Engineering Smart Behavior in Evacuation Planning using Local

Cooperative Path Finding Algorithms and Agent-based Simulations

obert Selvek and Pavel Surynek

Faculty of Information Technology, Czech Technical University in Prague, Th

akurova 9, 160 00 Praha 6, Czech Republic

Keywords: Evacuation Planning, Cooperative Path-ﬁnding, Local Algorithms, Simulations, Real-life Scenarios.

Abstract:

This paper addresses evacuation problems from the perspective of cooperative path ﬁnding (CPF). The evac-

uation problem we call multi-agent evacuation (MAE) consists of an undirected graph and a set of agents.

The task is to move agents from the endangered part of the graph into the safe part as quickly as possible.

Although there exist centralized evacuation algorithms based on network ﬂows that are optimal with respect

to various objectives, such algorithms would hardly be applicable in practice since real agents will not be

able to follow the centrally created plan. Therefore we designed a local evacuation planning algorithm called

LC-MAE based on local CPF techniques. Agent-based simulations in multiple real-life scenarios show that

LC-MAE produces solutions that are only worse than the optimum by a small factor. Moreover our approach

led to important ﬁndings about how many agents need to behave rationally to increase the speed of evacuation.

1 INTRODUCTION

Evacuation planning represents an important real-life

problem and is increasingly studied in artiﬁcial intelli-

gence (Chalmet et al., 1982; Mishra et al., 2015). The

task consists of evacuation of people or other agents

from the endangered area into the safe zone.

Various techniques have been applied to address

the problem including modeling the problem as net-

work ﬂows (Arbib et al., 2018) or nature inspired com-

putation such as bee colony optimization.

The map where the evacuation task takes place

is often modeled as a graph where vertices represent

locations for agents, and edges model the possibil-

ity of moving between pairs of locations (Liu et al.,

2016). Hence the evacuation problem can be inter-

preted as a variant of cooperative path ﬁnding (Sil-

ver, 2005; Wang and Botea, 2011; Surynek, 2014;

Surynek, 2015) (CPF). Similarly as in CPF, the evac-

uation modeling must take into account potential col-

lisions between agents and solving techniques must

ensure proper avoidance (Foudil et al., 2009). The

collision avoidance in CPF is usually represented by

a constraint of having at most one agent per vertex. In

contrast to CPF, where agents have unique individual

goals (locations), we usually do not distinguish be-

tween individual agents in the evacuation task. That

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

is, an agent can evacuate itself to anywhere in the safe

zone (not to a speciﬁc location in the safe zone).

Another important challenge in evacuation plan-

ning is represented by the execution of a plan by real

agents. In real-life evacuation scenarios, we cannot

simply assume that all agents will want to follow the

plan. The real agent may for example prefer the near-

est exit while a centrally created plan make it go else-

where, thus not being realistic for the agent. This

differs from classical planning (Ghallab et al., 2016),

where the planning authority fully observes the envi-

ronment, actions are assumed to be deterministic, and

plans created in advance are perfectly executed

Therefore we focus on local evacuation planning

relying on local cooperative path ﬁnding techniques

and agent-based simulations. Our assumption is that

evacuation paths planned locally using information

available to the agent will be more realistic. At the

same time we do not rule out the central aspect com-

pletely as we also consider some agents to be more

informed (about alternative exits, through a commu-

nication device) than others.

This paper begins with a formal introduction to

the concept of evacuation planning, followed by a

short summary of local cooperative path ﬁnding algo-

rithms which are the base of our novel evacuation al-

gorithm called Local Cooperative Multi-agent Evacu-

ation (LC-MAE), described and experimentally eval-

uated in multiple scenarios using agent-based simu-

Selvek, R. and Surynek, P.

Engineering Smart Behavior in Evacuation Planning using Local Cooperative Path Finding Algorithms and Agent-based Simulations.

DOI: 10.5220/0008071501370143

In Proceedings of the 11th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2019), pages 137-143

ISBN: 978-989-758-382-7

137

lations. As part of the simulations, the algorithm is

compared to a network-ﬂow based algorithm which

produces near-optimal plans.

2 BACKGROUND

The abstract multi-agent evacuation problem (MAE)

takes place in an undirected graph G = (V, E) which

has vertices divided into a set of endangered (D) ver-

tices and a set of safe (S) vertices. Agents from a set,

A = {a

, a

, ..., a

}, are distributed among the vertices

and the task is to evacuate them from endangered ver-

tices to safe vertices. This problem is similar to coop-

erative path ﬁnding (CPF) (Silver, 2005) from which

we took the model for movements of agents.

Each agent is placed in a vertex of G so that there

is at most one agent per vertex. The conﬁguration of

agents in vertices of the graph at time t will be de-

noted as c

: A → V . Similarly as in CPF an agent can

move into a vacant adjacent vertex. Multiple agents

can move simultaneously, provided they do not col-

lide with each other (that is, no two agents enter the

same target vertex at the same time).

Deﬁnition 1. Multi-Agent evacuation (MAE) is a

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

, D, S], where G repre-

sents the environment, A is a set of agents, c

: A → V

is the initial conﬁguration of agents, D and S such

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

0, and

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

vertices respectively.

The task in MAE is to ﬁnd a plan that moves

all agents into the safe vertices; that is a plan π =

, c

, ..., c

] so that c

(a) ∈ S ∀a ∈ A. The total time

until the last agent reaches the safe zone is called a

makespan; the makespan of π is m.

To increase chances of evacuation, the makespan

should be small. A near makespan-optimal evacua-

tion plan can be found in polynomial time using net-

work ﬂow techniques (Yu and LaValle, 2012; Yu and

LaValle, 2015; Arbib et al., 2018). However, these al-

gorithms require a centralized approach where agents

perfectly follow the central plan which is hardly ap-

plicable in real-life evacuation scenarios (Foudil et al.,

2009; Hudziak et al., 2015).

3 COOPERATIVE PATH FINDING

ALGORITHMS

We address MAE from a local point of view inspired

by CPF algorithms like Local Repair A* (LRA*) and

Windowed Hierarchical Cooperative A* (WHCA*)

(Silver, 2005). These algorithms feature a decentral-

ized approach to multi-agent path ﬁnding. Instead of

using optimization techniques or network ﬂow, each

agent’s path is found separately, resolving conﬂicts

between agents trying to enter the same vertex as they

occur.

While LRA* only resolves conﬂicts at the mo-

ment agent tries to enter an occupied vertex, a naive

strategy which can easily lead to deadlock, WHCA*

is more advanced. Instead of only planning their paths

in space, agents plan their paths in space-time and

share them with other agents using a data structure

called reservation table. When planning, vertices re-

served by another agent at a given time are considered

to be impassable.

If each agent planned and reserved its whole path

to destination, agents planning later would have infor-

mation about its complete route and their needs and

goals would not be taken into account, leading to self-

ish behavior and deadlocks. The ﬁx to this behavior is

windowing, in which agents plan their paths only for

a certain, small, number of time units and the plan-

ning is staggered, so that each agent has an option of

reserving a certain vertex.

4 LOCAL MULTI-AGENT

EVACUATION (LC-MAE)

Our new local multi-agent evacuation (LC-MAE) al-

gorithm divides the evacuation task into three sub-

problems:

• Evacuation Destination Selection: The most im-

portant difference between MAE and simple CPF

is that agents’ destinations are not speciﬁed.

• Path-ﬁnding to Safety: Once an agent has picked

its destination in S, it has to ﬁnd a collision-free

path to it.

• Behavior in the Safe Zone: Agents that have left

D do not disappear from the map. They must not

block other agents from entering S.

Agent movement in the last two sub-problems is

based on modiﬁed versions of WHCA* algorithm, de-

scribed in their respective sections.

4.1 Evacuation Destination Selection

The basic data structure used by LC-MAE when

choosing an evacuation destination is the frontier de-

noted F, F ⊆ S. The frontier is a set of safe vertices

which separates the endangered zone from the safe

zone. It holds that an agent must enter S by passing a

vertex from F.

KEOD 2019 - 11th International Conference on Knowledge Engineering and Ontology Development

138

In other other words, removing F from G will sep-

arate D and S into disconnected components. F is cre-

ated on algorithm initialization. It holds that an agent

must enter S by passing a vertex from F.

Destination selection uses a modiﬁed A* algo-

rithm, inspired by the RRA* algorithm (Silver, 2005).

Agent’s position is set as the path-ﬁnding goal, while

all nodes in F are added to the initial open set. Man-

hattan distance (Korf and Taylor, 1996) is used as the

heuristic.

The result is a vertex in F that is located at the

shortest true distance from the agent while, at the

same time, being reachable by the agent. With the

vertex at hand, the algorithm returns its true distance

from the agent. This matches many real-world evac-

uation scenarios in which people are being evacuated

from an area they know and thus have a mental map

of the nearest exits (Kurdi et al., 2018).

While evacuating, agents track the number of

steps they have taken to reach their destination. Since

the goal’s true distance from the starting position is

known, they can compare these two numbers. If the

number of steps taken is signiﬁcantly higher than the

distance, it may indicate the agent has veered off the

optimal path. This could be, for example, because the

path to the chosen destination is congested. In that

case, the agent repeats the destination selection pro-

cess, an action that we call retargeting.

4.2 Reservation Table

In LC-MAE we use a variant of the reservation table

used in the Cooperative A* algorithm (Silver, 2005).

Every vertex in G is associated with a mapping of

time steps to reservation structures. Every reservation

structure includes a reference to the reserved vertex,

the ID of the agent that created the reservation and a

priority. Associating priority with reservations is our

primary distinguishing feature. Agents can make a

reservation for vertex v and time step t provided they

fulﬁll one of the following conditions:

1. No reservation exists yet for v at time t and the

vertex can be reserved at time t + 1.

2. A lower-priority reservation exists for v at time t

and the vertex can be reserved at time t + 1.

3. The agent holds a reservation for vertex v at t − 1.

Condition 3 ensures that CPF algorithms used

in LC-MAE can always perform at least one ac-

tion, staying in place, without having to dynamically

change the order in which agents’ paths are planned

or performing invalid actions, like colliding with an-

other agent.

The t +1 reservability requirement in conditions 1

and 2 prevents the creation of so-called trains - lines

or crowds of agents which move in the same direction

at the same time and which reduce the simulation re-

alism. A simple example of a train being formed is

shown in the right column of ﬁgure 1.

4.3 Path-ﬁnding To Safety

Once the agent has picked its destination vertex s in

S, it plans a path towards s using WHCA* with the

RRA* heuristic. An agent plans its path on-demand

when it has to return an action for the next time step

and fulﬁlls any of these conditions:

• Is more than halfway through its planned path

• Has to retarget

• Has lost a reservation for a vertex on its planned

path

• Is making its ﬁrst step

Endangered agents are prioritized relative to

agents that are in S - they are processed before agents

located in S. This ensures that endangered agents gen-

erate their plans ﬁrst.

As soon as an agent enters S (even if it is not

its current destination vertex), it stops following the

planned path and switches to the behavior described

in the next section.

4.4 Safe Zone Behavior

While some parts of the behavior of an endangered

agent, e.g. on-demand planning for a speciﬁed num-

ber of steps in advance and reserving the vertices for

given times do not change once the agents enters a

safe zone, the costs for different actions that WHCA*

algorithm considers for each step are different and

more dynamic.

The major difﬁculty in the safe zone is that freshly

arriving agents must not impede the ongoing evacua-

tion. A simple approach is to move agents as far from

D as possible. However, knowing whether an agent is

getting away from D is not a trivial problem from the

local point of view.

The behavior agents adopt after entering S in LC-

MAE (called surﬁng) is based on modiﬁed WHCA*

algorithm. Costs for the passage from one vertex to

another are computed dynamically, depending on the

positions of other agents and the type of the agent’s

target vertex.

Only using half of the planned path before replanning is

a simple way of improving agent cooperation described in

(Silver, 2006)

Engineering Smart Behavior in Evacuation Planning using Local Cooperative Path Finding Algorithms and Agent-based Simulations

139

Algorithm 1: The algorithm for computing the number of

agents following agent a.

1 previous-reserved (E , π, a, t)

2 let π = [c

, c

, ..., c

]

3 V

← {c

t−b

(a) | b = 0, ...,

}

4 for v ∈ V

5 if reserved(v, t) then

6 r ← r + 1

7 return r

The basic idea is that an agent’s priorities should

vary according to the number of agents following be-

hind, on the same path. When no other agents are

following, it will prefer staying in place. With an in-

creasing number of agents behind, the cost of to stay

in place will increase.

The agent determines the number of following

agents by checking whether there are reservations cre-

ated for positions it has passed before. The process is

formalized in pseudo-code as Algorithm 1.

Since agents only make this check when they start

planning their next few steps, the results have to

be adjusted to account for the increasing uncertainty

about the steps that other agents will take. This is

done by subtracting the number of future time steps

from the number of following agents (see line 11 of

Algorithm 2).

Algorithm 2: Computing costs of different actions for

agents in the safe zone. Actions are considered relative to

agent a located at v at time t. t

speciﬁes the time at which

the plan is generated.

1 neighbors (E , π, a, t, v, t

)

2 let π = [c

, c

, ..., c

]

3 A

← previous-reserved(E ,π,a,t

)

4 costs ← []

5 foreach u ∈ S | {v, u} ∈ E do

6 if reservable(u, t + 1)∧u ∈ S then

7 if u ∈ {c

(a) | t = 0, 1, ..., t} then

8 costs ← costs ∪{(u, 3)}

9 else

10 costs ← costs ∪{(u, 2)}

11 b ← max(1, |A

| − (t −t

))

12 if reservable(v, t + 1) then

13 costs ← costs ∪{(u, 1 ∗ b)}

14 else

15 costs ← costs ∪{(u, 4 ∗ b)}

16 return costs

The complete cost-calculation algorithm can be

found in Algorithm 2. With increasing back-pressure,

Figure 1: Movement of agents in ordinary MAE (left) and

in relaxed MAE (right).

moving into a reservable adjacent vertex becomes the

cheapest option. The agent keeps a list of positions

it has already visited and assigns them a higher cost.

This leads to better diffusion of agents through S as

endangered agents can ”nudge” safe agents deeper.

5 RELATED

WORK - CENTRALIZED

EVACUATION

Near optimal solutions of MAE can be found by mod-

eling an MAE instance as network ﬂow (Arbib et al.,

2018; Yu and LaValle, 2012) and planning it centrally.

The core concept is to construct a time expanded net-

work having m copies of G in which a ﬂow of size |A|

exists if and only if the corresponding relaxed MAE

has a solution of makespan m. In the relaxed MAE

we do not require agents to enter vacant vertices, lead-

ing to the possibility of movement similar to the right

column of ﬁgure 1.

The solution for a relaxed MAE problem ob-

tained from the network ﬂow algorithms can be post-

processed into a solution of ordinary MAE by post-

poning moves that would violate the invariant of not

entering a vertex that has just been left by an agent.

However, postponing moves may lead to deadlocks,

so the post-processing algorithm swaps the paths

planned for deadlocked agents when a deadlock is de-

tected. We’re calling this planning algorithm based on

post-processed network ﬂows POST-MAE.

6 EXPERIMENTAL EVALUATION

We implemented LC-MAE in Python and evaluated

it in multiple benchmark scenarios. We also imple-

mented POST-MAE on top of Push-relabel max-ﬂow

algorithm (Goldberg and Tarjan, 1988). In order to es-

timate the difference between the makespans of plans

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140

(a) Concert scenario (b) Blocker scenario

(d) Shops scenario

Figure 2: Maps inspired by real-life evacuation scenarios.

generated by LC-MAE and makespans of optimal (if

completely unrealistic) plans, we also benchmarked

POST-MAE without the post-processing, denoted as

ﬂow in comparison tables. Our implementation re-

lies on data structures implemented in the networkx

library (Hagberg et al., 2008). The visualization is

implemented on top of the arcade library (Craven,

2019). In the LC-MAE implementation, the look-

ahead window was set to 10 steps.

6.1 Agent Types

To simulate real-life scenarios with higher ﬁdelity we

used agents of two types. They differ in their behav-

ior while in S all agents rely on surﬁng. Retargeting

agents fully implement the destination selection algo-

rithm while static agents plan a path to a vertex spec-

iﬁed in advance.

6.2 Setup of Experiments

We used 4 different maps in our evaluations as shown

in Figure 2 - they represent 4-connected grids with

obstacles. Free and safe vertices are white (surround-

ing area), free and endangered vertices are pink. Ver-

tices occupied by agents are green. Black squares sig-

nify walls, so no vertices are present in the underlying

graph at those positions.

6.3 Experimental Results

We ﬁrst compared the makespan of evacuation plans

generated by LC-MAE with optimal makespans cal-

culated by the ﬂow-based algorithm for relaxed MAE

Table 1: Makespans for evacuation plans.

Scenario Agents LC-MAE Flow POST-MAE

Concert 118 90 17 33

Ofﬁce 80 94 47 62

Shops 299 129 36 75

Blocker 414 146 23 69

and with makespans of solutions post-processed with

POST-MAE - see table 1. LC-MAE generates plans

that are only worse by a small constant factor (ranging

from 1.52 to 2.73) from those generated by POST-

MAE, which indicates that LC-MAE solutions are

close to the true optimal makespan. Moreover, plans

generated by LC-MAE are more realistic as they need

local communication only.

The performance of LC-MAE is better than the

performance of ﬂow algorithm and than that of POST-

MAE, as demonstrated in table 2. An additional ad-

vantage is that since LC-MAE is a local algorithm and

uses windowing, the plans can be used while they are

being generated, since the steps taken by agents do

not change.

Table 2: Seconds taken by plan generation.

Scenario LC-MAE Flow POST-MAE Speedup

Concert 7 52 62 8.9×

Ofﬁce 4 57 61 15.3×

Shops 20 379 403 20.2×

Blocker 27 220 243 9.0×

6.4 Agent-based Simulations

We also made a series of experiments to understand

the real process of evacuation in scenarios in which

various types of agents are mixed together, that is,

when some agents are better informed than others.

For each map, we created multiple scenarios with

some of the retargeting agents replaced by static

agents. These static agents try to exit through the

largest opening between the safe and endangered zone

(which could be described as the main exit from the

area) and ignore all other exits. With this setup, re-

targeting agents could be considered to be better in-

formed, given they take all the possible exits into ac-

count.

The percentage of agents that have reached safety

as a function of time is shown in Figure 3.

The Concert evacuation scenario is one of the sce-

narios with a large difference in the makespan be-

tween the relaxed optimum and the plan generated by

LC-MAE.

Our hypothesis is that this is caused by the fact

that the side emergency exits are very small and

the area behind them quickly becomes crowded with

agents that escaped through the emergency exit clos-

est to them.

Engineering Smart Behavior in Evacuation Planning using Local Cooperative Path Finding Algorithms and Agent-based Simulations

141

0 50 100 150 200 250 300

Time

100

Safe agents (%)

blocker

allstatic

half

third

0 20 40 60 80

Time

Safe agents (%)

concert

allstatic

staticcrowd

0 25 50 75 100 125 150

Time

100

Safe agents (%)

office

half

sixth

0 100 200 300

Time

Safe agents (%)

shops

allstatic

quarter

sixth

Figure 3: The percentage of safe agents in time. Line colors differentiate between different scenarios. Dashed lines represent

percentage of retargeting agents in S, dotted lines represent the percentage of static agents in S.

To test this hypothesis, we created two more sce-

narios. The ﬁrst one is called allstatic and all the

agents are static and try escaping through the large

opening in the lower part of the map. In the second

one, called staticcrowd, only the ﬁrst three rows in

front of the stage are static. The original scenario with

all retargeting agents is labeled r.

Both allstatic and the original version exhibit

relatively long makespan, although our hypothesis is

conﬁrmed by allstatic’s being shorter. The best

makespan is exhibited by staticcrowd. Retarget-

ing agents use the side exits which do not get over-

crowded and leave most of the endangered zone free

for static agents to pass through.

In the Ofﬁce scenario we tried two modiﬁed ver-

sions: half and sixth - where one half and one sixth

of the agents respectively are retargeting, while oth-

ers are static, trying to escape through the left exit.

For the Shops scenario, we created three modiﬁed ver-

sions where static agents are trying to escape through

the large exit at the bottom.

Finally, the Blocker scenario best illustrates how

static agents can impede the evacuation of retarget-

ing agents. Since exits from the endangered zone are

large and there is plenty of safe space on the map, the

shortest makespan is achieved when all of the agents

are retargeting and the longest when they are all static

and try to evacuate through a single exit.

7 CONCLUSION

We presented a new local algorithm called LC-MAE

for evacuation of agents in graphs. LC-MAE uses

a modiﬁcation of WHCA* as the underlying path-

ﬁnding process but also introduces several high-level

procedures that guide agents’ behaviour depending

on whether they are in the endangered or the safe

KEOD 2019 - 11th International Conference on Knowledge Engineering and Ontology Development

142

zone. Our experimental evaluation indicates that LC-

MAE generates solutions with makespan that is only

a small factor worse than the optimum. We also stud-

ied how different ratios of less informed agents af-

fect the process of evacuation. We found that de-

pending on the scenario, the presence of some unin-

formed agents can improve the evacuation outcome

for the well-informed agents. Additionally, even large

numbers of uninformed agents don’t impede informed

agents from reaching the correct exit.

ACKNOWLEDGEMENTS

This research has been supported by GA

CR - the

Czech Science Foundation, grant registration number

19-17966S. We would like to thank anonymous re-

viewers for their valuable comments.

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