al., 2002). Step 4 checks the termination conditions of the algorithm. The first condition is that the current loop number of the algorithm is equal to a predefined constant parameter. The second condition is that the solutions have not improved within the minimum number of population generations. Step 5 creates several new populations by using an evolutionary process with surrogates for evolutionary operators, including selection, genetic crossover and genetic mutation. The selection operation is based on tournament selection. 122 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 The crossover operation within a chromosome segment is based on single-point crossover, but from the perspective of the whole chromosome it is actually a multiple-point crossover operation. The mutation operator was not modified here; it is the same as that of the standard genetic algorithm. A detailed description of steps 3 and 5 can be found in the literature (Deb et al., 2002). Step 6 outputs the evacuation plans and their Pareto-optimal front solutions. 5. Computational experiments 5.1. Experimental design In this study, we selected the stadium and adjacent road network at the Wuhan Sports Centre in China as our evacuation environment (Fig. 7). The evacuation network included the walking network in the stadium and the road network for pedestrians and vehicles outside the stadium. The walking network in this stadium had 275 links, 137 nodes and 81 intersections, and the road network outside the stadium had 369 links, 135 nodes and 111 intersections. An intersection (i.e., a crossover or a T-shaped intersection) could include more than one node in the network. All pedestrians and vehicles needed to leave from eight exits in this evacuation environment. The links in the road network represented the lanes for vehicles to drive on and for pedestrians to walk on during the evacuation process. In this study, we tried to optimize only the turning movement directions in 33 candidate intersections outside the stadium, which are labeled with serial numbers from 1 to 33 in Fig. 7. In this experiment, pedestrians with cars needed to walk to the car park and then drive their cars to leave the study area. Therefore, the car park was an exit for pedestrians in one of the stages of the evacuation process. Pedestrians and vehicles chose the next part of their route when they were near to intersections. In the case of a turning-movement-direction-controlled intersection (Fig. 4), pedestrians and vehicles could choose the next direction of their route only from the directions in the turning movement direction combination of that intersection. The actual turning movement direction was defined by Eq. Fig. 7. The study environment. 123 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 (16). In the case of intersections without control, pedestrians and vehicles chose their next direction in accordance with Eq. (16) only. They traveled in their chosen direction at a speed defined by Eq. (15). The algorithm was implemented in a Visual C++ 6.0 environment, and run on a personal computer with an Intel Core Duo 3.06 GHz CPU and 2 GB of RAM. The algorithm used only one CPU in this experiment. The algorithm is computationally intensive (average 2 days of implementation and maximum memory requirement of 220 MB for this study area) because of many Pareto front solutions rather than only the best solution for one objective. Parallel computing methods can improve this implementation. The parameters used in this implementation are given in Table 1. The value of Vmax for pedestrians was taken from the work of Chen and Feng (2009), and that for vehicles was the travel speed on a side street during an evacuation given by Edara et al. (2010). 5.2. Analysis of results We analyzed the optimized results from three different perspectives, namely Pareto solutions, evacuation curves, and space–time use efficiencies in intersections and links. In relation to the first perspective, Fig. 8 gives the number of Pareto front solutions, measured in generations of the hybrid optimization algorithm. This algorithm terminated when a continuous 15 generations of the ant colony algorithm satisfied some condition, for instance, that the minimum value of the total space–time path length of the Pareto front solutions was larger than 99.5% of the average value of the total space–time path length of those Pareto solutions. Fig. 8 illustrates that there is a relatively stable number of Pareto front solutions at the end of the process. In this study, we found 26 Pareto front solutions by repeating the implementation 10 times. Fig. 9 illustrates the distribution of Pareto front solutions in the objective space. The two fitted surfaces represent the trend surfaces of the solutions at the first generation and at the Pareto front. The fitted surface generated from the Pareto front solutions is closer to the three objective axes than the first five generation solutions are. In other words, the first five generation solutions were improved on and replaced by the Pareto front solutions by using the proposed algorithm. Therefore, Fig. 9 validates the capability of the proposed algorithm. Figs. 8 and 9 show that the proposed algorithm can achieve better results. Table 2 lists statistical results for three kinds of solutions. Solution #0 is a solution of the first kind, in which none of the candidate intersections have the turning movement directions constrained as in Fig. 4. Solutions #1–#26 are solutions of the second kind, which are derived from our proposed hybrid optimization algorithm. The solution ‘TRANSIMS’ is a solution of the third kind; it was derived from a simulation done using the open source software package TRANSIMS (http://sourceforge.net/projects/transimsstudio/). TRANSIMS is an integrated development environment for a transportation analysis and simulation system. The TRANSIMS run in user (Nash) equilibrium mode of traffic flow theory where every individual attempts to optimize his or her individual travel times, and do not focus on the system level travel times and the proposed metric in the proposed algorithm. TRANSIMS performs well to capture the congestions, while the proposed algorithm optimizes the system performance of evacuation. In our simulation of an evacuation process using TRANSIMS, we converted the network to TransimsNet without traffic signals and turn prohibitions, and used the origin and destination demand, which is directly derived from the result of the #0, even if it used only two transportation models (i.e., walk and car) in TRANSIMS simulation. Pedestrians in the stadium who have cars need to pick up their cars needed to perform two kinds of movement, namely moving at a maximum walking speed of 2 m/s and driving at a maximum vehicle speed of 15 m/s. Other parameters of pedestrians and vehicles used in the TRANSIMS simulation are listed in Table 1. Table 1 Parameters used in this study. Parameter Meaning Value Parameter Meaning Value M Total pedestrian number Width of a cube 23,362 0.5 m Vn m Vehicle number Intersection number of type 1 1325 15 Height of a cube 1s n candidate intersection number 33 Maximum speed of pedestrians Maximum speed of vehicles 2 m/s 15 m/s D0s D0t Vmax Parameters of ant colony algorithm a b u and q Q Parameters of genetic algorithm Control the influence of sij ðtÞ Control the influence of gij ðtÞ 1 2 Population size Generation number 50 150 Pheromone evaporation rate Control the update rate of pheromone 0.1 1 Crossover rate Mutation rate 0.8 0.2 Vehicle Parameters used in TRANSIMS MaxVel Maximum velocity MaxAccel Maximum acceleration speed MaxDecel Maximum deceleration speed Length Length of vehicle Capacity Person in vehicle Pedestrian 15 m/s 3 m/s2 4.5 m/s2 7.5 m 4 person MaxVel MaxAccel MaxDecel Length Capacity 2 m/s 1 m/s2 1 m/s2 2m 1 person 124 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Fig. 8. Number of Pareto front solutions in generations. Fig. 9. Distribution of Pareto solutions. Six of the solutions (#5, #6, #8, #9, #21 and #24) in Table 2 are the best solutions in terms of one or two evaluation indices. Solution #5 has the minimum average evacuation time, solution #6 has the minimum number of intersections in which the turning movement directions need to be controlled, solution #8 has the minimum average path length, solution #9 has the highest space–time use efficiency, solution #21 has the minimum clearance time and solution #24 has the maximum space–time use efficiency in links. Also, several of the solutions between #1 and #26 outperform the solution obtained from TRANSIMS with respect to clearance time and space–time use efficiency. The 28 solutions in Table 2 provide candidate evacuation plans, with optimized vehicle and pedestrian turning movement, from which emergency management agencies can choose in order to determine feasible evacuation plans. For example, if the emergency management agencies do not wish to dispatch many police officers to maintain specified vehicle and pedestrian flows at intersections, they can choose solution #6 or #25. Solution #25 outperforms solution #6 with respect to the average path length and the space–time use efficiency, but solution #25 needs more police officers to control the vehicle and pedestrian turning movements at three more intersections than in solution #6. In relation to the second perspective, we analyzed evacuation curves derived from eight selected solutions. Fig. 10 illustrates the eight evacuation curves and shows the time-dependent evacuation performance among plans while they are compared with the solution of TRANSIMS. The evacuation curve for the TRANSIMS solution is smoother than that for the other solutions. This smoothness may reflect the Nash equilibrium achieved (Osborne and Rubinstein, 1994), which is a goal of the process of loading traffic onto the network in TRANSIMS. However, the evacuation curves of the other seven solutions (#0, #5, #6, #8, #9, #21 and #24) are not so smooth. In particular, the curves deviate from the TRANSIMS evacuation curve after 3000 s to a large extent. The evacuation times in these solutions when 95% of the evacuees have left the evacuation network from the eight exits in Fig. 7 are 4980s (#0), 4980 s (#21), 5100s (#6), 5130s (#5), 5160s (#8), 5790 s (TRANSIMS), 6120 s (#24) and 6420s (#9). From the evacuation curves in Fig. 10, solutions #0, #5, #6 and #21 have better performance than the other solutions (#8, #9, #24 and TRANSIMS). 125 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Table 2 Statistical results for the solutions. Solution no. #0 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #26 TRANSIMS ATL 1338.03 1333.65 1277.00 1529.19 1298.05 1423.08 1339.64 1534.80 1259.98 1567.66 1371.83 1318.96 1294.95 1506.83 1317.83 1481.61 1469.30 1514.99 1483.18 1415.86 1353.58 1351.64 1339.34 1302.10 1439.91 1274.81 1363.80 1686.79 AET 3431.52 3351.06 3976.92 3524.53 4300.00 3219.10 3423.94 3879.65 3624.45 3993.37 3413.00 3920.19 3998.02 3678.81 3523.83 3623.36 3507.21 4452.81 3991.66 3308.24 3438.57 3301.89 3527.47 4213.24 4413.80 4209.15 4435.90 3611.35 0 T 5065.33 5211.94 5433.66 6149.50 5699.50 5433.66 5151.94 6209.50 5211.94 6981.94 5729.50 5597.58 5789.50 6036.38 5493.66 5526.38 5814.45 6516.38 6516.38 5583.66 5510.50 5048.54 5523.66 5549.50 6216.38 5699.50 6359.50 6466.75 N’ 0 23 24 24 23 21 18 23 21 21 22 23 22 25 21 25 21 23 26 21 23 23 21 24 26 19 24 0 Ratio IUE IUE(net) IUE (m) IUE(Rds) IUE ðnetÞ N0 T N0 0.535 0.606 0.693 0.672 0.724 0.608 0.642 0.719 0.665 0.744 0.661 0.706 0.668 0.714 0.627 0.696 0.662 0.731 0.725 0.644 0.659 0.656 0.640 0.715 0.730 0.709 0.725 0.595 0.435 0.479 0.569 0.531 0.621 0.479 0.494 0.599 0.533 0.630 0.521 0.599 0.537 0.586 0.475 0.556 0.536 0.621 0.608 0.510 0.528 0.521 0.494 0.612 0.612 0.589 0.614 0.424 0.576 0.656 0.743 0.724 0.767 0.656 0.698 0.764 0.716 0.780 0.714 0.748 0.720 0.763 0.686 0.751 0.710 0.774 0.770 0.696 0.709 0.709 0.694 0.757 0.782 0.757 0.770 0.667 0.026 0.029 0.028 0.031 0.029 0.036 0.031 0.032 0.035 0.030 0.031 0.030 0.029 0.030 0.028 0.032 0.032 0.028 0.031 0.029 0.029 0.030 0.030 0.028 0.037 0.030 226.61 226.40 256.23 247.80 258.75 286.22 269.98 248.19 332.47 260.43 243.37 263.16 241.46 261.60 221.06 276.88 283.32 250.63 265.89 239.59 219.50 263.03 231.23 239.09 299.97 264.98 Where ATL is the average travel length, AEL is the average evacuation time, T 0 is the clearance time, N 0 is the controlled intersection number, IUE ðnetÞ, IUE ðmÞ and IUE ðRdsÞ represent the space–time use efficiencies of whole evacuation network, intersections and roads respectively. Fig. 10. Evacuation curves for eight solutions. In relation to the third perspective, we analyzed the space–time use efficiencies to find solutions. Table 2 lists the values of the overall space–time use efficiency index for all the solutions (#0–#26 and TRANSIMS). Most values for the links in the three solutions are higher than the values for the adjacent intersections. This indicates that interactions between vehicles 126 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Table 3 Distribution of space–time use efficiency for all solutions. Solution IUE 0 (0, 0.2] (0.2, 0.4] (0.4, 0.6] (0.6, 0.8] (0.8, 1.0] 95 90 106 118 113 99 127 103 153 146 140 138 121 143 120 130 125 116 111 106 108 106 99 103 72 63 63 65 60 65 65 69 75 75 51 42 42 57 43 52 124 154 173 175 200 174 190 187 Distribution of intersections #0 0 #5 0 #6 3 #8 5 #9 1 #21 0 #24 1 TRANSIMS 2 42 40 43 42 33 39 37 47 68 61 61 52 56 61 51 71 35 31 25 29 16 26 23 21 27 34 26 23 20 21 24 22 20 26 34 41 66 45 56 29 Distribution of links #0 #5 #6 #8 #9 #21 #24 TRANSIMS and pedestrians in intersections reduce the space–time use efficiency to some extent. To investigate the extent of the differences in space–time use efficiency between solutions, Table 3 lists the numbers of links and intersections in different intervals of the space–time use efficiency index. From this table, there are 90–127 links having a space–time use efficiency of 0 in a solution, while there are 0–5 intersections having a space–time use efficiency of 0. This observation indicates that many links are not used under the constraints of the turning movement direction combinations, which are aimed at improving the space–time use efficiency of the whole evacuation network. Although the number of links in the TRANSIMS solution with a space–time use efficiency between 0.8 and 1.0 (i.e., 187) is more than that for the five other solutions (#0, #5, #6, #8, #21) in Table 3, the overall space–time use efficiency is 0.6, which is lower than the values for most of the other solutions in Table 2. This may be caused by the low space–time use efficiencies of the intersections in the network of stadium environment. This observation suggests that high priority needs to be given to assigning reasonable turning movement directions in intersections in an evacuation plan. It also supports the motivation behind this paper by showing that optimizing the turning movement directions in intersections is important. 6. Discussion There are two interesting questions to be discussed here. The first question is whether, if we control more intersections in an evacuation plan, we can achieve a higher space–time use efficiency or a smaller clearance time in that plan. The second question is about what the most suitable turning movement direction combination is for each intersection. To discuss the first question, we calculated the ratio of the space–time use efficiency to the number of controlled intersections and the ratio of the clearance time to the number of controlled intersections; the values of these ratios are listed in Table 2. Solution #25 has the highest ratio (0.037) of the space–time use efficiency (0.709) to the number (19) of controlled intersections. Solutions #5, #8, #9, #14, #16, #19, and #22, with same numbers of controlled intersections no larger than 21, also have higher ratios than most other solutions. However, solution #1, where 23 intersections are controlled, has the lowest ratio of the space–time use efficiency to the number of controlled intersections. This observation suggests that emergency management agencies can maintain an appropriate space–time use efficiency without employing police resources to enforce specific turning movement directions in intersections in the evacuation network. The ratio of the clearance time to the number of controlled intersections is lowest for solution #21. Solution #15has more controlled intersections, but it does not have a smaller clearance time than solution #21. The ratios of the clearance time to the number of controlled intersections also indicate that limited police resources should be dispatched primarily to key intersections in order to achieve proper utilization of the clearance time. This demonstrates that the motivation behind this study is valid. With respect to the second question, Fig. 11 illustrates the turning movement direction combinations for solution #6, and Table 4 lists the turning movement combinations for all intersections in six solutions. Fig. 11 depicts the used and unused turning movement directions and the turning movement direction combinations for the controlled intersections. The number next to each intersection is the number assigned to the optimized turning movement direction combination for that intersection in solution #6. These turning movement direction combinations may help emergency management agencies give clear instructions to police in order to maintain specific turning movement directions. Vehicles and pedestrians interact in other intersections according to the velocity Eq. (15). From Table 4, when we look at the cases where turning movement directions are controlled, we see that intersections 1, 5, and 9, which are type 2 intersections, are assigned only the turning 127 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 Fig. 11. Turning movement direction combinations for solution #6. Table 4 Turning movement combinations of all intersections in six solutions. Intersection # (Type 2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Solutions Intersection # (Type 1) #5 #6 #8 #9 #21 #24 1 0 1 1 1 0 2 2 0 0 1 0 2 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 2 1 1 2 0 0 0 0 0 0 1 1 1 0 0 0 2 1 1 1 1 2 1 1 1 0 0 0 1 0 2 2 0 0 0 0 1 1 1 1 0 0 1 0 0 2 1 0 1 2 2 2 0 2 0 1 1 2 2 2 0 2 0 0 1 2 1 2 2 0 2 2 0 2 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Solutions #5 #6 #8 #9 #21 #24 1 11 5 0 0 1 4 2 10 9 6 3 0 10 0 0 2 6 2 8 0 0 4 0 9 0 8 5 0 8 5 6 5 0 8 6 8 2 0 7 5 0 5 0 0 0 11 11 6 7 9 0 5 1 0 11 0 5 1 8 10 2 0 6 9 11 1 8 0 1 4 9 11 2 0 7 2 2 6 0 5 5 4 9 6 1 1 0 6 9 movement combination 1 defined in Fig. 4, while intersections 12 and 15, which are also of type 2, are assigned only the turning movement combination 2. Also, intersection 22, which is of type 1, is mostly assigned turning movement direction combination6. This observation suggests that some interactions can be assigned specific turning movement direction combinations in all simulated evacuation plans. Some intersections of type 2, from intersection 1 to intersection 18, show varying assignments of turning movement combinations, and most of the intersections from 19 to 33 show changes in their turning movement direction combinations, which occur between two and five times. This indicates that optimization of the combi- 128 Z. Fang et al. / Transportation Research Part C 31 (2013) 112–130 nations of turning movement directions in an evacuation network is vital for implementing an efficient evacuation operation with high space–time use efficiency. 7. Conclusions In this paper, we have presented an approach to the assessment of space–time use efficiency, based on trajectories on road segments and intersections. This approach provides an alternative trajectory-based model for assessing the space and time usage of an evacuation network and for measuring the effectiveness of an evacuation plan. On the basis of this approach, we have proposed a two-tier hybrid optimization algorithm to plan vehicle and pedestrian turning movement directions for an evacuation in an integrated road and building-interior network. This algorithm may help emergency management agencies design evacuation plans by comparing the influence of controlled intersections, via the space–time use efficiency, on the effectiveness of various possible evacuation plans. The computational experiments in this study demonstrate that the intersections in an evacuation network need to be assigned reasonable vehicle and pedestrian turning movement directions; this assignment influences the ability to make full use of the evacuation network in terms of space–time use efficiency. A comparison between our calculated solutions and a TRANSIMS solution shows that our proposed approach is suitable and effective for organizing vehicles and pedestrians in space and time in an evacuation process. We plan to improve our approach in several directions. First, it would be useful to investigate the influence of the normal and abnormal behavior of evacuees, traffic controlling, and the evacuation uncertainty on the space–time use efficiency of an evacuation plan. Second, it would be valuable to extend this algorithm to fit large scale networks by parallel computing approaches. Third, it would be valuable to develop practical location techniques to detect evacuees in an evacuation environment, and to develop efficient guidance techniques for evacuees in emergency situations. For example, it is helpful to integrate variable message signs (Hooshdar and Adeli, 2004) and dynamic management techniques (Hamza-Lup et al., 2008) into evacuation processes. Improvements in these respects would help pedestrians and vehicles escape from evacuation environments efficiently, in accordance with an evacuation plan. Acknowledgements This research was supported in part by the National Science Foundation of China (Grants #40971233, #41231171, #61170202, #9112000), the project from State Key Laboratory of Resources and Environmental Information Systems, CAS of China (#2010KF0001SA), LIESMARS Special Research Funding, and the Funding for Excellent Talents in Wuhan University. The authors also would like to thank the ten anonymous reviewers for their valuable comments and suggestions. References Abdelgawad, H., Abdulhai, B., Wahba, M., 2010. Multiobjective optimization for multimodal evacuation. Transportation Research Record 2196, 21–33. Andreas, A., Smith, J., 2009. Decomposition algorithms for the design of a nonsimultaneous capacitated evacuation tree network. Networks 53 (2), 91–103. Blum, C., 2005. 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