Pramana – J. Phys. (2018) 91:62 © Indian Academy of Scienceshttps://doi.org/10.1007/s12043-018-1621-2

Investigating pedestrian evacuation using ant algorithms

SIBEL GOKCE∗, AHMET CETIN and RANA KIBAR

Department of Physics, Faculty of Arts and Sciences, Manisa Celal Bayar University,Muradiye, Manisa 45140, Turkey∗Corresponding author. E-mail: sibel.gokce@cbu.edu.tr

MS received 2 August 2017; revised 23 February 2018; accepted 6 March 2018; published online 6 September 2018

Abstract. Ants communicate with each other by depositing a chemical called pheromone on the substrate whilethey crawl forward. By this way, they follow their predecessor and large trail systems are built. Inspired by thecommunication via chemical signals of ants, we have proposed a model to investigate the collective motion inhumans during an emergency. It is considered that pedestrians use some kind of virtual chemotaxis to find theshortest way to the exit. This basic idea is implemented with the floor field model which is the most popular cellularautomata model. The dependence of the evacuation from a room on the virtual chemotaxis evaporating rate f and thepresence of the obstacle are investigated in this paper. The simulation results show that the increase in evaporationrate has been seen to slow down the evacuation. Moreover, it is found that positioning the obstacles in the roomcould lead to the phase transitions and decrease the evacuation time.

Keywords. Emergency; evacuation; collective motion; ant algorithm; cellular automata.

PACS Nos 05.65+b; 45.70.Vn; 05.50.+q; 05.70.Jk

1. Introduction

An emergency is an unusual and uncontrollablehazardous event that exposes the society either totallyor partially to danger and distorts the social order andstructure. Fire, natural disasters, armed assaults andbombings are some such possible daily events and theevacuation of pedestrians in an emergency situationis crucial. It is observed that pedestrians in an emer-gency situation exhibit collective behaviour. Collectivebehaviour is the motion in which an individual unit’saction is dominated by that of its neighbours and allunits simultaneously change their behaviour to a com-mon pattern [1] and is observed not only in humans [2–9]but also in macromolecules [10,11], bacterial colonies[12–15], amoebae [16,18], cells [19–23], fish schools[24–27], bird flocks [28–30], mammals [31–33], midges[34] and ants [6–9,35–38].

Evacuation models can be classified into two types:the macromodel and the micromodel. The macromodelprovides ease of calculation, but it does not tackle humanbehaviour comprehensively and the results obtainedusually deviate from real data. In the micromodel,human behaviour is investigated after considering allkinds of evacuation factors such as the structure of the

building, number and size of exits, obstacles, etc. Themicromodel can be broadly divided into continuous anddiscrete models. Social force model, introduced by Hel-bing et al [4] and improved by Lakoba et al [39], is acommonly used continuous model. This model treatsan individual as a molecule in the fluid dynamics anduses partial differential equations to calculate velocity,density and flux. The lattice gas model [40–51] and thecellular automaton [52–59] model are the most famousdiscrete models.

Cellular automata (CA) has been adopted widely inareas such as biology [60] and fluid dynamics [61] sincethe 1940s when Neumann et al [62] studied biologicalreproduction. In the CA model, space is divided into aregular grid of cells and the set of these cells with theirvalues is named as floor field that is classified into twotypes: static and dynamic floor fields. The static floorfield is the shortest distance to the exit and its valuedoes not change with time. As for the dynamic floorfield, it can be defined as the tendency of pedestriansto follow each other. In cellular automaton simula-tions, the current state of a cell is determined by thestates of its neighbours, and Von Neumann and Mooreneighbourhood approximations have been commonlyused in the literature. Von Neumann neighbourhood

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comprises four cells that are orthogonally surrounding acentral cell on a two-dimensional square lattice (north,south, west and east). As for Moore neighbourhood, itis the set of all cells that are orthogonally or diagonallyadjacent to the region of interest and consists of eightcells surrounding it (north, south, west, east, northeast,northwest, southeast and southwest).

The CA model has been applied to the modellingof emergency evacuation because of the similaritiesbetween the evacuation and pedestrian dynamics.Burstedde et al [52] investigated the transition from astable flow phase to a complete jamming by using a two-dimensional CA. The choice of an evacuation route isessential, so evacuation from a room with one or twoexits was studied [53,54]. Another approach based onhuman behaviour was proposed by Yuan and Tan [55].Zhou et al [56] investigated the influence of smokeon pedestrians’ movement during evacuation in a fire.By applying the floor field model, the exit choice inrooms with obstacles and multiple doors [57], how tochange the pedestrian outflow with evacuees’ competi-tive behaviour and an obstacle [58], extended floor fieldCA model [59], were studied.

Ants, termites and bees are the most common socialinsects in nature. The ability of the colonies of thesesocial insects to function without a leader has attractedthe attention of scientists from different disciplinessuch as computer science [63], communication engi-neering [64], artificial swarm intelligence [65] andmicro-robotics [66]. Shiwakoti et al [6] studied howsafe evacuation scenarios can be designed by usingthe collective behaviour of other biological entities tomodel the pedestrian movement and whether a vigor-ous model can be developed to explain the collectivebehaviour of different biological entities in spite ofdifferences in size, speed and other biological features,and proposed a mathematical model for modificationto simulate the collective traffic [7]. Ants are socialorganisms, and so their behaviour, in certain ways, canbe compared to that of humans [67]. Considering thisanalogy, in this paper, pedestrians trying to escape froma room are simulated by the CA model by using antalgorithm. The ants in a colony communicate with eachother by releasing a chemical, called pheromone, onthe substrate as they crawl forward so that they canfind the shortest route between their nest and a foodsource. It has been shown experimentally that ants, ingeneral, follow the route where there is more concentra-tion of pheromone. From this point of view, in this study,each pedestrian will leave a ‘virtual pheromone’ on thefloor and after a while, the most preferred route will bean ‘attractive force’ for the other pedestrians. Like theant pheromones [33,68,69], ‘virtual pheromones’ tooevaporate with time. If pedestrians pass through a certain

site frequently, the possibility of a person choosing thissite increases. In contrast, if pedestrians pass through acertain site rarely, the ‘virtual pheromone’ on it evap-orates with some probability and the possibility ofchoosing the site decreases.

The paper is organised as follows: In §2, the descrip-tion of the model is given. This is followed by adiscussion of the simulation results in §3. Section 4 endswith a short summary of the model and its simulationresults.

2. Model description

In our model, the room is a two-dimensional systemwhich consists of an L × L cell grid. Here L defines thesystem size and is taken as L = 20. Each cell can beeither empty or occupied by no more than one pedes-trian. In other words, each cell is designed as one-to-oneassociated with an individual pedestrian. All pedestri-ans move synchronously and the movement can be onlyfrom one cell to its unoccupied neighbouring cell pertime step.

2.1 The static floor field S

The square room is divided into many cells, the dark bluecells represent the wall and the light blue cells show theexit door, lying in the middle of the top wall of the room(figure 1).

The static floor field S is the shortest distance to theexit door and does not evolve with time. In order to cal-culate the value of the static floor field, the Euclidean,Manhattan and Dijkstra methods can be used. TheEuclidean method is used for a room without obstacles

Figure 1. Schematic representation of the room (20 × 20).

Pramana – J. Phys. (2018) 91:62 Page 3 of 11 62

while the other methods are suitable for a room with orwithout obstacles [70].

The Euclidean method is used to investigate the effectof ‘virtual pheromone’ evaporation rate on evacuationin a room without obstacles

Si j =√

(ic − ie)2 + ( jc − je)2, (1)

where (ic, jc) denotes the cell position and (ie, je)denotes the exit position.

The Manhattan method is used to examine howevacuation time changes in a room in the presenceof an obstacle. Each lattice site is assigned a con-stant value that is increased in the direction to theexit. The corresponding floor field values are given intable 1.

2.2 States

We assume that a cell can be 0 or 1 depending on whetherthe site is empty or occupied by a pedestrian or has a wallor an obstacle. If the cell is not occupied, then εi j = 1.According to this state of the cell, pedestrians can moveto this empty cell:

εi j =(

1, cell (i, j) is empty0, cell (i, j) is occupied by a pedestrian or has a wall or an obstacle

)

2.3 The dynamic floor field D

As mentioned in §1, the ants in a colonycommunicate with each other by depositing a chemi-cal, called pheromone, on the substrate as they moveforward so that they can find the shortest route betweentheir nest and a food source. The state of the ant system isupdated synchronously at each time step in two stages:position and pheromone updating, respectively [68,69].In the first stage, ants are allowed to move and the posi-tions Pi j (t + 1) are obtained at time t + 1 by using theposition Pi j (t) from the previous time step. In the sec-ond stage, the pheromone is allowed to evaporate and(ph)i j (t) is updated to (ph)i j (t + 1). Finally, the newconfiguration {Pi j (t + 1), (ph)i j (t + 1)} at time t +1 isobtained. In this work, Ci j and Di j are substituted forposition and pheromone, respectively. Ci j indicates thestate of the cell and equals 1 or 0 depending on whether

it is occupied or not occupied. Di j , the dynamic floorfield that is inspired by the pheromone trace of ants,is a virtual trace left by pedestrians moving from onecell to the other. Di j represents the amount of virtualchemotaxis and is assumed to be 0, 0.5 or 1 dependingon f , the evaporation probability per unit time. Just likea pheromone which is a chemical that evaporates, thevirtual trace gradually decreases according to thefollowing rules: if the cell is occupied by a pedestrianat time t , then Ci j (t) = 1 if the pedestrian moves toanother cell, then Ci j (t + 1) = 0. A virtual chemo-taxis is left at each cell that is occupied by a pedestrian;if Ci j (t + 1) = 1, then Di j (t + 1) = 1. However, ifCi j (t + 1) = 0, then the virtual chemotaxis evaporateswith the probability:

Probability =

⎛⎜⎜⎜⎝

1, if Ci j (t + 1) = 1,

1 with probability 1 − f, if Ci j (t + 1) = 0 and Di j (t) = 1;or else Di j (t + 1) = 0.5

0.5 with probability 1 − f, if Ci j (t + 1) = 0 and Di j (t) = 0.5;or else Di j (t + 1) = 0

⎞⎟⎟⎟⎠

According to these evaporation rules, when a cellis not occupied by a pedestrian, the value of virtualchemotaxis at time t + 1 decreases by – 0.5. On theother hand, whenever a cell is occupied by a pedestrian,the amount of virtual chemotaxis at this cell is set toDi j (t + 1) = 1.

2.4 Neighbourhood

In CA, the current state of a cell is determined bythe states of its neighbours. Described in §1 in detail,Von Neumann (figure 2) and Moore neighbourhoodapproximations (figure 3) have been commonly usedin the literature. Moore neighbourhood is used in oursimulations.

2.5 Pedestrian movement

Each pedestrian moves to the target cell based on theprobability pi, j :

pi, j = N exp(kDDi j

)exp

(kSSi j

)εi j .

Here, the static floor field Si j is the attraction of thedoor, kS is the static floor field’s weight coefficient (kS ∈[0, ∞]), the dynamic floor field Di j is the amount of

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Table 1. The static floor field values used to runthe evacuation.

virtual chemotaxis, kD is the weight coefficient of thedynamic floor field (kD ∈ [0, ∞]), εi j is the occupationnumber of the target cells and N is the normalisationparameter for ensuring

∑i j pi j = 1.

Figure 2. Von Neumann neighbourhood.

Figure 3. Moore neighbourhood.

Figure 4. Target cells.

In each time step, each pedestrian chooses a target cell(figure 4) according to the following rules:

1. The adjacent empty cell with the highest probabil-ity pi, j is preferred.

2. If two or more neighbouring cells have the samehighest probability pi, j , the cell to which thepedestrian prefers to move will be chosen at ran-dom.

3. When more than one pedestrian chooses the samecell, who will be selected with equal probabilitywill be determined.

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Figure 5. Snapshots of the evacuation with N = 120, f = 0.1 and the time step is 0, 4, 8, 12, 16, 20, 24, 28 and 32,respectively for figures 5a–5i.

3. Simulation results

Using the above model, the dependence of theevacuation from a room whose size is 20 × 20 cellson the virtual chemotaxis evaporating rate f and thepresence of the obstacle are investigated in this paper.Initially, N pedestrians are randomly distributed in theroom and each pedestrian chooses a target cell randomlybased on the moving probability pi, j for every timestep.

Figure 5 shows the snapshots of the evacuation whereparameters are set as f = 0.1, N = 120 and the timestep is 0, 4, 8, 12, 16, 20, 24, 28 and 32. The staticfloor field (S) values of the cells are calculated by theEuclidean method.

The randomly distributed locations of thepedestrians in the initial configuration turn towardsthe exit and it is observed that the number ofpedestrians in the room decreases at each timestep.

Figure 6. The relation between the chemotaxis evaporatingrate and the time step of the evacuation in different initialisedpedestrian numbers with values from 0 to 100. Red, dark blueand green lines stand for f = 0.1, 0.6 and 0.9, respectively.

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Figure 7. Snapshots of the evacuation with N = 120, f = 0.1, asymmetric obstacle and time step 0, 4, 8, 12, 16, 20, 24, 28and 32, respectively for 7a–7i.

3.1 Virtual chemotaxis evaporating rate

The evacuation dynamics are analysed underdifferent virtual chemotaxis evaporating rates: f = 0.1,0.6 and 0.9 which are represented by red, dark blue andgreen lines, respectively (figure 6). Using this applica-tion, we aim to present the evacuation of pedestriansfrom a large room with reduced visibility, e.g. due tolights being switched off or smoke. It must be notedthat the selection of such a rate has a slight influence onthe evacuation time when the pedestrians are familiarwith the exit. In figure 6, we can see that the evac-uation time step decreases with the decrease in thechemotaxis evaporating rate f . When f is small, ‘theinstinct of following’ produces a repulsive effect on thepedestrians moving towards the exit and the evacuationends at an earlier time step. Besides, it is worth notingthat the greater the number of initialised pedestrians,the more the effect of virtual chemotaxis evaporation.The possible reason for this result is that pedestriansleave virtual chemotaxis in most of the cells in higherdensities.

3.2 Obstacle

Obstacles are expected to modify the trajectory ofpedestrian movement during the evacuation. Thus, theEuclidean method, which is used for a room withoutobstacles, is not suitable and the static floor field needsto be recalculated by the Manhattan method. The corre-sponding floor field values are shown in table 1.

Figure 7 shows the snapshots of the evacuation wherethe parameters are set as f = 0.1, N = 120 and thetime step is 0, 4, 8, 12, 16, 20, 24, 28 and 32. The staticfloor field values S of the cells are calculated by theManhattan method and are given in table 1. It is seenthat the presence of two-part four units asymmetricalpositioned obstacle provides an order on the edges ofthe obstacles and prevents the pedestrians from beingjammed.

As shown in the graph of figure 8, the effect ofvariation of evaporation rate f on the evacuation belongsto the asymmetrically positioned obstacle and the rateof pheromone evaporation seems to be effective fromthe values of low pedestrian density.

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Figure 8. The relation between the chemotaxis evaporatingrate and the time step of the evacuation from the room with anasymmetric obstacle in different initialised pedestrian num-bers with values from 0 to 100. Red, dark blue and green linesstand for f = 0.1, 0.6 and 0.9, respectively.

The static floor field values S of the cells are calculatedby the Manhattan method and are given in table 1. Bylooking at the snapshots in figures 9a–9i, it can be seenthat the pedestrians randomly placed in the room haveformed a regular lane between the obstacles on the exitroute and a pedestrian jam occurs in front of the obstacleinstead of the exit.

The graph in figure 10 is obtained from the simu-lation results of the existing symmetrically positionedobstacle and shows that for each pheromone evapo-ration rate, the sudden drop observed in the curvesindicate phase transitions during the evacuation. Itis also understood that due to the geometry of theobstacles, the pedestrians determine ‘the tendency tofollow’ according to the evacuation lanes rather than thepheromone.

The values of the static floor field of the cells,calculated by the Manhattan method, are given in table 1.The snapshots for this evacuation process, as shownin figure 11, indicate that the pedestrians form anevacuation lane along with the exit route. The mainreason for the formation of this lane is the static floorarea values of the cells.

Figure 9. Snapshots of the evacuation with N = 120, f = 0.1, symmetric obstacle and time step 0, 4, 8, 12, 16, 20, 24, 28and 32, respectively for 9a–9i.

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Figure 10. The relation between the chemotaxis evaporatingrate and the time step of the evacuation from the room with asymmetric obstacle in different initialised pedestrian numberswith values from 0 to 100. Red, dark blue and green lines standfor f = 0.1, 0.6 and 0.9, respectively.

As shown in the graph of figure 12, if the pheromoneevaporation rate f = 0.9, an unexpected situation isobserved in the evacuation curve, and the increase in theevaporation rate accelerated the evacuation. This may bedue to the fact that the pedestrians use evacuation lanesinstead of following each other.

Figure 13 shows the effect of the obstacle on theevacuation when the value of virtual pheromone evap-oration rate is set at f = 0.1. As can be seen fromthe graph, the asymmetrically positioned obstacle seri-ously affects the pedestrian escape time as it dividesthe exit pathway and causes the pedestrians to con-centrate in an area rather than spread out. A phasetransition is observed in the curve of the symmetricobstacle. There are three phases to be observed in thepedestrian traffic: free-flow phase, synchronised phaseand jammed phase [71,72]. In the free-flow phase,the interaction between the pedestrians (the state ofslowing each other) is less and the velocity increaseslinearly with intensity. In the synchronised phase,the flow continues for a long time at a constantspeed – either the speed of the motion gradually slows

Figure 11. Snapshots of the evacuation with N = 120, f = 0.1, no obstacle and time step 0, 4, 8, 12, 16, 20, 24, 28 and 32,respectively for 11a–11i.

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Figure 12. The relation between the chemotaxis evaporatingrate and the time step of the evacuation from the room withoutan obstacle in different initialised pedestrian numbers withvalues from 0 to 100. Red, dark blue and green lines stand forf = 0.1, 0.6 and 0.9, respectively.

Figure 13. The effect of the obstacle present in the roomduring the evacuation time. Red, green and dark blue linesstand for asymmetric obstacle, symmetric obstacle and noobstacle, respectively.

down or an irregular flow (varying between accelerationand deceleration) is observed. In the jammed phase, theflow decreases with the increase in density. When thesymmetrical obstacle curves are examined, it is thoughtthat there can be a phase transition (from the synchro-nised phase to the free-flow phase) in the direction of

acceleration at the evacuation due to the effect of ‘virtualpheromone’.

4. Conclusion

In §3, we have discussed the simulation results of thefloor field model inspired by the ant trail model and itwas observed that pedestrians choose the path with theshortest travel time. However, that is not necessarily thepath with the shortest spatial distance. The purpose wasto investigate the influence of the virtual chemotaxisevaporating rate and the presence of an obstacle on theevacuation time.

Inspired by the pheromone used by ants, theevacuation process was investigated for various valuesof the virtual chemotaxis ( f = 0.1, 0.6 and 0.9) and theincrease in evaporation rate has been seen to slow downthe evacuation.

In the simulations performed by positioning obstaclesin the room, it has been observed that an obstacle leadsto phase transitions and shortens the evacuation time.When the obtained phase transition curves are exam-ined, it is observed that the speed of the movement isgradually slowing down as the number of pedestriansincreases during the process and the evacuation timeincreases. There is an irregular acceleration in thoseregions, with an increase in the number of pedestriansbefore the phase transition. Briefly, the curve has syn-chronous phase properties before the phase transition.As a result of the increase in the speed of movementafter the phase transition, the transition from the syn-chronised phase to the free phase is observed.

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