Evaluation of Emergent Structures in a ”Cognitive” Multi-Agent System

based on On-line Building and Learning of a Cognitive Map

Abdelhak Chatty

1,2

, Philippe Gaussier

, Ilhem Kallel

, Philipe Laroque

, Florence Pirard

and Adel M. Alimi

REGIM: REsearch Groups on Intelligent Machine,

University of Sfax, National School of Engineers (ENIS), Sfax, Tunisia

ETIS: Neuro-cybernetic Team, Image and Signal Processing,

Cergy-Pontoise University, National School of Electronics and its Applications (ENSEA), Paris, France

eywords:

Cognitive Multi-Agent System, Cognitive Map, Emergent Structures, Optimization.

Abstract:

This paper tries to analyze and evaluate emergent structures in a multi-agent system which is able to resolve

the warehouse location problem. These emergent structures allow agents to optimize their planning time and

to improve their adaptive behavior in an unknown environment. In our multi-agent system, each agent is

based on an on-line building and learning of its own cognitive map. It alters the positive impact of individual

behavior in the improvement of the overall performance of the system. We also suggest the evaluation of

the emergent structures by comparing the performance of our multi-agent system with a linear programming

approach. A series of simulations enables us to discuss and validate our system.

1 INTRODUCTION

To produce global emergent behaviors for multi-

agents system (MAS) (Simonin et al., 1998; Billing,

2010; Pepin et al., 2009; Chatty et al., 2011; Math-

ieu and Secq, 2012) the interaction between agents

based on stigmergy needs not to be complex (Mataric,

1992; Brooks, 1994; Bonabeau and Theraulaz, 1994).

Based on this idea, researchers have been able to de-

sign a number of successful algorithms in the ﬁeld of

self-organized deposit of objects: (Deneubourg et al.,

1990) has proposed a model relying on biologically

plausible assumptions to account for the phenomenon

of the clustering of dead bodies by ants. (Gaussier and

Zrehen, 1994) showed that acting on objects simpli-

ﬁes the reasoning needed by MAS and allows the de-

posit of scattered objects. The question which poses

itself to us is thus how to evaluate the emergent struc-

tures of MAS in the ﬁeld of deposit systems? We be-

lieve that stimergy-based MAS, where agents are not

aware of all of the informations regarded with the en-

vironment, prove to be adaptive. However the MAS

do not guarantee the best solution, not even always a

good one. As an alternative, mathematical program-

ming approaches, such as linear programming (LP)

are widely used as an optimization tool (Matsui and

Matsuo, 2012) since they are able to compute the

best possible conﬁguration of a constrained system.

However the distributed computing requires the over-

all knowledge of the system, including the informa-

tion that is difﬁcult to obtain (such as the cost of re-

trieving informations, the initial number of agents so

on). The aim of this article is to analyze and to eval-

uate the emergent structures and their inﬂuence in a

MAS to resolve a warehouse location problem. To

prove the effectiveness of the emergent structures, we

suggest comparing our MAS approach and the results

provided by the LP approach. The paper is organized

as follows: section 2 describes the neural network

(N.N). Section 3 presents the behaviors of the cogni-

tive agents. Section 4 and 5 are devoted respectively

to the description and to the analysis of the relevance

of the emerging warehouses. Section 6 evaluates and

compares the performance of the multi-agent system

approach with the linear programming approach on

an optimization problem. The ﬁnal section concludes

the paper.

2 THE N.N ARCHITECTURE

Several MAS approaches for navigation have been

proposed (Prodan et al., 2012; Portugal and Rocha,

269

Chatty A., Gaussier P., Kallel I., Laroque P., Pirard F. and M. Alimi A..

Evaluation of Emergent Structures in a ”Cognitive” Multi-Agent System based on On-line Building and Learning of a Cognitive Map.

DOI: 10.5220/0004258702690275

In Proceedings of the 5th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2013), pages 269-275

ISBN: 978-989-8565-38-9

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

2012). Based on a bio-inspired architecture, we

present in this part a cognitive multi-agent system

(CMAS) in which each agent is able to navigate, learn

and create its owncognitivemap on-line, whose struc-

ture depends on their own experience of the environ-

ment in which they live. Starting from neurobiologi-

cal hypotheses on the role of hippocampus in the spa-

tial navigation, several works (O’Keefe and Nadel,

1978) revealed special cells in the rats hippocampus

that strike off when the animal is at a precise loca-

tion. These neurons have been called place cells (PC).

(Martinet et al., 2011) also proposed a model of a cog-

nitive map in the prefrontal cortex, which is based on

cortical columns. In our model, we do not directly use

PC to navigate, plan or construct a map, we rather use

neurons called transition cells (TC) (Gaussier et al.,

2002). This kind of cell type represents the basis of

the neurobiological model of temporal learning se-

quences in the hippocampus (Lubenov and Siapas,

2009). A transition cell encodes for a spatio-temporal

transition between two PCs consecutivelywinning the

competition, respectively at time t and δt. The set of

the PCs and the TCs constitute a non-cartesian cogni-

tive map. The interest of using transition cells is that

their association with an action is univoque and quite

straightforward. There is no need for an external algo-

rithm to extract the action from the cognitive map. To

develop our CMAS we will take inspiration from the

model of (Gaussier et al., 2002). A schematic view of

the architecture of our CMAS is shown in ﬁgure 1.

Action

Motivation

Cognitive Map

Planing PFC

Selection of Transition

CA3

Prediction of transitions

Places

Memory

CA1

Figure 1: Model of hippocampo-cortical for the building of

an agent cognitive map.

To create the PC, the agent takes, a visual

panorama of the surrounding environment. The views

are processed to extract visual landmarks. After learn-

ing these landmarks, a visual code is created by com-

bining the landmarks of a panorama with their az-

imuth. This conﬁguration serves as a code for PCs.

During exploration of the environment, the cognitive

map is gradually created when the agent moves from

one place to another. The equations that govern learn-

ing in the cognitive map is dW

(t)/dt = T(t).((γ−

).X

(t).X

(t) − W

(t).(λ1.X

(t) − λ. T(t) is

a binary signal (0 or 1) which is active when a tran-

sition is made (moving from one place to another).

This signal controls the learning of recurrent connec-

tions W

. Each agent has motivations related to the

kind of plants. When the corresponding motivation

is riggered, the agent has to reach a plant allowing

the satisfaction of its needs. γ is a parameter less

than 1 which regulates the distribution of the moti-

vation activity on the map. λ1 and λ2 are param-

eters of respectively active and passive oblivion re-

spectively on the recurrent connections. S(t) is a sig-

nal marking the satisfaction of a goal (for example the

plant discovery). This signal controls the learning of

synaptic connections between neurons in W

moti-

vations activity X

and neurons of the cognitive map

of activity X

where the equation is dW

(t)/dt =

S(t), f or

i, j

= arg max

k,l

(t).X

(t)). After having

explored the environment, the agents are able to pre-

dict, in each position the locations directly reachable.

This model has been used in Cognitive Multi-Robot

System navigation tasks (Chatty et al., 2012) in which

where the agents were able to build their cognitive

maps and learn how to move towards various goals in

an unknown environment.

3 THE COGNITIVE-MAS

We suppose an economic environment composed by

several Animats and three plants with an abstract rep-

resentation namely A, B and C. The CMAS are mo-

tivated by the simulation of three types of needs re-

lated to the three plants and each need can be satis-

ﬁed by a corresponding plant. The level of each type

of need is internally represented by an essential vari-

able, ei(t) whose value is in [0; 1] and varies with time

as in this equation de

/dt = −α

(t). In the equa-

tion, α

represents the decreasing rate of the essential

variable. When a satisfaction level e

(t) falls bellow

a given satisfaction threshold (ST), the correspond-

ing motivation is triggered so that the agents reach a

plant allowing to satisfy their needs using their cog-

nitive maps. Thus, the satisfaction of the motivation

allows an association of the current transition with the

cognitive map and the node (PC) associated with this

motivation. When discovering a plant, the satisfaction

of the motivation associated with it is associated with

the cognitive map at the location where it was found.

This motivation then spreads to the graph, indicating

the shortest path to reach the source from whichever

location known. Thus, the agents are able to take the

shortest path in order to satisfy the activated moti-

vation. If plant from the corresponding type haven’t

been found by the agent,the level decreases to 0 and

the agent dies. To maintain the satisfaction level of

our CMAS, instead of only navigating between the

three plants, it is interesting if the accumulation of in-

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270

dividual decisions creates relevant warehouses. Ware-

house creation is possible if agents are able to carry

and deposit a quantity of products taken from plants.

The localisation of warehouses is important because

when agents reach them easily, they can increase their

average satisfaction level and optimize the planning

time spent looking for warehouses. In the context of

situated cognition, local rules can lead to create emer-

gent structures allowing the creation of warehouses

relevant to the sorting strategy used by (Deneubourg

et al., 1990). We propose generic local rules depend-

ing of the number of twithdrawals and deposits of

warehouses according to the number of agents per-

ceived. The agent can indeed, tend to favour the lo-

cation which contains other agents rather than empty

regions in order to create new warehouses. Thus, the

perception of local agents will control the rules of

withdrawals and deposits. The condition for with-

drawing is computed by equation 1: the probabil-

ity that an agent needs to take some plant goods in-

creases when it perceives that the plant is less used

by other agents. So, the more agents are near a plant,

the more the probability of withdrawal decreases and

vice versa.

(Taken)

= exp

−λN

(1)

where N

is the number of agents in the neighbor-

hood, λ is a positive constant. Equation 2 describe

the condition for deposits as follows: the probabil-

ity of deposit increases with time and distance from

the origin plant (when the agent is far from the origin

plant where it took the last goods) and it depends of

the number of the agents in the neighborhood (when

the current place of the agent is frequented by other

agents). For this reason, we tried to restrict the ability

of agents to perceive the environment that limists the

range of visual perception. Moreover, the deposit op-

eration is also built on the concept of refueling : the

agent puts goods in the warehouses that already exist.

(Deposits)

= (1− exp

−αN

) ∗ (1− exp

−βt

) (2)

where α,β are environmental factors, N

is the num-

ber of agents in the neighborhood and t is the time

since the taking.

4 BUILDING OF WAREHOUSES

We use the environment as shown in ﬁgure 2a at t=

0 where the three original plants are scattered. This

environment has a continuous topology and to cross it

diagonally agent needs 200 time steps. The agents

start to move randomly in the environment, with a

limited range of visual perception that can restrict

the ability of agents to perceive the environment (see

Figure2b). While passing through a plant, an agent

increases its level of satisfaction and carries out the

local rule of taking and transporting a quantity from

the associated product. The probability of taking in-

creases when the agent does not detect other agents

next to the sources. If the decision of transporting

some products is taken, the agent continues its travel.

The probability of deposits increases when the agent

detects other agents and it moves away from the orig-

inal sources.

(a) t=0 time steps (b) agents in the environment

(e) t=7720 time steps (f) stable configuration

Figure 2: The ﬁgure shows 3 plants A, B and C whose

positions are ﬁxed and can deliver an unlimited amout of

products. They provide warehouses of 3 different kinds

(”a” is a warehouse-type A, ”b” is a warehouse-type B

and ”c” is a warehouse-type C). Through the individual de-

posit process of agents, warehouses emerge and become sta-

ble after a while. The video is available in http:// perso-

etis.ensea.fr/ neurocyber/ Videos/ Cognitive Multi-Robot

System/CMAS.

This means that the locations chosen for the deposit

are often common to several agents. Once deposited,

goods represent a new warehouse allowing others to

increase their satisfaction level. Agents also have the

possibility of refueling warehouses by adding prod-

ucts to them. This provides stability for warehouses

in relevant locations which are close to several agents

in order to prevent loss. During the refuelling the

available products in the warehouses will increase.

However, warehouses which are abandoned or poorly

visited will eventually disappear since the amount

of goods available will decrease rapidly. Figures 2c

and d show the disappearance of isolated warehouses.

When a planning agent tries to reach a previously

known warehouse and realizes that has disappeared,

EvaluationofEmergentStructuresina"Cognitive"Multi-AgentSystembasedonOn-lineBuildingandLearningofa

CognitiveMap

271

two things happen: (i) the agent dissociates the cur-

rent PC from the formerly-corresponding warehouse,

and (ii) it resets the motivation to 0. Since the PC

does not ﬁre any more when the agent feels the need

for this warehouse, there are chances that the use of

transitions leading to this place be progressively for-

gotten. Similarly, when a new matching warehouse

is discovered, the paths leading to the warehouse are

immediately reinforced, making the cognitive map

evolve synchronously with the environment. Finally,

ﬁgure 2e shows that the CMAS converges to a stable

solution with a ﬁxed number of warehouses in ﬁxed

places at 7720 time steps and remains the same for

more than 20000 time steps (see ﬁgure 2f). Here we

note the emergence of stable large warehouses which

in some cases emerge to create warehouses ”village”

(narrow regions containing all 3 warehouses). We

tried to experimentally count the number of ware-

houses’ visits compared to the number of plants’ vis-

its for 20000 time steps. The average number of visits

to warehouses (115) is more important than that of the

original sources (27), which shows that their location

is more relevant. The same behavior also allows to

keep a ﬁxed number of warehouses (here 6) and re-

move others located in irrelevant places without hav-

ing to use thresholds in order to limit the number of

warehouses nor to specify their locations. The adap-

tive capability of the cognitive map, allows cognitive

agents to create an emergent structure which is the

stable state for the whole multi-agent system allow-

ing the optimization of planing. Table 1 shows that

agents can optimize their planning time with the help

of relevant warehouses. This leads to a higher average

satisfaction level. These values show the performance

of our CMAS to keep the agents in their comfort zone.

Table 1: Optimization of planning time until 20000 time

steps (ts).

Only Plants Plants+Warehouses

Planning Time 1600ts 450ts

Satisfaction Level 59.89 88.07

We calculate the average satisfaction level (ASL) ac-

cording to this equation:ASL = (

3nN

) ∗

∑

i=1

(SL

+ SL

). Where SL is the satisfaction level of

warehouses, n is the number of iterations, N is the

number of experiments. Based on an adaptive cog-

nitive map, this experiment allows our CMAS (i) to

optimize the planning time of agents and the number

of deposits thanks to the learning of the new places of

warehouses, (ii) to improve the adaptive behavior and

the level of satisfaction of agents and ﬁnally (iii) to

lead a ﬁxed number of deposits in ﬁxed places by the

creation of relevant emergent structures.

5 ANALYSIS OF EMERGENT

STRUCTURES

We describe here the relevance of the warehouses’ lo-

cation. It is a key factor of our system’s performance.

We placed the three original plants (A, B and C) in

the summits of an isosceles triangle because we know

that the center of gravity is indeed the relevant place

in this case. When it includes the warehouses, it al-

lows to optimization of the distance walked by the

agents to satisfy their needs. Thus, we tried to change

the satisfaction threshold (ST) to see its effect on the

agents’ behaviors as shown in ﬁgure 3. Basically the

agents have two behaviors. The ﬁrst one is the explo-

ration mode that allows thgem to discover the envi-

ronement without needing to satisfy their motivations.

When the need arises and the motivation increases,

the agents change the planning mode to reach a plant

or warehouse to satisfy their needs. With low ST sit-

uation, the motivation decreases. However the agents

continue to create relevant warehouses in the path be-

tween plants (see ﬁgure 3a and b). When ST=50, the

agents can perform the two modes. In this case, we

note that the agents were able to adapt to environmen-

tal change and created villages of warehouses, which

consist of three types of warehouses in an appropriate

location at the gravity center of triangles (see ﬁgure 3c

and d). When we increase the ST (ST is stressful), the

agents will seek to satisfy their needs. Figure 3e and

f show that agents create villages of different kinds

of warehouses which are located near to the plants,

therefore the agents will stay near the villages. We

also note that the change of initial position of plants

doesn’t change the global conﬁguration of the en-

vironment (see the ﬁrst conﬁguration of warehouses

with ﬁgure 3a,c and e; and the second conﬁguration

with ﬁgure 3b,d and f). Thus, no matter the value of

ST and the position of the initial plants, the agents

can create warehouses in relevant locations. Instead

of browsing an Euclidean distance between the three

original plants which is equal to 59.2 to satisfy the

needs, agents can reduce this distance with the cre-

ation of near-perfect villages. The average Euclidean

distance according to 3a is 12.08, a value well be-

low 59.2 (the cost distance without warehouses). This

shows that the simple rules of withdrawals and de-

posits can generate emergent structures, including the

appropriateness of the location of warehouses, ensur-

ing optimization of the planning time of our CMAS.

These experiments allowed us to conﬁrm the adaptive

behavior capacity of our CMAS, based on our rules

of withdrawals and deposits. Our cognitive agents are

able, regardless of the position of the original plants

and the shape of the environment, to choose - based

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272

(a) ST=10 (b) ST=10

(e) ST=70 (f) ST=70

Figure 3: Different maps obtained after convergence of the

CMAS according to the satisfaction threshold (ST). The

agents were able to adapt to the position change by the orig-

inal plants and created a village of different kinds of ware-

houses in relevant places which allowed them to optimize

the planning time and to satisfy their needs.

Figure 4: The average distance of the followed paths ac-

cording to the ST and the number of agents. Figure shows

that between warehouses (visited by agents) the average dis-

tance is much less than the distance between the original

plants (D max =59.2). The ﬁgure also shows that agents are

able to choose - based on an individual cognitive process

- a better location for warehouses in order to optimize the

planning time and satisfy their needs.

on an individual cognitive process - a better location

for warehouses in order to optimize the planning time

and satisfy their needs.

Now, If we focus on the paths followed by agents,

ﬁgure 4 shows that between warehouses the average

distance is much less than the distance between the

original plants, regardless of the number of agents and

the satisfaction threshold (ST). To prove this, we cal-

culated using this equation L

∑

i=1

∑

j=1

d(a,b) +

d(a,c) + d(b,c)/N

∗N

the average Euclidean length

of the paths followed by the agents between the

warehouses of different types for each simulation (du-

ration of 20000 time steps).

Finally, we calculated the average distance Av(L

)

on all of the n experiments: with L

: distance of one

experience, a,b and c: warehouses, N

: number of

agents, N

: number of cycles. This distance reaches

its maximum 48.86 which is less than 59.2 (distance

between the original plants) with 50 agents and with

TS equal to 70. This shows that the warehouses allow

the agents to optimize their paths in an emergent way,

to satisfy their needs without the use of an optimiza-

tion model of navigation. Thus, the simple rules of

withdrawals and deposits can generate emergent be-

haviors, including the appropriateness of the location

of warehouses, ensuring the optimization of the plan-

ning time of our CMAS.

6 EVALUATION OF EMERGENT

WAREHOUSES’ LOCATION

To make the application ﬁeld of our CMAS more con-

crete and to test the adaptability of our agents when

changing the context, we have added customers to

the environment in order to switch back to a classi-

cal warehouse location problem: We distribute a set

of products to a set of demand zones either directly

from production plants or through warehouses. In-

deed, trying to use MAS to supply chain-like prob-

lems is not new (Yadati et al., 2010); however in most

cases dedicated and pecialized agents are used. In this

part we describe a formal instrument of performance

that shows how our CMAS can be adapt to an opti-

mization problem and reasonably give a sound result

related to MAS

IAA

(Laroque et al., 2010) which is a

deposit system that takes inspiration from ant sorting

skills used to build a cemetery and with a MAS

Random

which makes random deposits. Initially, the ware-

houses which have a limited capacity don’t exist. We

assume that the transport cost is lower between plants

and warehouses than between plants and customers.

A set of potential sites to locate the warehouses is

determined a priori (in our case a regular paving of

the environment to try to ﬁnd the optimal set of lo-

cations). We assume that the production plant capac-

ity is sufﬁcient to satisfy the customer’s requests. We

want to determine which warehouses should be used

and where. To determine then the product ﬂows (i)

between the production plants and the customers (di-

rect delivery), (ii) between the production plants and

the warehouses (internal trafﬁc) and (iii) between the

warehouses and the customers (indirect delivery). To

materialize the cost of transport in our simulations,

during a deposit, the agent must wait for θ = 29 sec-

ond which represents the time of the creation of such

deposit, so the level of needs will decrease.

EvaluationofEmergentStructuresina"Cognitive"Multi-AgentSystembasedonOn-lineBuildingandLearningofa

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6.1 Modeling the Warehouse Location

We start to express the warehouse location problem

and its constraints, and then we designed a mixed in-

teger program. We used the following sets of indexes

in our model: Product (P), Demand zone (customers)

(D), Production plant (U) and Warehouse (W). To ex-

press the model, the following data are required: d

is the number of units u of product p required by de-

mand zone d. c

is the maximum number of units u of

products which can come through the warehouse w.

pud

,ic

puw

,ic

′

pwd

are the unit delivery cost of prod-

uct p from plant u and warehouse w to respectively

demand zone d, warehouse w and demand zone d.

is the ﬁxed cost associated to the use of ware-

house w. The decision variables are W

: Binary

variable indicating the use of w (use of w =1; else=

0). Qd

pud

,Qiw

puw

, Qid

pwd

are the number of units p

shipped by plant u and warehouse w to respectevely

demand zone d, warehouse w and demand zone d. As

objective function, we chose the minimization of the

total cost of transport to converge to an optimal solu-

tion.

min( f ) =

∑

w=1

∑

p=1

∑

u=1

∑

d=1

pud

.Qd

pud

∑

p=1

∑

u=1

∑

w=1

puw

.Qiw

puw

∑

p=1

∑

w=1

∑

d=1

′

pwd

.Qid

pwd

where the constraints: The model must satisfy the

demand zone from warehouses or/and plants.

∑

u=1

pud

∑

w=1

Qid

pwd

= d

(∀p ∈ P∀d ∈ D),

The model must not exceed the warehouses capacity.

∑

p=1

∑

u=1

Qiw

puw

≤ c

(∀w ∈ W)

The quantities must be concerned between plant to

warehouses and warehouses to demand zone.

∑

u=1

Qiw

puw

∑

d=1

Qid

pwd

(∀p ∈ P∀w ∈ W)

The model must also respect the constraints of inte-

grality and non negativity and ensure ﬂows between

plants, warehouses and demand zone.

∈ 0,1,Qd

pud

> 0,Qiw

puw

> 0,Qid

pwd

0,(∀w ∈ W, p ∈ P, u ∈ U, d ∈ D,)

6.2 MAS vs. Linear Programming

To make the comparison between the LP and the MAS

approachs possible, we must extract from each MAS

system (MAS

Random

, MAS

IAA

and our CMAS) the cus-

tomer demand to inject it into the LP in order to have

an equivalent demand (because it’s not the same in

the three systems). Thus the LP will give us the op-

timum warehouses’ positions for each system. For

this reason, our instrument of performance consists of

the computing of the average distance between MAS

warehouses’ location and LP warehouses’ location for

each system. Unlike LP, the MAS is not deterministic

because it does not provide the same results on sev-

eral tests with the same parameters. We performed 10

tests of MAS and 1 test of linear programming and

then compared the average of the 10 tests of MAS

with LP. For each warehouse W

of LP (equation 3),

we summed the minimum distance between the W

warehouse and the corresponding MAS W

’:

= min(d(W

′

)) (3)

where d is the Euclidean distance on the environment.

The average distance of an experiment Exp

(equa-

tion 4) is summed with a penalty p which depends on

the difference between the number nof warehouses in

LP and the number n’ of warehouses in MAS:

d(Exp) = ((

∑

i=1

) + p(|n

′

− n|)) (4)

Finally, we calculated the average distance of all the

Ne experiments. Table 2 shows that our CMAS could

optimize the average cost of the warehouses loca-

tion better than the MAS

IAA

and the random sys-

tem MAS

Random

. We also note that with a homoge-

neous distribution of plants and customers, we obtain

a small average distance with a quasi-optimal number

of deposits compared to mathematical programming

with a very low standard deviation, which means that

in CMAS the warehouses are well placed if we com-

pare them to a MAS

IAA

and to a MAS

Random

and close

to the locations given by the mathematical program-

ming solution in the environment. The results ob-

tained conﬁrm the performance of the emergent struc-

tures based on cognitive process which allows us to

have good solutions that approximate the solution of

LP in a time equal to 40 minutes (non optimized java

simulation), while LP approximately requires on av-

erage several hours with a very large standard devi-

ation, going from 2 minutes to more than 24 hours

(GLPK software) to solve the same problem (with the

same conﬁguration of machines).

Table 2: The average distance of the MAS systems relative

to the LP solution.

MAS

Random

MAS

IAA

CMAS

Average number

of deposits

22 15 4

Average cost of

the solution

40671.3 55606.4 15210.6

Average distance

relative to LP

42.7 27.3 6.9

Standard

deviation of

average distance

9.0 10.7 1.8

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7 CONCLUSIONS

In this paper we describe how the local learning with

the accumulation of individual decisions advocates

the creation of new emergent structure. We suggest a

set of simulations that analyze the positive impact of

individual behavior in the improvement of the global

performance of the system. This individual behavior

that is based on the bio-inspired cognitivemap, allows

the agents to avoid planning problems before a com-

plete exploration of the environment. It also leads to

the same results as a pheromon-based system without

the need to leave a physical trace in the environment.

Thus, the coupling of the individual behavior with the

embodiement of the agents (satisfaction of their moti-

vations) can solve multi-objective planning problems

although formally the algorithm is not able to ”mix

and to merge and to optimize” several objectives. In

conclusion, we suggest an emergent multi-objective

optimization. Finally we suggest the evaluation of

the emergent structures in MAS by comparing our

CMAS, the MAS based on cemetery organization of

ants and the random MAS with a linear programming

approach. The results obtained conﬁrm the perfor-

mance of our emergent behavior based on cognitive

processes which allow us to have adequate solutions

that approximate the linear programming solution. To

study the limits of emergent structures in real world,

we started to validate the adaptive capability of the

cognitive map in a real multi-robot system (Chatty

et al., 2012) and now we are trying to add the deposit

system in the multi-robot system.

ACKNOWLEDGEMENTS

The authors would like to thank the ﬁnancial sup-

port of the Tunisian General Direction of Scientiﬁc

Research and Technological Renovation (DGRSRT),

under the ARUB program 01/UR/11 02, the Institut

Francais de Tunisie

REFERENCES

Billing, E. A. (2010). Cognitive perspectcoives on robot

behavior. In ICAART (2), pages 373–382.

Bonabeau, E. and Theraulaz, G. (1994). Intelligence Col-

lective. Hermes.

Brooks, R. A. (1994). Coherent behavior from many adap-

tive processes. In in SAB, pages 22–29, Cambridge,

MA, USA. MIT Press.

Chatty, A., Gaussier, P., Kallel, I., Laroque, P., and Alimi,

A. (2012). Adaptation capability of cognitive map im-

proves behaviors of social robotics. In in IEEE ICDL-

EpiRob (to appear).

Chatty, A., Kallel, I., Gaussier, P., and Alimi, A. (2011).

Emergent complex behaviors from swarm robotic sys-

tems by local rules. In IEEE Symposium Series on

Computational Intelligence, (RiiSS), pages 69 –76.

Deneubourg, J. L., Goss, S., Franks, N., Franks, A. S., De-

train, C., and Chr´etien, L. (1990). The dynamics of

collective sorting robot-like ants and ant-like robots.

In SAB, pages 356–363, Cambridge, MA, USA. MIT

Press.

Gaussier, P., Revel, A., Banquet, J. P., and Babeau, V.

(2002). From view cells and place cells to cognitive

map learning: processing stages of the hippocampal

system. Biological Cybernetics, 86(1):15–28.

Gaussier, P. and Zrehen, S. (1994). Avoiding the world

model trap: An acting robot does not need to be so

smart! Robotics and Computer-Integrated Manufac-

turing, 11(4):279 – 286.

Laroque, P., Pirard, F., Archambault, F., Quoy, M., and

Gaussier, P. (2010). Comparing multi-agent system

and mixed-integer programming approaches on a sim-

ple optimization problem. In IC-AI, pages 977–981.

Lubenov, E. V. and Siapas, A.G. (2009). Hippocampal theta

oscillations are travelling waves. volume 459, pages

534–539. Nature Publishing Group.

Martinet, L.-E., Sheynikhovich, D., Benchenane, K., and

Arleo, A. (2011). Spatial Learning and Action Plan-

ning in a Prefrontal Cortical Network Model. PLoS

Comput Biol, 7(5).

Mataric, M.-J. (1992). Designing Emergent Behaviors:

From Local Interactions to Collective Intelligence. In

Meyer, J.A., R. H. and Wilson, S., editors, Proceed-

ings of the Second Conference on Simulation of Adap-

tive Behavior, pages 1–6. MIT Press.

Mathieu, P. and Secq, Y. (2012). Environment updating and

agent scheduling policies in agent-based simulators.

In ICAART (2), pages 170–175.

Matsui, T. and Matsuo, H. (2012). Analysis for distributed

cooperation based on linear programming method. In

ICAART (2), pages 228–233.

O’Keefe, J. and Nadel, L. (1978). The hippocampus as

a cognitive map / John O’Keefe and Lynn Nadel.

Clarendon Press ; Oxford University Press, Oxford.

Pepin, N., Simonin, O., and Charpillet, F. (2009). Intelligent

Tiles: Putting Situated Multi-Agents Models in Real

World. In AAAI, A., editor, ICAART, Porto, Portugal.

Portugal, D. and Rocha, R. P. (2012). Extracting topological

information from grid maps for robot navigation. In

ICAART (1), pages 137–143.

Prodan, I., Olaru, S., Stoica, C., and Niculescu, S.-I. (2012).

Predictive control for trajectory tracking and decen-

tralized navigation of multi-agent formations. In Fil-

ipe, J. and Fred, A. L. N., editors, ICAART (2), pages

209–214. SciTePress.

Simonin, O., Ferber, J., and Decugis, V. (1998). Perfor-

mances analysis in collective systems. ICMAS, pages

469–. IEEE Computer Society.

Yadati, C., Witteveen, C., and Zhang, Y. (2010). Coordi-

nating agents - an analysis of coordination in supply-

chain management tasks. In ICAART (2), pages 218–

223.

EvaluationofEmergentStructuresina"Cognitive"Multi-AgentSystembasedonOn-lineBuildingandLearningofa

CognitiveMap

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