Hierarchical Control of Swarms during Evacuation

Krist

yna Janovsk

a and Pavel Surynek

Faculty of Information Technology, Czech Technical University in Prague, Thakurova 9, 160 00 Praha 6, Czech Republic

Keywords:

Evacuation, Multi-agent Pathﬁnding, Hierarchical Control of Swarms, Conﬂict-based Search.

Abstract:

The problem of evacuation is addressed from the perspective of agent-based modeling (ABM) in this paper.

We study evacuation as a problem of navigation of multiple agents in a known environment. The environment

is divided into a danger and a safe zone while the task of agents is to move from the danger zone to the safe

one. Unlike previous approaches that model the environment as a discrete graph with agents placed in its

vertices our approach adopts various continuous aspects such as grid-based embedding of the environment

into 2D space continuous line of sight of an agent. In addition to this, we adopt hierarchical structure of

multi-agent system in which so called leading agents are more informed and are capable of performing multi-

agent pathﬁnding (MAPF) via centralized algorithms like conﬂict-based search (CBS) while so called follower

agents are modeled using simple local rules. Our experimental evaluation indicates that suggested modeling

approach can serve as a tool for studying the progress and the efﬁciency of the evacuation process.

1 INTRODUCTION

We address the problem of evacuation (Kurdi et al.,

2018) from the perspective of agent-based modeling

(ABM) (Wilensky and Rand, 2015; Zia and Ferscha,

2020) and multi-agent path ﬁnding (MAPF) (Silver,

2005; Ryan, 2007; Surynek, 2009; Standley, 2010).

The evacuation is understood as a navigation problem

for agents that need to relocate themselves from the

danger zone to the safe zone in a known environment.

Typically the environment is modeled as a discrete

graph where vertices represent locations and edges

deﬁne the topology and each agent has the full knowl-

edge of the graph. An agent can be located in a vertex

at a time and can instantaneously move across an edge

to a vertex in its neighborhood. Similar setup is used

in multi-agent path ﬁnding, a problem from which we

borrow the centralized algorithmic approach and en-

vironment modeling.

The basic characteristic of evacuation is that usu-

ally we do not care about the precise goal locations of

agents. Any location in the safe zone is acceptable as

a goal location for an agent. This is an important dif-

ference from MAPF where each agent has its speciﬁc

goal location. In addition to this, centralized control

of all agents is hardly reachable in practice hence we

need to assume that agents are controlled locally to a

signiﬁcant extent. Individual agents in evacuation do

https://orcid.org/0000-0001-7200-0542

not share the knowledge of locations of other agents.

This precludes direct application of MAPF algorithms

in solving evacuation problems at the level of individ-

ual agents. On the other hand, ﬁne-grained behaviour

of individual agents can be captured using the ABM

approach.

Previous works often model the evacuation prob-

lem as a network ﬂow (Chalmet et al., 1982; Even

et al., 2014; Arbib et al., 2018) in a discrete graph.

Such approaches however model the problem at a

too coarse level where for example interactions (colli-

sions) between individual agents in a limited space are

not modeled nor the individual behaviour of agents.

Hence these approaches are rather suitable for evacu-

ation modeling at the level of cities and road networks

(Kamiyama et al., 2006). More detailed modeling

of agents in required for evacuation inside buildings

where ABM techniques are more suitable (Liu et al.,

2016; Liu et al., 2018; Zafar et al., 2016).

On the other hand, ABM models often lack cen-

tralized aspect which often results in insufﬁcient per-

formance of the evacuation process (Trivedi and Rao,

2018).

1.1 Contribution and Organization

We attempt in this work to integrate centralized plan-

ning from MAPF and an ABM-based framework for

modeling detailed agents’ behaviour.

Janovská, K. and Surynek, P.

Hierarchical Control of Swarms during Evacuation.

DOI: 10.5220/0010678200003064

In Proceedings of the 13th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2021) - Volume 2: KEOD, pages 61-73

ISBN: 978-989-758-533-3; ISSN: 2184-3228

Agent behaviour in our approach uses a hierar-

chical model in which some usually more informed

agents follow the evacuation plan constructed by the

centralized algorithm. Conﬂict-based search (Sharon

et al., 2014), an optimal MAPF algorithm, is used in

our case. We call these more informed agents lead-

ers. We can assume, that the leader agents can be

equipped with some electronic device that informs

them about the plan and the current situation.

Less informed agents are called followers in our

hierarchical model and they are controlled locally us-

ing various rule-based methods. These agents are

assumed to follow the leader agents using the local

rules.

At the level of environment modeling, our ap-

proach is a synthesis between discrete graph-based

models and continuous models from which we bor-

row continuous reasoning about the topology of the

environment. Namely, the environment is modeled as

a grid embedded in the 2D space where agents are

placed in the cells of the grid. Agent themselves have

a volume and when using local rules they consider

continuous line of sight to localize a leader agent.

We demonstrate that our hierarchical ABM ap-

proach for evacuation can serve as a tool for study-

ing the progress and the efﬁciency of the evacuation

process.

The paper is organized as follows: we ﬁrst intro-

duce formal deﬁnition of discrete evacuation and ba-

sic concepts from related MAPF. Then our novel hi-

erarchical agent-based model of evacuation is intro-

duced. Various models of behaviour of agents are de-

scribed. Finally, we analyze performance of the evac-

uation model in diverse scenarios empirically.

2 BACKGROUND

Evacuation is an anonymized form of the multi-agent

path ﬁnding (MAPF) problem. It takes place in an

undirected graph G = (V, E), where each vertex is

marked either as safe or endangered, that is V = S ∪D,

where S are safe vertices and D are endangered ver-

tices. The goal vertex of an agent is not just one ver-

tex, but any vertex from a set of safe vertices.

The task of is to ﬁnd a set of paths for a set of

agents A = {a

, a

, ..., a

} that navigates them from

endangered vertices D to safe vertices S. Each agent

from A starts in its own vertex, so that no more than

one agent is present in a vertex at a given time. The

solution of this problem is a plan π = [c

, c

, ..., c

(a) ∈ S ∀a ∈ A and c

: A → V is the conﬁguration

of agents in vertices at time t.

The following deﬁnition summarizes the evacua-

tion problem as introduced in (Selvek. and Surynek.,

2019).

Deﬁnition 1. Discrete multi-agent evacuation

(MAE) is a 5-tuple E = [G = (V, E), A, c

, D, S], where

G represents the environment, A is a set of agents,

: A → V is the initial conﬁguration of agents, D and

S such that D ⊆ V , S ⊆ V , V = D ∪ S with D ∩ S 6=

and |S| ≥ k represent a set of endangered and a set of

safe vertices respectively.

We usually try to minimize the evacuation time,

the total number of steps from the beginning of the

evacuation until the moment when the last agent

reaches a safe vertex. We call this value the

makespan.

In our model, the leader agents have access to cen-

tralized plan obtained by MAPF planning algorithm.

Speciﬁcally we use the Conﬂict-Based Search (CBS)

algorithm, a makespan optimal MAPF algorithm. It is

an algorithm, in which for each agent the shortest path

is found from the starting position to the target posi-

tion so that it does not collide with other agents during

the course, that is, no two agents are in the same loca-

tion at the same time. The algorithm is makespan op-

timal considering assuming a solution exists (Sharon

et al., 2014) (existence of solution can be checked by

a different algorithm, however in environment with

enough free space a solution always exists).

The algorithm consists of two levels - at the higher

level, as shown in Algorithm 1, the construction of a

conﬂict tree takes place, where individual nodes con-

tain a set of conﬂicts for given agents. A conﬂict is

determined by a pair of agents, a vertex, and a time

step where the conﬂict occurred. The conﬂict tree

then branches to two nodes - one for each agent in

the conﬂict with a constraint forbidding the agent to

enter the conﬂict. In the new nodes, a path-ﬁnding

algorithm is run for the given agent based on the con-

straint arising from the conﬂict, determining the new

path for this agent, but without the given conﬂict.

At the lower level, there is a local path-ﬁnding

algorithm for each agent - in this paper A* (Hart

et al., 1968) algorithm is used. The selected path-

ﬁnding algorithm works with the limitations given by

the higher level of CBS.

The lower level sends the best solution for a given

agent to the higher level, which evaluates past con-

ﬂicts (collisions) based on those solutions and con-

structs a conﬂict tree.

The algorithm is guaranteed to ﬁnd the makespan

optimal solutions. For details see (Sharon et al.,

2014).

KEOD 2021 - 13th International Conference on Knowledge Engineering and Ontology Development

Algorithm 1: Higher level of CBS (Sharon et al., 2014).

Input: MAPF instance

1 R.constraints =

2 R.solution = set of individual agent paths;

3 R.make ← compute makespan(R.solution);

4 OPEN ← R;

5 while OPEN not empty do

6 P ← lowest makespan node(OPEN);

7 OPEN ← OPEN \ {P};

8 f irst con f lict ← validate(P);

9 if ﬁrst conﬂict =

0 then

10 return P.solution;

11 for agent

in ﬁrst conﬂict do

12 N ← new node;

13 N.constraints ← P.constraints ∪

new constraint(agent

, vertex, time);

14 N.solution ← P.solution;

15 N.solution.update(new constraint());

16 N.make ← compute makespan(N);

17 Insert N to OPEN;

3 MODEL DESIGN

In this section we describe our hierarchical agent

model and individual agent types. We also discuss

the design of the environment and the combination of

discrete and continuous approach.

3.1 Agents

Agents are divided into two types. The motivation for

this decision is the evacuation situation in the school

environment. Thus, agents can represent teachers and

students. We therefore divide them into leaders and

followers. Leaders search for a way out of the build-

ing, and followers form swarms around leaders, fol-

low them, and evacuate with their help. We assume

that leaders have the full knowledge and can be con-

trolled centrally in the principle while the followers

can only get information from their neighborhood and

are controlled locally.

3.1.1 Follower

The follower must be able to observe the leader in

its immediate neighborhood if no obstacle prevents it

from doing so. If there are more leaders, it is able

to decide which one is closer. It follows either the

nearest leader or an assigned leader. If it loses the

sight of its leader, it tries to get to the last position

where the leader was when the follower still saw it.

Algorithm 2: Agent function of a follower.

Input: MAPF instance, list of leaders’

positions

1 f ollower.leader ← choose nearest(leaders);

2 if distance(follower, leader) <

follower.sight length or not

follower sees leader() then

3 return random free neighbour ;

4 if not follower.obeys() then

5 return move(follower, leader, away)

6 else

7 return move(follower, leader,

towards)

In the base design, the follower is designed as a

purely reﬂex agent (Russell and Norvig, 2010). That

was decided because following the example of evacu-

ation in the school environment, follower should fol-

low orders of an authority - in our case the leader.

Thus, the follower does not try to evacuate itself, it

only has to ﬁnd a leader who will lead it to the exit.

It has an overview only of its immediate surroundings

in its ﬁeld of view. If it sees a leader in its proxim-

ity and decides to be obedient and follow it, it moves

to a free cell that is closer to the leader. Otherwise,

follower tries to move away from the leader. If the

agent does not ﬁnd a leader in its vicinity, it moves to

a random neighbouring free cell or remains in place.

Each model uses a speciﬁc version of agent func-

tion shown in Algorithm 2, adapted to the needs of

individual models.

3.1.2 Leader

The goal of a leader is to ﬁnd the shortest way out of

the dangerous area while keeping a certain distance

between itself and other leaders. Each leader has a

swarm of followers around itself, which it leads to the

nearest exit. After each step, leaders must respond to

changes in the environment, whether they are obsta-

cles or other leaders. If the leader is prevented from

moving by followers, it is able to move them from

their positions so that it can perform the next step. A

leader is designed as an agent with a goal and an en-

vironment model. (Russell and Norvig, 2010) It has

a constant overview of the map. It searches for the

shortest path to the nearest exit on the map, to which

it leads his followers.

A leader in the lower level of the Conﬂict-Based

Search searches for its own path regardless of other

leaders. For this A* (Hart et al., 1968) algorithm

is used, which is modiﬁed so that the agent respects

the restrictions set by the CBS. When determining

the conﬂict between two leaders, we cannot rely only

Hierarchical Control of Swarms during Evacuation

on speciﬁc coordinates, but on the area around both

agents, which is deﬁned by their parameter of conﬂict

distance, which is a distance the agents need to keep

between them.

Conﬂict is deﬁned as a quintuplet (a

, a

, con f lict

position o f a

, con f lict position o f a

, t). The con-

ﬂict involves two different positions, one for each

agent. It was chosen in this way because a conﬂict

can occur for agents even if they are not standing next

to each other. It is enough for one of the agents to

get into the area too close to the other agent, but for

each of them there will be a different coordinate by

which they would get into this area. Therefore, each

leader has a different coordinate restriction. This con-

ﬂict search is implemented in the validate function as

shown in Algorithm 3.

Algorithm 3: Validate.

Input: Node N

1 conﬂicts =

2 for i ∈ {1, 2, ..., len(N.solution)} do

3 for j ∈ {i + 1, i + 2, ..., len(N.solution)} do

4 steps ← min(len(solution[i],

len(solution[j]));

5 for t ∈ {1, ..., steps} do

6 geometry ←

compute geometry(solution[i],

solution[ j], N.state);

7 if geometry.in sight(a

, a

, t) then

8 conﬂicts ← conﬂicts ∪ {(i, j,

solution[i][t], solution[j][t],

t)};

9 return conﬂicts;

In the validate function, positions of each pair of

leaders are compared at each step of their paths. If

two leaders come too close to each other and there

is no obstacle between them, they have a conﬂict in

that particular steps. Further conﬂicts between those

agents are not searched, as their paths will change

when the ﬁrst conﬂict is removed.

3.2 Environment

The environment where the evacuation takes place is

expressed by means of a discrete grid map which is

embedded in 2D space so continuous geometric rea-

soning can be made in the environment. The agents

are expressed as circles with a ﬁxed radius chosen on

the basis of preliminary experiments. To make the

distribution of agents in the environment more real-

istic, each agent is placed randomly within its square

cell.

Figure 1: Discrete representation of the environment.

Figure 1 depicts the discrete representation of the

environment. Vertices marked a

...a

are vertices oc-

cupied by an agent, green vertices represents exits and

white vertices are free vertices.

Figure 2: Continuous representation of the environment.

In ﬁgure 2 we show continuous representation of

the environment, blue dots represent followers, green

dot represents a leader and red squares represent

walls.

3.2.1 Geometry of the Environment

The follower can only follow a leader if it sees it.

We use simulation of line of sight as follows. The

follower F sees the leader L if the distance of the

agents given by the Euclidean distance is less than the

value of the ﬁeld of view parameter of the follower

and at the same time there is no obstacle between the

agents, which may be a wall or another follower. If

the line given by the agents’ centers intersects another

follower or wall, the agent does not see the leader.

For leaders, the only possible obstacles are walls,

which are expressed as squares occupying the entire

area of one cell.

4 MODELS OF BEHAVIOR

Using multi-agent modeling, we examine the evacu-

ation process and determine which of the following

KEOD 2021 - 13th International Conference on Knowledge Engineering and Ontology Development

Figure 3: Followers depicted yellow see the leader.

Figure 4: Followers depicted yellow don’t see the leader.

evacuation models is the best. Individual models dif-

fer in the behavior of both leaders and followers. Al-

though all models work with hierarchical swarming,

the methods of maintaining and guiding these swarms

differ in what behavioral rules are used.

4.0.1 Model A: Simple Following

In this model, followers always choose the nearest

leader in sight to follow. In the basic design of this

model, after separation from leaders, followers do not

attempt to evacuate themselves on their own. Leaders

only try to get to the safe area without conﬂicts and as

quickly as possible, but they do not have an assigned

swarm of followers and therefore do not check if any

agents have separated along the way. This can lead to

signiﬁcant losses of followers in individual swarms.

4.0.2 Model B: Assigned Swarms

To prevent signiﬁcant losses of followers, each fol-

lower has exactly one leader assigned to it, which

it must follow all throughout the evacuation. At the

same time, in the basic design of the model, followers

never try to evacuate on their own. Leaders look after

their respective swarms, regularly checking to see if

any agents have separated from the swarm, and if the

number of lost agents rises above a given acceptable

limit, the leader stops and waits for a certain number

of steps to allow lost agents to rejoin the swarm.

Thus, during the CBS, the leader sends only its

current location to the algorithm as its path and does

not plan a complete path to the exit, as it is not clear

how long it will wait on the spot. It is however possi-

ble that due to the inability to move, it will get into a

conﬂict with another leader.

However, there is an even greater need for effec-

tive planning of individual steps, as the evacuation

time increases compared to model A due to frequent

stops and waiting. Experiments have shown that the

fewer followers a leader can afford to lose, the slower

its evacuation will be.

Partially Informed Followers. If the initial posi-

tion of a purely reﬂex follower is unfavorable (no

leader is in sight and the position is not near the exit),

or it loses its leader, it is likely that its evacuation

will fail. Therefore, it is appropriate to put in place a

mechanism to increase the follower’s chances of sur-

vival.

Followers are unaware of the ongoing evacuation

and therefore do not attempt to reach the exit on their

own. However, it is possible to leave them k ran-

dom steps, after which they will start trying to get to

an exit, which however may not necessarily be the

nearest exit available. They do not take into account

any dynamically emerging barriers that other agents

present, because unlike leaders they do not cooper-

ate and have no way to obtain information about the

position of other agents.

Because these are only followers, they plan their

path using an algorithm simpler than A* used by lead-

ers.

The moment the desired leader appears in the ﬁeld

of view of the follower after a number of steps, the

follower becomes a part of the swarm of this leader

and no longer searches for a path to the exit.

We have therefore introduced a modiﬁcation of all

models, which allows followers outside of swarms to

perform planned movement. If a leader (in Model A

any leader, in Model B one speciﬁc leader) no longer

appears in their ﬁeld of view after 30 time steps, they

can get the opportunity to evacuate themselves. They

use the Breadth-First Search algorithm (BFS) to ﬁnd

their path to the exit. A value of 30 was chosen based

on preliminary experiments. We assume that agents

have the knowledge of the environment (not the posi-

tions of other agents) hence individual pathﬁnding in

the environment can be regarded as a local behaviour.

4.0.3 Model C: Plane

The motivation for this model is evacuation in an air-

plane or on a ship. The leaders do not try to evacuate

themselves ﬁrst, but let followers be evacuated before

them and leave the space last. As in model B, at the

beginning of the evacuation, leaders divide the indi-

Hierarchical Control of Swarms during Evacuation

vidual followers into groups that do not change dur-

ing the evacuation. The leader thus keeps track of

whether his assigned swarm has already been evacu-

ated and, if so, only then does it leave the area itself.

Thus, at each step, the leader ﬁrst determines the

direction in which it is best to move. It then communi-

cates this information to its followers, and they move

in response to this instruction. Leader itself moves

last.

Followers recognize three basic types of their lo-

cation - they can be located in an aisle, on a seat,

or near an exit. Based on this, they perform speciﬁc

movements.

• Aisle - in this case, the follower moves in the di-

rection speciﬁed by its leader. In this case, the

follower primarily moves to the right / left, but

if a wall, seat or a leader prevents it from mov-

ing, it has the option to bypass him. Followers in

this model are also partially informed, so if they

do not see their leader for a given period of time,

they try to evacuate themselves through one of the

exits, which, however, may not be the nearest exit

for them.

• Seat - a seat is a narrow space surrounded on at

least two sides by rows of seats. If a follower is in

a seat, it tries to move to an aisle.

• Near the exit - if a follower is located near the exit,

it stops listening to the instructions of the leader

and moves directly to the exit.

5 EXPERIMENTAL EVALUATION

In this section we will discuss modiﬁcations per-

formed to improve the course of experiments and

evacuations themselves. Then we will discuss se-

lected experiments.

5.1 Experimental Setup

5.1.1 Constraining the Depth of the Conﬂict

Tree

The implementation of the model uses a variant of

the CBS algorithm that constructs only the ﬁrst n ver-

tices of the conﬂict tree, because non-constrained tree

created by the algorithm can have thousands of ver-

tices, which leads to a very long computation time

and would make the model impractical for real-life

applications. In the experiments, CBS was greatly

constrained to save computational time. This could

also have contributed to creation of conﬂicts and con-

gestions during the evacuation. This approach may

not return a makespan optimal result, it is only sub-

optimal. However, since the map space is very large,

we don’t have to worry that the algorithm won’t ﬁnd

a solution.

However, if that happens, the agent who did not

ﬁnd a solution will not move. When replanning oc-

curs in the next step, a position where an agent pre-

viously had a conﬂict with another agent may already

be unblocked and the agent may continue on its route.

After each agent performs a step, replanning oc-

curs - the CBS algorithm is therefore run repeatedly.

This makes it possible to respond to emerging obsta-

cles on the map, which might be other leading agents.

5.1.2 Processing of the Resulting Vertex

The original CBS algorithm returns a conﬂict-free

vertex. However, since a modiﬁcation limiting the

depth of the search was made, in many cases the ver-

tex identiﬁed as the best solution contained conﬂicts.

CBS resolves those conﬂicts that it encounters ﬁrst.

However, it may not get to all the conﬂicts that are to

take place in the next step. Therefore, for the resulting

solution, the set of all coming conﬂicts is found again,

and on the basis of this, the solution is replanned for

each agent with a conﬂict. The ﬁnal result is this mod-

iﬁed solution.

5.2 Selected Experiments

The most important experiments we carried out stud-

ied impact of numbers of evacuated agents, follower

obedience, level of communication between leaders

on makespan and other parameters. We will discuss

these experiments in this section.

All selected experiments on models A and B were

carried out on map building, whereas selected exper-

iment on model C used map plane.

Figure 5: Map building.

KEOD 2021 - 13th International Conference on Knowledge Engineering and Ontology Development

Figure 6: Map plane.

5.2.1 Comparison between Models a, B and

Usage of Partially Informed Followers

Number of evacuated agents

Model A - uninformed followers

Time steps of evacuation

Model B - uninformed followers

Model A - partially informed followers

Model B - partially informed followers

Figure 7: Progress of evacuation depending on the model

being used and the usage of partially informed followers.

Comparison of Models a and B using Partially In-

formed Followers. Figure 7 shows that the evacua-

tion process is very similar in both models, with small

deviations in favor of model A.

In model B, swarms consist of at least d

n agents

1 agents, while in model A a leader often breaks away

from its followers and evacuates alone, so in model A,

the ﬁrst agents begin to evacuate themselves earlier

than in Model B. These are the solitary leaders.

Thus, in model B, unlike model A, a larger num-

ber of agents typically arrive at the exit at once. This

is reﬂected in the plot where places with faster and

slower growth alternate in this model, while in places

with faster growth model B catches up with the num-

bers of evacuated agents in model A, where the evac-

uation after the ﬁrst 130 steps is almost linear.

We can determine that the most important part of

the evacuation is, for example, the ﬁrst half of the

evacuation - typically the sooner the agents are evac-

uated, the better, because there is never an inﬁnite

amount of time for the evacuation (Ng and Chow,

2006).

In the ﬁrst part of the experiment, the numbers

of evacuated agents in model A slightly outweighed

model B. However, Model B quickly catches up with

occasional shortcomings, and variations in evacuated

agent numbers are minimal for the remainder of the

experiment. In terms of speed, the evacuation time is

the same for both models. According to the ﬁrst met-

ric, model A could be considered more successful. In

terms of the rate of evacuation, the models are equal.

However, the realism of these models must also be

taken into account. We consider model B to be more

realistic.

Comparison of Models a and B using Uninformed

Followers. Figure 7 shows that model A leads in

the number of evacuated agents throughout the whole

evacuation process. In model B, there are large de-

lays in the evacuation process. Whole parts of swarms

always evacuate at once, which is reﬂected in the

plot by signiﬁcant jumps in the number of evacuated

agents.

Because the swarms in Model A are much more

scattered, due to the behavior of leaders, there are no

places where no agents would be evacuated for a long

time - in the order of units up to tens of steps. How-

ever, after all the agents who were part of a swarm

have been evacuated, in both models any additional

abandoned agents may evacuate themselves only after

approaching the exit by a sequence of random steps.

Comparison of Models based on Usage of Par-

tially Informed Followers. Models using partially

informed followers have a visible advantage over

models working with uninformed followers, both in

terms of evacuation rate and in terms of the number

of evacuees. Model A with uninformed followers be-

gins to visibly lose to models with partially informed

followers after about 100 steps, when the growth in

the number of evacuated agents begins to slow down

to almost a complete halt.

It is unlikely that models with uninformed follow-

ers can undergo a complete evacuation because un-

informed followers do not actively try to evacuate on

their own.

5.2.2 Impact of Number of Evacuated Agents on

Makespan

We observed the development of the makespan -

the evacuation time - depending on the number of

agents. In models A and B, there are always 9 lead-

ers, while the number of followers is 1–216. The ob-

served values always differ by 10 agents. In model

C, 165 agents are evacuated, out of which 3 are lead-

ing agents. In all models, followers are partially in-

formed.

Model B. Outliers in ﬁgure 8 are caused by con-

gestions in experiments. Congestion that would pro-

long the average evacuation time occurred with both

Hierarchical Control of Swarms during Evacuation

Number of evacuated agents

Evacuation time

Figure 8: Evacuation time as a function of the number

of evacuated agents and the map used in the experiment -

model B.

a lower number of agents (eg 40 agents) and a higher

number (eg 220 agents). However, such cases most

often occurred in the range of 100-225 agents.

The value of the average evacuation time increases

with the increasing number of agents, but the variabil-

ity of these values also increases. With a higher num-

ber of agents, congestion is more common because

several swarms can enter narrow corridors at once and

block each other’s path. Leaders also have to wait

for more followers, which again seems problematic

if the escape route of agents from narrow spaces is

blocked by other swarms or followers from the same

swarm, who are currently waiting for the movement

of a standing leader. This phenomenon is partially

eliminated with a lower number of followers, as there

are not so many agents in the corridors at once, and

they do not block each other’s path. However, it is not

possible to expect the complete elimination of a cer-

tain deviation in evacuation times, because followers

can signiﬁcantly prolong the evacuation time by their

disobedient behavior.

Due to the problems observed starting with 100

evacuated agents, we can state that the map used be-

comes dangerous for the number of agents of 100 or

more.

Model A. Figure 9 shows that the evacuation time

increases with the number of evacuated agents. How-

ever, unlike in Model B, congestions do not occur,

and with the vast majority of agents, evacuation time

variations are in the order of units only.

In contrast to model B, several differences are no-

table – there are no congestions, nor does the variabil-

ity of evacuation times increase with the increasing

number of evacuees. This is due to the behavior of

leaders, who throughout the evacuation only proceed

smoothly to the exit and do not stop to wait for any

followers. As a result, there are no accumulations of

Number of evacuated agents

Evacuation time

Figure 9: The evacuation time as a function of the number

of evacuated agents and the map used in the experiment -

model A.

swarms in one place, and therefore no congestions.

The average evacuation times in this model are

lower than in model B, except in the case of only

10 agents, that is 9 leaders and one follower. In this

case, leader waiting for his respective follower helped

the evacuation in model B, as the follower had a bet-

ter chance of catching up with his leader and did not

have to wait for his own path planning to begin, which

could have happened in model A.

Number of evacuated agents

Evacuation time

Figure 10: The evacuation time as a function of the number

of evacuated agents and the map used in the experiment -

model C.

Model C. As the number of evacuated agents in-

creases, so does the evacuation time. However, be-

tween lower and higher numbers of agents, deviations

of the evacuation time occur in matter of tens of steps.

In contrast to models A and B, a higher variance

of values between the individual numbers of agents

occurs in most of the values examined. This may be

due to the nature of the environment, in which there

are only narrow alleys that support congestions.

KEOD 2021 - 13th International Conference on Knowledge Engineering and Ontology Development

Avg. % of evacuated agents - model B

Avg. % of evacuated agents - model A

Makespan

Average percentage of evacuated agents

Figure 11: Average percentage of evacuated agents depend-

ing on makespan.

5.2.3 Impact of Makespan on Average

Percentage of Evacuated Agents

We observed what percentage of evacuees have been

evacuated, if we constrain the makespan at a certain

number of time steps. We can also choose a percent-

age of successfully evacuated agents after which the

evacuation is deemed successfull. We can also deter-

mine what is the minimal time an evacuation needs to

take in order to evacuate enough agents.

We can see model A surpassing model B in aver-

age percentage of evacuated agents. 10 measurements

were taken for each observed value. Observed values

were 0-390 time steps, noted every 30 steps. If we

deem for example 80% as a sufﬁcient percentage of

successfully evacuated agents, evacuation in model

A would need around 270 time steps to achieve this

number. Evacuation in model B would need to take

about 300 steps to evacuate at least 80% of agents.

5.2.4 Impact of Minimal Swarm Size

Time steps of evacuation

Number of evacuated agents

Figure 12: Progress of evacuation as a function of the η

parameter.

We introduce the minimal swarm size

η ∈ {d

n agents

e, d

n agents

e, d

n agents

e, d

n agents

e},

which represents a minimal number of followers a

leader has to keep in a swarm to be able to freely

move towards an exit. If the swarm size falls below

this limit, the leader has to wait for a set amount of

time or until the swarm size rises above the set limit

again. This experiment was carried out on model B

with partially informed followers.

It can be seen in ﬁgure 13 that although there

is a noticeable difference in the evacuation rate of

η = d

n agents

e compared to other cases, the evacu-

ation rate of η = d

n agents

e, η = d

n agents

e a η =

n agents

e is very similar throughout the evacuation,

with η = d

n agents

e lagging slightly behind the two

fastest cases. At the same time, it can be noted that

in the case of η = d

n agents

e there was a congestion

during the evacuation, which increased the ﬁnal time

of evacuation of this case.

Figure 13 shows that there is a limit to the min-

imum swarm size below which the evacuation rate

no longer differs much. For the performed exper-

iments, the results of the evacuation are very simi-

lar for η ≤ d

n agents

e, throughout the evacuation pro-

cess. For higher values of η, the rate of evacuation

increased, which was also caused by the congestion,

but a slower course of evacuation compared to other

cases can be noted in the part of the evacuation pre-

ceding this complication.

5.2.5 Impact of Follower Obedience

Time steps of evacuation

Number of evacuated agents

Figure 13: Progress of evacuation as a function of the β

parameter.

In this experiment we observed the follower obedi-

ence parameter β ∈ {90%, 80%, 70%, 60%, 50%,

40%}, which is the probability that a follower will

decide to follow its leader at a given step and will not

try to break away from the swarm. This experiment

was carried out on model B with partially informed

followers.

Hierarchical Control of Swarms during Evacuation

As β decreases, the evacuation time increases by

hundreds of time steps. Followers with lower β more

often do not follow the steps of their leaders, thus hin-

dering evacuation. With a lower β, as a result of their

disobedience, followers more often break away from

their swarm and deliberately move away from it. As

a result, they will lose sight of their leaders, and un-

til they begin to evacuate on their own, they will drop

behind signiﬁcantly. This leads to increasing evacua-

tion time with decreasing β. Lower β can also lead to

an increased incidence of congestions.

5.2.6 Impact of Communication Level between

Leaders on Makespan

Average evacuation time

% probability of leaders being informed

Average evacuation time

Figure 14: The average evacuation time as a function of the

α parameter.

Here we observed the parameter α ∈ {100%, 90%,

80%, 70%, 60%, 50%, 40%}, the percentage proba-

bility of leaders being informed, therefore participat-

ing in the CBS. This experiment was carried out on

model B with partially informed followers.

Unlike followers, if a leader is informed is de-

cided only once, before the start of path planning.

Thus, the same leaders always participate in the CBS.

6 experiments were performed for each value of α.

As the value of α decreased, there were more

and more conﬂicts, often multiple, which greatly pro-

longed evacuation times, as the emergence of these

conﬂicts caused congestions, which lasted hundreds

of time steps in a conﬂict of three or more swarms.

The average α = 90% that exceeds α = 80% or α =

70% that exceeds α = 60% indicates that even a lower

number of uninformed agents can cause signiﬁcant

problems .

Thus, this experiment showed the advantage of

Conﬂict-Based Search – α = 100% has a noticeable

advantage over lower values, and although conges-

tions can occur even at this value, their occurrence is

more rare. It is therefore important that leaders com-

municate with each other and try to avoid conﬂicts.

5.2.7 Impact of Corridor Width

Time steps of evacuation

Number of evacuated agents

Figure 15: Progress of evacuation as a function the ι param-

eter.

Figure 16: Used map building with highlighted corridor

whose width has been tested.

We observed how the course of evacuation will de-

velop depending on the width of escape routes ι ∈ {1,

2, 3, 4, 5, 6} , ie corridors in which the largest oc-

currence of congestions occurred in previous experi-

ments. This experiment was carried out on model B

with partially informed followers.

Figure 15 shows the slowest evacuation process

was at ι = 1. ι = 2 lags behind by several tens of

steps. The pairs ι = 3, ι = 4 and ι = 5, ι = 6 reached

a comparable evacuation time. As the value of ι de-

creases, the evacuation time increases. It can be seen

that the biggest problems are caused by ι = 1, so this

setting is inappropriate. We chose ι ≥ 3 as an appro-

priate setting for this parameter.

5.2.8 Summary of Results

Experiments have shown the importance of coordi-

nated agent behavior. Conﬂict-Based Search has

proven to be an effective tool for constructing plans

for informed leader agents which in combination with

swarms of the follower agents that do not communi-

cate with each other resulted in an efﬁcient evacuation

algorithm for large groups of agents.

KEOD 2021 - 13th International Conference on Knowledge Engineering and Ontology Development

Another observation is that it is also important to

maintain order inside the swarm, which affects the

evacuation of the swarm as a whole. It is therefore

necessary for followers to listen to their leaders.

Furthermore, the number of evacuees has been

shown to affect evacuation time not only because

more agents need to be evacuated, but also because

more agents lead to a higher risk of congestions, as

the space is easier to ﬁll, which may prevent individ-

ual swarms from evacuating.

Experiments also show that in order to evacuate

as quickly as possible, it is important that the leaders

take into account followers who may be behind them

and wait for them. However, if followers are lost and

cannot rejoin the swarm, they should try to evacuate

themselves.

6 RELATED WORK

This work follows (Selvek. and Surynek., 2019),

which also deals with simulation of evacuation in

buildings using a multi-agent system. The authors

propose a local algorithm for LC-MAE evacuation

planning, which is based on sub-optimal algorithms

for MAPF. The paper also studies how the course of

evacuation affects the presence of uninformed agents,

those who plan by themselves in isolation, among in-

formed agents, that plan centrally.

In (Mas et al., 2015) authors simulate evacuation

using ABM focusing on the evacuation of cities dur-

ing the tsunami. The authors present the beneﬁts of

simulating evacuations during a tsunami using ABM.

They also mention the obstacles that realistic mod-

eling of human behavior poses for successful ABM

simulation. Apart from the evacuation simulation, the

model proposed by the authors is used to estimate the

number of victims, analyze the behavior of evacuees,

reveal the limits of the use of shelters or evaluate the

use of means of transport.

Evacuation during a natural disaster is also dis-

cussed in (Tsurushima, 2021), in which the author

bases his model on a video

of an actual evacua-

tion during the 2011 T

ohoku earthquake. Based on

the video, the behavior of agents, which is also repro-

duced as a group behavior, is divided into ﬂeeing and

falling to the ground depending on a distance from the

exit. The author performs simulations in the environ-

ment and settings that correspond to the video.

In (Galea et al., 2003), the authors describe the

rules for the evacuation of an aircraft and propose the

airEXODUS evacuation model, which is a modiﬁca-

https://www.youtube.com/watch?v=tejlDDKeg8s

tion of the EXODUS software tool, which is used to

simulate the evacuation of a large number of people

from complex environments. According to the au-

thors, this model is able to predict with high accuracy

the results of certiﬁcation tests of an aircraft, but also

to predict the sequence of events that may occur dur-

ing these tests.

In (Chen et al., 2020) authors deal with the issue

of hierarchical swarm management. They apply this

technique to swarms of autonomous drones, in which

the hierarchy of leader and follower aircraft applies.

The authors deal with the problem of controlling the

formation of drones. They propose solutions using

group hierarchical swarm control, which achieve co-

ordination outside and inside individual groups of

aircrafts. The architecture proposed by the authors

reduces the complexity of coordinated planning, as

there is no need to plan routes for all aircraft in in-

dividual swarms. The authors also propose rules for

the control of the formation for the pilot aircraft and

the follower aircraft in each group, which guarantee

the stability of the entire swarm, even with possible

restrictions.

The evacuation and behavior of children in the

school environment, which is also the motivation of

this work, is discussed in (Chen et al., 2018). Based

on experiments on groups of children, the authors

reveal several typical behaviors related to distance,

obstacles or clogging of space. They also examine

group behavior scenarios, which they further com-

pare with the behavior of individuals. They reveal

problems during a group evacuation, where children

stop and play during the evacuation, or wait for their

friends instead of their own evacuation. They also

point to the fact that group behavior has an effect on

the child’s path choice. However, the observations did

not take place during the crisis and the children were

not helped or inﬂuenced by teachers’ behavior.

It is important to note that evacuation modeling in-

cludes as diverse approaches as ﬂuid-dynamic models

that regard the evacuation as fully continuous process

solved via differential equations (Sikora et al., 2011).

Cellular automata represent another popular tool for

studying evacuation (Bazior et al., 2018). Often ﬁne

grained modeling of interactions between individual

agents such as resolving collisions between agents is

studies through the concept of cellular automaton.

7 CONCLUSION

Many studies focus on modelling evacuation using

only local algorithms. We have decided to pro-

pose a combination of more informed centralized ap-

Hierarchical Control of Swarms during Evacuation

proaches with local approaches to multi-agent evac-

uation in a hierarchical model via ABM techniques.

The designed models can be used in testing efﬁciency

of evacuation plans, building safety, and evacuation

progress depending on various parameters.

In our model, agents were divided into two types

- leaders, who controlled their swarms and guided

the swarm to a safe area using a modiﬁed global

Conﬂict-Based Search algorithm, a popular algorithm

for multi-agent path ﬁnding, and followers, who aim

to follow the leaders to the safe zone.

We compared different models of behavior of both

types of agents and experimentally veriﬁed their im-

pact on the progress of evacuation. The results of our

work pointed out the importance of communication

between leaders in this type of evacuation. Imple-

menting partially centralized approach has increased

the efﬁciency of the evacuation over scenarios using

only local approach, where leaders didn’t communi-

cate. We also showed how mistakes or disobedience

of the follower agents affect the progress of evacu-

ation and we identiﬁed the problems that can occur

during evacuation.

In future work, we plan to expand the experi-

ments and propose further modiﬁcations of our pro-

posed model, so that the idea of hierarchical control of

swarms during evacuation could be tested in a wider

range of situations. We also plan to verify how real-

istic our models are. For this we plan to acquire data

from evacuations that are unfortunately rare and difﬁ-

cult to obtain. Another option is to perform tests using

volunteers.

ACKNOWLEDGEMENT

This work has been supported by GA

CR - the Czech

Science Foundation under the grant registration num-

ber 19-17966S, and by the V

yLet 2021 project spon-

sored by the Faculty of Information Technology,

Czech Technical University in Prague.

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