Quorum Sensing Re-evaluation Algorithm for N-Site Selection in

Autonomous Swarms

Shreeya Khurana

and Donald Sofge

2 a

Montgomery Blair High School, 51 University Blvd. East, Silver Spring, Maryland, U.S.A.

Distributed Autonomous Systems Group, Navy Center for Applied Research in Artiﬁcial Intelligence,

Naval Research Laboratory, Washington DC, U.S.A.

Keywords:

Quorum Sensing, Re-evaluation, Autonomous Swarms.

Abstract:

Flexible decision-making is a vital aspect of swarm behavior. Nature offers a level of uncertainty that could

force a swarm to reconsider a site previously abandoned. While efforts are being made to allow for ﬂexible

decision-making in autonomous swarms, there is little literature in the area of re-evaluation functions as most

models utilize site abandonment functions. The research in this paper produces a re-evaluation algorithm

for discrete n-site selection by autonomous swarms, taking inspiration from prior work with quorum sensing

models and ant colony optimization algorithms. The algorithm’s success in re-evaluation trades off with

decision time, but increases the accuracy of decisions made.

1 INTRODUCTION

The applications of autonomous swarms have in-

creased tremendously in recent years with prefer-

able uses in unsafe or inaccessible locations (Tan

and Zheng, 2013). Efforts to develop more ﬂexible

decision-making models in order to successfully and

efﬁciently select the best target or site within a search

space are being made. Several decision-making mod-

els that address value-sensitive site selections have

been proposed, but all these models abandon the sites

with lower values (Cody and Adams, 2017; Reina

et al., 2015). Therefore, there is a need for more ﬂex-

ible decision-making models in autonomous swarms

that are capable of revisiting the sites that were previ-

ously abandoned.

The use of autonomous swarm systems in Human-

itarian Assistance and Disaster Response (HADR)

missions can signiﬁcantly facilitate the relief opera-

tions conducted (Diamandis, 2019). As a result of

natural disasters, damage caused by ﬂooding, or toxic

chemicals and radioactive materials, can cause a level

of uncertainty with regard to safety in certain areas.

Further, the sustainability of buildings used for tem-

porary shelters may change rapidly as a result of dam-

age. Additionally, overcrowding of shelters can cause

signiﬁcant problems. In 2017 Hurricane Maria dev-

https://orcid.org/0000-0003-0153-3581

astated Puerto Rico, resulting in a signiﬁcant power

outage and lack of drinking water on the island. Med-

ical centers were overcrowded and had limited capa-

bilities to respond as a result of the shortages in sup-

plies and personnel at the shelters. When it is the

job of the swarm system to locate supportable shel-

ters for those in need, the system needs to implement

proper decision-making to account for the level of un-

certainty in the community environment during such

natural disasters.

Therefore, an algorithm in which the swarm sys-

tem makes re-evaluations of past quorum decisions is

needed to address the uncertainties and potential in-

stability of a shelter location. Rather than discarding

visited sites that have been deemed unsuitable, as in

most swarming decision-making models that imple-

ment site abandonment, an algorithm that keeps all

of the sites in its memory is needed. Thus, when

a selected shelter has deteriorated, the agents of the

swarm system should be able to re-evaluate the re-

maining sites to select the next best site.

This research paper proposes a discrete n-site se-

lection model that allows swarms to re-evaluate past

quorum decisions. The proposed model allows swarm

agents to explore a deﬁned search space, and com-

municate with each other about sites in the proxim-

ity. This communication then allows the agents to

come to a consensus about the best site for reloca-

tion. The model takes inspiration from the decision-

Khurana, S. and Sofge, D.

Quorum Sensing Re-evaluation Algorithm for N-Site Selection in Autonomous Swarms.

DOI: 10.5220/0008957801930198

In Proceedings of the 12th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2020) - Volume 1, pages 193-198

ISBN: 978-989-758-395-7; ISSN: 2184-433X

193

making mechanisms of ant swarms as well as the

quorum-sensing decision-making model for discrete

site selection model detailed by Cody and Adams

(Cody and Adams, 2017). However, our model

keeps visited-sites in memory rather than discarding

the sites deemed dangerous or problematic a trait

common to swarming algorithms that implement site

abandonment such as the one developed by Cody and

Adams (Cody and Adams, 2017). Our model allows

for the agents to perform the re-evaluations necessary

to select the best site in the search space. The aim

of the model is to enable a swarm to re-evaluate its

decisions to select the best site and increase decision

accuracy allowing for a more ﬂexible swarm behav-

ior.

The paper is organized as follows. Section 2 re-

views the biological inspiration and the swarm site

selection research. Section 3 describes our proposed

quorum sensing re-evaluation model. Section 4 de-

scribes the experimental design for simulations. Sec-

tion 5 presents the results. Sections 6 and 7 discuss

the results and areas of future work.

2 BACKGROUND

2.1 Natural Swarms

The Diacamma indicum ant species, also known as

Indian queen-less ant, utilizes a process known as tan-

dem running for nest relocation. Tandem running in-

volves one ant leading another ant to a nesting loca-

tion, one at a time and keeping close physical con-

tact with the other ant. Additionally, the D. Indicum

performs re-evaluations in response to changes in the

target nest during nest relocation, with a negligible er-

ror (1.65%) according to a study conducted by Anoop

and Sumana (Anoop and Sumana, 2015).

The Temnothorax Albipennis ant species, also

known as rock ant, utilizes tandem running as well

as a population dependent decision-making mecha-

nism known as quorum sensing. As more and more

ants visit a nesting location, a quorum of ants favor-

ing that particular site over other sites starts to build.

Once a certain known threshold is surpassed, the ants

disperse to recruit other agents to the site that has been

decided upon (Pratt, 2005). This recruitment mecha-

nism has a recruitment rate three times that of tandem

runs.

The decision-making model we developed draws

inspiration from the recruitment methods of the Dia-

camma indicum and the Temnothorax Albipennis ant

species.

2.2 Swarm Models

Several artiﬁcial swarm decision-making models have

been developed (Tan and Zheng, 2013). The Cody

and Adams value sensitive quorum sensing decision

making model is one model involving discrete site

selection in autonomous swarms (Cody and Adams,

2017; Reina et al., 2015).

The quorum sensing re-evaluation model de-

scribed in this paper utilizes principles of the Cody

and Adams model. In this model (Figure 1), agents

can be in one of three states: uncommitted, favor-

ing, or quorum, and one of two categories: latent

and interactive. Agents in the uncommitted state do

not have a preference towards a particular site in the

search space, while favoring agents do have a prefer-

ence towards a site. Agents in the quorum state have

decided on a particular site and work towards recruit-

ing other agents to that site. Latent agents explore the

search space for sites and interactive agents remain

in the nest and interact with other agents and recruit

those agents to a particular site.

Figure 1: The Quorum Sensing Re-evaluation behavior

model with its nodes and transitions. State types are rep-

resented as: U , uncommitted; F, favoring; and Q, quorum.

Categories are represented as: L, latent and I, interactive.

Transitions between states are depicted using symbols P

and ψ, where P is a speciﬁc probability function detailed in

Equations 1-8 in the text and ψ is the population of agents

in the speciﬁed state (shown in subscripts). i and j denote

speciﬁc sites the agent is interacting with.

3 QUORUM RE-EVALUATION

ALGORITHM

The agents in the swarm start in the nest and have

the goal of selecting the best site out of a total of

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

194

n sites. For simplicity of this model, each site has

a starting value between 0 and 1 based on its dis-

tance from the nest. Sites that are closer to the nest

have a larger value. However, in real-world situa-

tions the site values will be determined by a number

of other factors, including quality, size, and distance.

Each agent has a known sensing and communication

range. As compared to an algorithm that does not re-

evaluate decisions when necessary, the re-evaluation

algorithm proposed would increase decision accuracy

but increase decision time.

3.1 States and Transitions

Using principles from the Cody and Adams model,

the agents in the swarm system start in the nest as

uncommitted latent agents. Agents can transition be-

tween uncommitted latent and uncommitted interac-

tive with a probability P

and P

, where R is the in-

verse of the average site round trip time and i and l are

the population of agents that are interactive and latent

respectively as referenced in equations 1 through 3.

p(i,l) =

i + l

(1)

(

R P

≤ 1

0 P

= 0

(2)

(

p(i,l)R p(i,l)R < 1

1 p(i,l)R ≥ 1

(3)

Once a site has been explored long enough, the agent

has the option to favor the site or leave the site and

explore another site. When a site is favored, the agent

can be in either the favoring interactive or the favoring

latent state.

Much of the agents decision making is governed

by properties of ant colony optimization (ACO),

speciﬁcally through pheromone production (Ab Wa-

hab et al., 2015). Ants produce pheromones to com-

municate with other ants, typically when recruiting

other ants in the colony. The use of pheromones for

communication is an integral part of emergent behav-

ior seen in nature (von Thienen et al., 2014).

In ACO the probability of any one agent relo-

cating from site i to site j is determined by equation 4.

(τ

i j

)

(η

i j

)

∑

(τ

i j

)

(η

i j

)

(4)

i j

= v

= [0,1] (5)

i j

= (1 − r)τ

i j

+ ∆τ

i j

(6)

∆τ

i j

(

(7)

Probability P

is governed by the amount of

pheromone on the path to site j (τ

i j

) and the site de-

sirability value, which in this case is the site qual-

ity value of site j, denoted by v

. The amount of

pheromone on a path is determined by the amount re-

maining after evaporation at rate r and the amount that

is deposited on the path denoted by ∆τ

i j

When an agent in the model transitions from un-

committed latent state to favoring interactive state, the

agent utilizes the pheromone probability rule moving

from the nest to the site it began to favor. When tran-

sitioning from uncommitted latent to favoring latent,

the agent drops ”pheromone” at the site it favors in

order to help attract other agents to that site. In the

case of unmanned vehicles this ”pheromone” is rep-

resented as increases to the site value by a predeter-

mined value. In this paper that predetermined value

is 0.025. Additionally, the rate of evaporation is also

set to 0.25 units per iteration. When an agent has de-

termined a site better than the one it currently favors,

rather than abandoning the site, as in previous mod-

els, the agents drop a different type of ”pheromone”,

which has a lower evaporation rate, before reverting to

the uncommitted latent state. In the case of unmanned

vehicles, this ”pheromone” is also represented as de-

creases to the site value by the same value; however,

the evaporation rate is 0.75 units per iteration. This

allows for the site value to decrease faster, indicating

to other agents that this site is not suitable, but can be

reconsidered if a re-evaluation is necessary.

When enough agents are favoring a site, such that

the quorum threshold is surpassed, these agents tran-

sition to the quorum state. These agents then re-

cruit other agents to the determined quorum site. In

the case that the site value of the quorum site has

changed, the agent can revert back to the uncommit-

ted interactive state at probability P

and perform a

re-evaluation.

(

< 1

≥ 1

(8)

The agents compare the previous site value with the

changed site value. If the new value is lower than the

previous one and the value is less than the value of

the other sites, the agent transitions to the uncommit-

ted interactive state and re-evaluates the other sites to

choose the next best site.

4 EXPERIMENT

It was our hypothesis that our quorum-sensing re-

evaluation algorithm would increase both the decision

time and decision accuracy.

Quorum Sensing Re-evaluation Algorithm for N-Site Selection in Autonomous Swarms

195

To test our hypothesis, the model developed was

simulated using the Processing programming lan-

guage (Reas and Fry, 2014). A total of 50 agents

were used to simulate site selection with two, three,

four, and ﬁve sites. The search space is depicted by a

450 x 450 pixel square. The nest, in the center of the

search space, is represented by a 60 x 60 pixel square

and the other sites are represented by 70 x 70 pixel

squares. The original site value of each site was in-

versely proportional to the distance from the nesting

location (Figure 2). The optimal sensing range and

speed for the agents were determined to be 13 pixels

and 10 pixels/s, respectively. The threshold for transi-

tioning to a quorum state was determined to be at least

5 agents per site. The simulations were run with and

without changes in the quorum site value. Changing

the quorum site value allows the testing of the efﬁ-

ciency with which the algorithm allows the agents to

re-evaluate past quorum decisions. To test the ability

of the swarm to re-evaluate decisions, once the agents

sense a quorum at a particular site, the site value is

reduced by 0.3. After this reduction, if the value of

the site is less than the value of other sites, the value

reduces to 0.0 to allow for a re-evaluation of the other

sites. Otherwise, if the site value after reduction is

still greater than the value of other sites, there is no

additional change to the site value. The simulation

terminates after all agents have reached a quorum de-

cision. For each simulation group, 100 trials were run.

For each trial, the decision time and the number

of agents that found a quorum at each site were noted.

For trials involving two sites, the accuracy was de-

termined by the number of agents that chose the best

site. For trials involving three, four, and ﬁve sites, the

accuracy was determined by the number of agents that

chose the best two sites, based on the ﬁnal site values.

Accuracy was determined using the following: n/50,

where n is the number of agents that selected the best

sites (one or two, depending on the total number of

sites) and 50 is the preset total population of agents

used in the simulation.

5 RESULTS

The graphs in Figure 3 show the change in decision

time over the number of sites in the search space and

the change in decision accuracy over the number of

sites in the search space.

Between the trials without re-evaluations and with

re-evaluations, the average decision time increased

by roughly 100 milliseconds. The average decision

time also generally increased with the number of sites

in the search space. Additionally, decision accuracy

showed an increase for the trials with re-evaluations

as compared to the trials without re-evaluations. De-

cision accuracy did, however, decrease as the number

of sites in the search space increased. For 2-site selec-

tion, the accuracy increased from 99.0% without re-

evaluations to 100.0% with re-evaluations. For 3-site

selection, the accuracy increased from 80.7% without

re-evaluations to 93.9% with re-evaluations. For 4site

selection the accuracy increased from 77.6% without

re-evaluations to 89.0% with re-evaluations. For 5-

site selection, the accuracy increased from 80.6% to

93.84%.

Figure 2: A: Screenshot of an original setup of the search

space for a 4-site selection simulation. The original site

value of each site is inversely proportional to the distance

from the nesting location. Site 1 (red) has a highest site

value of 1.0, Site 2 (blue) has a site value of 0.8, Site 3

(green) has a site value of 0.6 and Site 4 (purple) has a site

value of 0.7. B, C, and D: Screenshots of examples of sim-

ulations after agents have sensed a quorum. Accuracy in

examples B and C is 100% and accuracy in example D is

74%.

A t-test analyzing the decision time for 2, 3, 4,

and 5 sites produced p-values of 0.001, 2.154 ∗ 10

−8

1.120 ∗ 10

−5

, and 0.042 respectively. Additionally,

the same test analyzing decision accuracy for 2, 3, and

4 site selection produced p-values of 0.160, 0.0003,

0.0086, and 0.0004 respectively. Based on these val-

ues, we can not conclude that the re-evaluation algo-

rithm signiﬁcantly increases decision accuracy for 2-

site selection. However, we have reasonable evidence

to suggest that the re-evaluation algorithm increases

accuracy for 3, 4, and 5-site selection.

The model was able to successfully increase the

accuracy of the decisions made by the swarm with de-

cision time as a trade-off.

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

196

Figure 3: Box-plots showing distribution of the decision time (in milliseconds) by number of sites in the search space with

average decision time, depicted with x (Left). Decision Accuracy (%) by number of sites in the search space (Right).

6 DISCUSSION

The ability to make ﬂexible decisions is imperative

for the development of swarm robotics and decision-

making. Our algorithm permits the swarm agents

to successfully re-evaluate sites in a deﬁned search

space. The algorithm can be adapted in HADR mis-

sions where local citizens need to be evacuated to

safe shelter locations. In a disaster-struck community,

agents in a swarm system can assess the shelter sites

in the area using our algorithm to reach an accurate

consensus regarding the safest shelter to transport the

citizens to. If a potential shelter location has suddenly

deteriorated, our algorithm permits the agents to re-

evaluate their past quorum decisions to reach a new

consensus regarding the next best shelter.

Information regarding the safest shelter location

can be transmitted to ﬁrst responders to safely evacu-

ate citizens to the selected shelter. The ability to re-

evaluate decisions could also help mitigate issues like

overcrowding and supply shortages in shelters during

such disasters, signiﬁcantly contributing to the efﬁ-

ciency and improvement of HADR missions.

This paper demonstrates the efﬁciency of a

quorum-sensing re-evaluation algorithm using inspi-

ration from biological swarm systems, allowing for

more accurate decisions to be made with decision

time as a trade-off. In the future this model may

very well prove itself useful in the location of sus-

tainable shelters for areas devastated by disaster and

be of good aid to HADR missions.

7 FUTURE WORK

Future work should focus on testing the algorithm us-

ing swarms of autonomous drones in a physical space.

For simplicity, the assigned site values in our model

were inversely proportional to the distance from the

nest. To evaluate the suitability of our model for real-

world situations, the site values will have to take into

account a number of other factors, including quality,

size, and distance, depending on the operation.

Additional testing can also be done with more

sites in the search space. Sites of different sizes and

shapes can also be tested to assess the behavior of the

algorithm in more varied situations. Improvements

can also be made to address the issue of agents that

have traveled out of the search area and are no longer

able to sense other agents or sites as well as defec-

tive agents that have developed capability issues. Ad-

dressing this issue can contribute to decreasing the de-

cision time while increasing decision accuracy.

Future work should also focus on developing

algorithms that account for multiple cycles of re-

evaluation. The proposed and future quorum-sensing

models will be capable of revisiting the sites that were

previously abandoned and re-evaluating them under

the dynamic conditions of the real-world scenarios.

In addition, we would like to explore extensions of

the algorithm to search large state spaces for potential

solutions using multiple agents as processors.

ACKNOWLEDGMENTS

Shreeya Khurana, a fellow of the Science and Engi-

neering Apprenticeship Program, would like to ac-

Quorum Sensing Re-evaluation Algorithm for N-Site Selection in Autonomous Swarms

197

knowledge the Ofﬁce of Naval Research for provid-

ing an opportunity to conduct this research at the US

Naval Research Laboratory in Washington DC during

the summer of 2019.

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