Cohérence et robustesse dans un système multiagent perturbé : application à un système décentralisé de collecte d’information distribué

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Cohérence et robustesse dans un système multiagent

perturbé : application à un système décentralisé de

collecte d’information distribué

Quang-Anh Nguyen Vu

To cite this version:

Quang-Anh Nguyen Vu. Cohérence et robustesse dans un système multiagent perturbé : application à

un système décentralisé de collecte d’information distribué. Autre [cs.OH]. Université Claude Bernard

- Lyon I, 2012. Français. �NNT : 2012LYO10232�. �tel-00987118�

ED InfoMaths

No Ordre : 232 - 2012 Ecole doctorale Informatique et Math´ematiques´

Coh´

erence et robustesse dans un

syst`

eme multiagent perturb´

e :

application `

a un syst`

eme d´

ecentralis´

e

de collecte d’information distribu´

e

TH`

ESE

pr´esent´ee et soutenue publiquement le 05 d´ecembre 2012

pour l’obtention du

Doctorat de l’Universit´

e Claude Bernard Lyon I

(sp´

ecialit´

e informatique)

par

Quang-Anh NGUYEN VU

Composition du jury

Rapporteurs :

Michel Occello, Professeur, Universit´e Pierre-Mendes-France (Grenoble, France)

Laurent Vercouter, Professeur, INSA de Rouen (Rouen, France)

Examinateurs :

Marie-Pierre Gleizes, Professeur, Universit´e Paul Sabatier (Toulouse, France)

Giovanna Di Marzo Serugendo, Professeur, Universit´e de Gen`eve (Gen`eve, Suisse)

Directeur :

Salima Hassas, Professeur, Universit´e Claude Bernard (Lyon, France)

Encadrants :

Richard Canal, l’institut de la Francophonie pour l’Informatique (Hanoi, Vietnam)

Benoit Gaudou, Maˆıtre de conf´erences, Universit´e Paul Sabatier (Toulouse, France)

Fr´ed´eric Armetta, Maˆıtre de conf´erences, Universit´e Claude Bernard (Lyon, France)

i j i i j i j i i

f (x) = 1 x f (x) = 1 √ x f (x) = 1 4 √ x f (x) = 1 6 √ x f (x) = 1 8 √ x j i i − → Fi i

wi

wi

w8− w10

(T Ei)t i t

(T Ei)t i t (Tii)t+1

i m n

i

robot team robot team rescue team Participatory Multi-Agent Simulation Geographic Information System rescue and robots perceptions Goals Global level Local level what-if scenarios Spatial Decision Support System Communications

Robust System

“Acceptable”

Outputs

Performance

Power

Data Integrity

Availability

Security

Design errors ,

Software failures

Malicious attacks,

Human errors

Radiation ,

Noise

Defects,

Process variation,

Degraded transistors

Input

s(t) = s(t_{− 1) + v} s(t) t v s (t) = s0 s (t) = s (t− 1) + v v s (t) = as (t− 1) (1 − s (t − 1)) a Ps(s′(t) ; t) = _s′_(t)Ps(s′(t)| s′(t− 1)) Ps(s′(t)| t − 1) P (s; t) s t P (s_{| s}′_{) s}′ s W Q △U = W + QoDeltau= Uf− Ui △U Uf Ui W Q Q T Q/T

t t + 1 A = (d, G, S, f ) d G S f

A = (2, M oore,_{{vivant, mort} , f)} f

A B

A A

A B B

[0, 1]

V =_{{i, j, k, m...}}

inf o =_{cl´e, valeur}

(x, y) , couleur (x, y)_{∈ Z}2 _couleur

∈ COULEUR

Di ={info}

i Di={(x1, y1) , bleu , (x2, y2) , rouge} i (x1, y1) (x2, y2) IN Di={cl´e, {valeur, {ax}}} i cl´e valeur; {ax} ax∈ V {ax}

(x, y) , {couleur, {ax}} (x, y)∈ Z2 couleur∈ COULEUR ax∈ V

IN Di ={(x1, y1) ,{bleu, {k, l} , rouge, {m, n}} , (x2, y2) ,{rouge, {j}}}

i (x1, y1) k, l (x1, y1) rouge m n (x2, y2) j t ij V E (V ) =_{ij | i, j ∈ V, i = j} − →_ij V E′_{(V ) =}−→_{ij | i, j ∈ V, i = j} V E (V ) E′_{(V )} i ∈ V T Gi = (Vi, Ei′, wi) i Vi ⊆ V E′ i ⊆ E′(Vi) Vi wi: E′i→ [0, 1]

i i i j k i i −→ij −→jk wi −→ ix i T Gi x i x DTix wi −→ ix T Gi j (Di) (Dj) wi(−xy)→ x y (y= x) T Gi x y ITxy j k ITjk ITjk j k j i Tix i x DTix i x T Gi 1 T Gi i Tix i x Tix= DTix i x Tii 1 1 i _{Tix| x ∈ Vi} T Ti T Si i T Gi T Ti T Si= (T Gi, T Ti) i j i j

i T Gi =  {i, j, k} ,−→ij ,−→jk, wi  wi −→ ij= DTij wi −→ jk= ITjk T Ti ={Tii, Tij, Tik} i, j, k DTij i j ITjk j k i j Tii i Tij i j DTij ITxj j

ŝ

ũ

Ŭ

i

i j i j (Di)0 (IN Di)0 i j t (Di)t (IN Di)t i i j (Di)t+1 (IN Di)t+1 j i j Di Di i (IN Di)t+1 i j ΨData j i (Di)t+1= (Di)t

(IN Di)t+1= ΨData(INDi)t,(Dj)∗t,(IN Dj)t

 i j j j j j i j

ΨData(INDi)t,(Dj)∗_t,(IN Dj)t = (INDi)t∪(Dj)∗t ∪(IN Dj)t

D∗ j

t={cl´e, valeur, {j }} cl´e, valeur ∈ Dj

(Di)t={(x, y) , blue} (IN Di)t={(x, y) , red, {k, l}} (Dj)t={(x, y) , yellow} (IN Dj)t={(x, y) , {blue, {m}}} Di (Di)t+1 ={(x, y) , blue} (Dj)t j (IN Di)t (Dj)t (IN Dj)t (IN Di)t

(IN Di)t+1={(x, y) , {red, {k, l} , yellow, {j} , blue, {m}}}

(Di)t, (IN Di)t i

t

(Dj)t, (IN Dj)t j t

(Di)t+1= (Di)t i t + 1

(IN Di)t+1= ΨData (INDi)t, (Dj)∗_t, (IN Dj)t

i t + 1

(cl´esIN Di)t← (IN Di)t

dj =cl´ej, valeurj dj ∈ (Dj)t

cl´ej∈ (cl´esINDi)t

indi=cl´ei,{valeuri,{ax}} IN Di cl´ei= cl´ej

AT T s_{← {valeur | ∃valeur ∈ {valeur}i,{ax}}}

valeurj ∈ AT T s/

indi=cl´ei,{valeuri,{ax} ∪ valeurj,{j }}

indi=cl´e, {valeuri,{ax} ∪ {j}}

d∗

j =cl´ej,valeurj,{j}

(IN Di)t+1= (IN Di)t∪ d∗j

indj =cl´ej,{valeurj,{bx}} (IN Dj)t

cl´ej∈ (cl´esINDi)t

indi=cl´ei,{valeuri,{ax}} IN Di cl´ei= cl´ej

AT T s← {valeur | ∃valeur ∈ {valeuri,{ax}}}

valeurj ∈ AT T s/

indi=cl´ei,{valeuri,{ax} ∪ valeurj,{j }}

indi=cl´ei,{valeuri,{ax} ∪ valeurj,{bx}}

1 T Si= (T Gi, T Ti) T Gi = {i} ,  /O , wi T Ti ={Tii} Tinit j i j i j i j i i DTij j i j i i j i j i β i j δ δ (x, y) x i Di y Dj δ (x, y) = 0 δ (x, y) > 0 i j Inc level Inc level =  k∈{1,β}δ (xk, yk) β∗ δM axinf o (xk, yk) δM axinf o i μ

Inc level < μ i j τ+

Inc level > μ i j τ−

Inc level = μ i j

τ+ _τ−

(U pp) (Low )

Upp 1 Upp Low

0 Low N I

ρstab ρstab ∈ [0, 1]

ρstab∗ NI

Tinit U pp Low Tinit+

N I_{∗ ρ}stab∗ τ+= Upp τ+ τ− τ+= (Upp− Tinit) ρstab∗ NI τ−= (Tinit− Low) ρstab∗ NI i j i DTij Tinit i (T Gi)t+1= (Vi∗, Ei′∗, w∗i) (T Gi)t= (Vi, Ei′, wi) (T Gj)_t= Vj, Ej′, wj Vi∗= Vi∪ Vj E′ i E′j −→ij i j i Ei′∗= −→ ij_{∪ E}i′∪ Ej′\ −→ yi, y_{∈ V}i∪ Vj  DTij i j w∗i −→ ij = DTij w∗ i(−xy) =→  wi(−xy)→ if −xy→∈ Ei′, −xy /→∈ Ej′ wj(−xy)→ if −xy→∈ Ej′, −xy /→∈ E′i −→ xy∈ E′ i∩ Ej′ wi(−xy)→ = wj(−xy)→ 2 i j k −→ xy T Gi T Gj −xy→ ITxyi T Gi ITxyj T Gj P athi P athj T Gi T Gj −→ xy P athi P athj i ITxyij xy i j

ITxyij =  u∈P athiTiu∗ ITxyi+  v∈P athjTiv∗ ITxyj  u∈P athiTiu+  v∈P athjTiv P athi P athj ITxy −−→ xyij −xy→ i j j i x Tix= Tii∗ DTix+y∈{z∈V∗ i|−zx→∈E′∗i } (Tiy∗ ITyx) Tii+_y∈{z∈V∗ i|−zx→∈E ′∗ i } Tiy i x DTix ITyx T Gi x i DTix ITyx x Tix= DTix i x −→ix Tii 1 j t (T Si)t= ((T Gi)t, (T Ti)t) (T Gi)t= (Vi, Ei′, wi) = 

{i, o, n, m} ,−→io, −on, −→→ nm, wi

 wi −→ io= 0.8, wi(−on) = 0.9→ wi(−→nm) = 0.5 T Ti ={Tii, Tio, Tin, Tim} = {1, 0.8, 0.6, 0.7} (T Sj)_t= (T Gj)_t, (T Tj)_t (T Gj)t= Vj, Ej′, wj = 

{j, u, o, n, m} ,−ju, −→ un, −→ uo, −→→ nm, wj

 wj −→ ju= 0.6, wj(−un) = 0.7, w→ j(−uo) = 0.3→ wj(−→nm) = 0.2 (T Tj)_t={Tjj, Tju, Tjo, Tjn, Tjm} = {1, 0.6, 0.4, 0.8, 0.3} i i j DTij j i j DT∗ ij = 0.5 i j β = 20 j

i

0.8

o

0.9

n

0.5

m

T

ii

=1

T

io

=0.8

T

in

=0.6

T

im

=0.7

TrustSet de l’agent i:

j

0.6

u

0.7

n

0.2

m

T

jj

=1

T

ju

=0.6

T

jn

=0.8

T

jm

=0.3

TrustSet de l’agent j:

o

T

jo

=0.4

0.3

i j δ (x, y) > 0 δ (x, y) = 2 δ (x, y) = 3 δ (x, y) = 0 δM axinf o = 4 i j Inc level = 10∗2+5∗3+5∗0 20∗4 = 0.4375 μ = 0.1 Inc level > μ i j τ− _DT ij = DTij∗ − τ− = 0.5_{− 0.02 = 0.48 τ}− ₌ (Tinit−Low) ρstab∗NI = 0.5−0.4 0.5∗10 = 0.02 Tinit = 0.5 Low = 0.4 ρstab∗ NI = 10 i j (T Gi)t+1 = (Vi∗, Ei′∗, wi∗) (T Gi)t= (Vi, Ei′, wi) (T Gj)_t= Vj, Ej′, wj V∗ i = Vi∪ Vj={i, o, j, u, n, m} E′∗ i = −→ ij_{∪ E}′ i∪ Ej′ \ −→ yi, y_{∈ V}i∪ Vj 

=−→ij ,−ju, −→ un, −→ uo,→ −→io, −on, −→→ nm w∗ i Ei′∗ w∗ i −→ ij= DTij = 0.48 w∗ i −→ ju= 0.6 w∗ i (−un) = 0.7→ w∗ i (−uo) = 0.3→ w∗ i −→ io= 0.8 w∗ i (−on) = 0.9→ w∗ i (−→nm) = ITnm i −→nm∈ E′ i∩ Ej′ wi(−→nm)= wj(−→nm) P athi ={o, n} P athj ={j, u, n} wi(−→nm) = ITnm= 

u_{∈P athi}Tiu∗ITnmi+v_{∈P athj}Tiv∗ITnmj



u_{∈P athi}Tiu+v_{∈P athj}Tiv =

(Tio+Tin)∗ITnmi+(Tij+Tiu+Tin)∗ITnmj

(Tio+Ton)+(Tij+Tiu+Tin)

=(0.8+0.6)∗0.5+(0.48+0.5+0.6)∗0.2_{(0.8+0.6)+(0.48+0.5+0.6)} = 0.34

Tii i j Tiu= Tii∗DTiu+  y∈{j,o,n,m}(Tiy∗ITyu) Tii+  y∈{j,o,n,m}Tiy = 1∗0.5+(0.48∗0.6) 1+0.48 = 0.53 {Tio, Tin, Tim, Tij} Tio= Tii∗DTio+y∈{j,u,n,m}(Tiy∗ITyo) Tii+y∈{j,u,n,m}Tiy = 1∗0.8+(0.5∗0.3) 1+0.5 = 0.63 Tin= Tii∗DTin+y∈{j,o,u,m}(Tiy∗ITyn) Tii+y∈{j,o,u,m}Tiy = 1∗0.6+(0.63∗0.9+0.53∗0.7) 1+0.63+0.53 = 0.71 Tim= Tii∗DTim+y∈{j,o,n,u}(Tiy∗ITym) Tii+y∈{j,o,n,u}Tiy = 1∗0.7+(0.63∗0.34) 1+0.6 = 0.57 Tij = 1∗0.48₁ = 0.48

i

o

0.8

n

m

0.9

0.34

T

ii

= 1

T

io

= 0.63

T

in

= 0.71

T

_im

= 0.57

j

0.6

u

T

ij

= 0.48

T

_iu

= 0.53

0.48

0.3

_0.7

i j i T Si= (T Gi, T Ti) T Gi = 

{i, o, j, u, n, m} ,−→ij ,−ju, −→ un, −→ uo,→ −→io, −on, −→→ nm, wi

 wi −→ ij= DTij = 0.48, wi −→ ju= 0.6, wi(−un) = 0.7, w→ i(−uo) = 0.3, w→ i −→ io= 0.8, wi(−on) =→ 0.9, wi(−→nm) = 0.34 T Ti ={Tii, Tio, Tij, Tiu, Tin, Tim} = {1, 0.63, 0.48, 0.53, 0.71, 0.57}

(T Ti)t={Tix| x ∈ Vi} (T Gi)t= (Vi, Ei′, wi) (T Gj)t= Vj, E′j, wj (T Gi)t+1= (Vi∗, Ei′∗, w∗i) (T Gi)t, (T Gj)t (T Ti)t+1={Tix| x ∈ Vi∗} τ+ ← (Upp−Tinit) ρstab∗NI τ−_← (Tinit−Low) ρstab∗NI Inc level_←  k∈{1,β}δ(xk,yk) β∗δM axinf o V∗ i = Vi∪ Vj − →_{ij /} ∈ E′ i DTij = Tinit E′∗ i = −→ ij_{∪ E}′ i∪ Ej′ \ {−→yi, y∈ Vi∪ Vj} Inc level < μ DTij = DTij+ τ+ DTij = DTij− τ− −→ xy E′∗ i −→ xy =−→ij w∗ i(−→ij ) = DTij −→ xy∈ E′ i && −xy /→∈ Ej′ w∗ i(−xy) = w→ i(−xy)→ −→ xy /_{∈ E}′ i && −xy→∈ Ej′ w∗ i(−xy) = w→ j(−xy)→ −→ xy_{∈ E}′ i && −xy→∈ Ej′ P athi← T Gi xy P athj← T Gj xy w∗ i(−xy) =→ 

u∈P athiTiu∗ITxyi+v∈P athjTiv∗ITxyj

 u∈P athiTiu+v∈P athjTiv x V∗ i Tix= Tii∗DTix+  y∈_{z∈V ∗ i|zx∈E′∗i }(Tiy∗ITyx) Tii+y∈_{z∈V ∗_i|zx∈E′∗_{i }}Tiy

(Tii)_t i t i j i i i (T Ei)t i t j k l m ... i i ITji ITki ITli ITmi ... Tii (T Ei)t i t Tii t + 1 i t + 1 (Tii)t i t (T Ei)t i t (ITkj)_t k j i t j i (Rj)t j i t (Rj)t k j (ITkj)t i (Rj)_t= 

k∈Acom(j)(ITkj)t

|Acom(j)| (ITkj)_t k j t Acom(j) = {j, k, m, ...} ⊂ Vi i j |Acom(j)| j (Ri)t i t i (R_∗i)_t i i i t

(R_∗i)_t i j (ITji)_t

i j (Rj)_t

(R∗i)t=



j∈Areli(i)(Rj)t∗ (ITji)t



j∈Areli(i)(Rj)t

(Rj)_t j t

(ITji)_t j i t

Areli(i) j i

(Rj)t≥ (Ri)t Areli(i)⊂ Acom(i)

(Tii)t+1 i t (R_∗i)_t (R_∗i)_t−1 (Tii)t+1= (Tii)t+ ∆Tii ∆Tii= (R∗i)t− (R∗i)t−1 (R_∗i)_t−1 i t_{− 1 (T}ii)t i t (T Ei)t i (Tii)t+1 i t + 1 Acom(i)← i (Tii)t+1= (Tii)t x← 0 y← 0 (Ri)_t←  k∈Acom(i)(ITki)t |Acom(i)| j_{∈ A}com(i) (Rj)_t=  k∈Acom(j)(ITkj)t |Acom(j)| (Rj)_t> (Ri)t x = x + (Rj)_t∗ (ITji)_t y = y + (Rj)_t y ! = 0 (R∗i)t= x y (Tii)t+1= (Tii)_t+ (R∗i)t−(R∗i)t−1 Tt ∗i i Rt ii = 1 R t−1

∗i = 0.6 j k m Acom(i) ={j, k, m}

i j m i m

j k i k m i Acom(j) ={m, i} Acom(m) ={j, k, i} Acom(k) ={m, i}

i

0.9

j

k

0.3

m

0.7

0.1

0.8

0.7

0.4

i (T Ei)t j m k i 0.5 0.4 0.1 (T Ei)t i t (Tii)t+1 i j k m (Ri)_t, (Rj)_t, (Rk)_t, (Rm)_t i (Ri)t= ITji+ITki+ITmi |Acom(i)| = 0.5+0.1+0.4 3 = 0.33 (Rj)_t=IT_|Amj_com+IT_(j)|ij = 0.8+0.9₂ = 0.85 (Rk)t= ITmk+ITik |Acom(k)| = 0.7+0.7 2 = 0.7 (Rm)t= ITjm+ITkm+ITim |Acom(m)| = 0.4+0.3+0.1 3 = 0.26 Areli(i) = {j, k} i m (Rm)t< (Ri)t i (R∗i)t (R_∗i)_t=0.85∗ 0.5 + 0.7 ∗ 0.1 0.85 + 0.7 = 0.495 1.55 = 0.32 (Tii)t+1= (Tii)t+ ∆Tii= (Tii)t+ (R∗i)t− (R∗i)t−1 = 1 + (0.32 − 0.6) = 0.72 Low

i T Si= (T Gi, T Ti) i i j _{∈ A}t com(i) i At com(i)← i t j∈ At com(i) Tt ij > Low j j i j j j (θ,{i...n}) θ {i...n}

inf o = [ui, vi] ui∈ Info1, Card(Inf o1) =

n vi∈ Info2, Card(Inf o2) = m ni=1pi=

1n j=1pij = 1, Ai(i∈[1,R]) ⊂ V A∗i(i∈[1,S]) ⊂ V u3, v2 p3_{∗ p32} 1

v

v

₂

v

m

...

...

1

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u

₂

u

3

u

n

{

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p

₃

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A

₁

...

A

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...

{

}

(

* *

)

1 32

,

A

...

A

S

p

T W U pp Low α γ β

T W (_{a1, ..., an}) =

α_{∗ Card ({j | j ∈ {a}1, ..., an} , Upp ≤ Tij})

+β_{∗Card ({j | j ∈ {a}1, ..., an} , Low < Tij< Upp})

+γ_{∗ Card ({j | j ∈ {a}1, ..., an} , Tij ≤ Low}) Tij j i α β γ T W p _{G1(p) , ..., Gn(p)} p px p Gx(p)∈ {a1x, ..., anx} px f(px) = T W (Gx(p))  k∈[1,n]T W (Gk(p)) i {(x, y) , red} j

{(x, y) , blue} k {(x, y) , blue} l {¬ (x, y)} m i

i Tij = 0.8 Tik= 0.4 Til= 0.5 Tim= 0.3

m

j

l

k

i

T

im

= 0.3

T

il

= 0.5

T

ik

= 0.4

T

ij

= 0.8

i Low = 0.25 Upp = 0.8 i T W (_{{m}) = 1} T W (_{{j, k, l}) = 3 ∗ 1 + 1 + 1 = 5} α β γ (x, y) 1 6 (x, y) 5 6 (x, y) blue 0.83_{∗ 0.4 = 0.33} (x, y) blue

F

T

(x,y)

black

blue

yellow

red

(0.17,{m})

_{(0.83,{j,k,l})}

f (px)

indi=< cl´e,{< attributx,{ax} >} > (IN Di)t

attrM axCl´e indi=< object,{< attributex,{ax} >} >| indi∈ (INDi)t

taille (_{attributx,{ax}}) > 1 attributx∈ {< attributx,{ax} >} f(< cl´e, attributx>) =  T W({ax}) k∈[1,n]T W({ak}) max (f (< cl´e, attributx>))← f(< cl´e, attributx>) attributx∈ {< attributx,{ax} >}

< cl´e, attributx>= max (f (< cl´e, attributx>)) attrM axCl´e = attributx

δ(i, j) i j

V N ={i | i ∈ V, ∃j ∈ V, i = j, δ(i, j) ≤ rc}

rc

EN (V ) _{{ij | i, j ∈ V N}

1 _{1 Ϯ} Ϯ Niveau Social Niveau Spatial 1 1 Ϯ Ϯ Temps Boucles de rétroaction >ŝĞŶĚĞĐŽŶĨŝĂŶĐĞ >ŝĞŶĚĞĐůƵƐƚĞƌ >ŝĞŶĚĞĐŽŵŵƵŶŝĐĂƚŝŽŶ i j ij_{∈ EN (V ) ; i, j ∈ V} Cl = (VCl, ECl) t VCl= ∅ ECl= ∅ VCl⊆V N ECl⊆EN(V ) ∀x, y ∈ V2 Cl xy∈ ECl

∀xy ∈ ECl Txy ≥ Upp Tyx ≥ Upp U pp U pp∈ [0, 1]

Clx x∈ V x x∈ VClx y _{∃y ∈ V}Clx, y= x, xy ∈ EClx T _{⊂ V Cl}T VClT = T Cl_{x} Clxy x, y ∈ V2 x y VClxy = {x, y} EClxy ={xy} Clxy= Cl{x,y} Tinit = 0.5

x, y Clxy Txy≥ Upp x y Tyx≥ Upp y x x Clxy y Clxy = Clyx x y y Clx z∈ Clx Tzy ≥ Upp Clx Cly t_{∈ Cl}x r∈ Cly Ttr ≥ Upp x, y x Clx Clx Tzy ≥ Upp, ∀z ∈ Clx x y ∃Cly&& (Tkx ≥ Upp, ∀k ∈ Cly) y x x Clx= Clx⊕ Cly y ∄Cly&& Tyx≥ Upp y x Cly= (xy, xy) x Clx= Clx⊕ Cly y ⊕ ⊕ Clx = (VClx, EClx) Cly = (VCly, ECly) Clz= Clx⊕ Cly Clz= (VClz, EClz) VClz = VClx∪ VCly EClz = EClx∪ ECly∪ {xy}

x Clx Cl′x Clx= Cl′x ∃Clx x∈ Clx ∃Cl′x x∈ Cl′x ⊕ Clx= Clx⊕ Cl′x Cl′x= Clx⊕ Cl′x=⇒ Clx= Cl′x y Clx z Clx Tzy U pp ⊖ Clx = (VClx, EClx) y ∈ VClx Clz = Clx⊖ y Clz= (VClz, EClz) VClz = VClx {y} EClz = EClx ky | ∀k ∈ VClx  −→ ij,←ij−_{∈ E}′_{(V )}2 ←→_{ij T} ij≥ Upp Tji≥ Upp x y x Txy y Clxy −→ xy ←xy→ x y x i y y i TCl y =  x∈VClT i xy Card (VCl)

TCl y Cl y Ti xy x x∈ VCl y i 1 2 3 4 5 6 7 8 X Agent Lien de communication X Agent du cluster

Gspa = (Vspa, Espa) Vspa = {1, 2, 3, 4, 5}

Espa = 12, 23, 34, 45

1 2 3 4 5 6 7 8 Lien bidirectionnel X Agent Lien directionnel X Agent du cluster

Gsoc= (Vsoc, Esoc)

Vsoc ={1, 2, 3, 4, 5, 6, 7, 8} Esoc = ←→ 12 , ←23 , ←→ 34 , ←→ 45,−→→38,−→36,−→63,−→56,−→67 Esoc ←₁₂→ ₁ 2 T12≥ Upp T21≥ Upp −→36,−→63 3 6 U pp 6 GiT G = (ViT G, EiT G) ViT G = {1, 2, 3, 4, 5} EiT G={←xy→| x, y ∈ ViT G; x= y}

1 2 3 4 5 6 7 8 Lien bidirectionnel X Agent Lien directionnel X Agent du cluster

50 0, 5 1 0, 6 0, 55 2, 11 0, 64 0, 6

A B

B Low

B A Low

B Low

S (S1, S2) S3 S = (S1, S2, S3) S1: R1 S2: R2 S3: S1 S2 S′ _S i j k m X Y Z

Aper(i) = {i, j, k, m...} i

Acom(i) ={i, j, k, m...} i

At

com(i) ={i, j, k, m...} i

t Pf ront(i) ={X, Y, Z, ...} i Di i IN Di i Di(X) i X IN Di(X) i X δ (i, j) i j δ (i, X) i X

δ (Xcurr, Xnext) i Xcurr i Xnext N (i, X) i X X i f (i, X) X i g (i, X) X i gdist(i, X) X i i X ginf(i, X) X i i X greli(i, X) X i i X gagent(i, X) X i −→ Fij i j − → Fi i −−→ ViX i X p (i) i p (i, j) i j preli(i, j) i j j pdur(i, j) i j i j pnew(i, j) i j p (i, j, Di(X)) i j X p (i, j, IN Di(X)) i j X

L’espace occupé

L’origine du robot

La frontière

L’espace inconnu

L’espace connu

La trajectoire du robot

La cible du

robot

X

δ (i, X) X gdist(i, X) = 1 n_{δ (i, X)} n 1 n gdist n N (i, X) i X n n_{= 2}

f (x) =_x1 f (x) = √1 x f (x) = 1 4 √ x f (x) = 1 6 √ x f (x) = 1 8 √ x X i ginf(i, X) = 1 n_{N (i, X) + 1} f (i, X) X

greli(i, X) = 1− f (i, X)

gagent(i, X) 0 1 i Aper(i) gagent(i, X) i j −→ Fij

(

x

_i

y

_i

)

i

,

F

_ij

j

(

x

_i

,

y

_i

)

j i −→ Fij = (Tij− 0.5) 0.5 . −→ Vij δ (i, j) Tij > 0.5 −→Fij Tij = 1 −→Fij = −→ Vij δ(i,j) Tij= 0.75 −→Fij =1₂. −→ Vij δ(i,j) Tij < 0.5 −→Fij Tij = 0.25 −→Fij =−1₂. −→ Vij δ(i,j) Tij = 0.5 −→Fij = 0 −→ Fij x−→_F ij = (Tij−0.5) 0.5∗δ(i,j). (xj− xi) y−→ Fij = (Tij−0.5) 0.5∗δ(i,j). (yj− yi) i −→Fi i i − → Fi =

k∈Aper(i)

−→ Fik − → Fi  x−_F→ i = 

k∈Aper(i)

(Tik−0.5)

0.5∗δ(i,j). (xk− xi)

y−_F→

i=



k∈Aper(i)

(Tik−0.5) 0.5∗δ(i,j). (yk− yi) − → Fi − → Fi gagent(i, X) α −→Fi −−→ ViX 180◦ − → Fi −−→ ViX    −−→ ViX    −−→ ViX i X

gagent(i, X) gdist(i, X)

gagent(i, X)) = − → Fi.−−→ViX    −−→ ViX    = x−→Fi.x−−→ViX + x−−→ViX.x−→Fi  x2 −−→ ViX + y2 −−→ ViX x−−→_V iX = xX− xi y−−→_V iX = yX− yi x−→ Fi =

k∈Aper(i)

(Tik− 0.5)

i

F

(

x

i

y

i

)

i

,

H

G

E

F

α

y−→ Fi =

k∈Aper(i)

(Tik− 0.5) 0.5∗ δ (i, j). (yk− yi) − → Fi.−−→ViX − → Fi X    − → Fi    − →_F i g (i, X) i wi X g (i, X)

g (i, X) = w1. gdist(i, X)

maxZ∈Pf ront(i)(gdist(i, Z))

+ w2. ginf(i, X)

maxZ∈Pf ront(i)(ginf(i, Z))

+ w3. greli(i, X)

maxZ∈Pf ront(i)(greli(i, Z))

+ w4. gagent(i, X)

maxZ∈Pf ront(i)(gagent(i, Z))

w1+ w2+ w3+ w4= 1

positiont+1(i) = M : g (i, M ) = maxZ∈Pf ront(i)(g (i, Z))

w w1 w2 w3 w4 (w1, w2, w3) w4 i i j k l m i i Tij = 0.8 Tik= 0.9 Til= 1 Tim= 0.1 i Q O P R 24

N (i, Q) = 3 N (i, O) = 5 N (i, P ) = 1 N (i, R) = 0 f (i, Q) = 0.4 f (i, O) = 0.5 f (i, P ) = 0.6 f (i, R) = 0.1

Xcurr Pf ront(i) i Xnext i X′ next i Xcurr Xcurr Xnext i X i

gdist(i, X) = n√_δ(i,X)1

ginf(i, X) = n√_N(i,X)+11

greli(i, X) = 1− f (i, X)

gagent(i, X)← − → Fi.−−→ViX |−−→ViX| X i

g (i, X) = w1._max gdist(i,X)

z∈Pfront(i)(gdist(i,Z))+ w2.

ginf(i,X)

max_zfront(i)(ginf(i,Z))+

w3._max greli(i,X)

zfront(i)(greli(i,Z))+ w4.

gagent(i,X)

maxz_∈Pfront(i)(gagent(i,Z))

X′

next ← M : g(i, M) = maxZ∈Pf ront(i)(g(i, Z))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 j (6,4) m (6,6) i (5,5) k (4,7) l (3,4) n (12,2) v (12,8) u (8,9) 1 2 3 4 5 6 7 8 9 10 (2.3, 3.9) Q (3,7.5) O (5.6, 9.4) P (11, 6.2) R

gdist(i, X) ginf(i, X) greli(i, X) Q O P R

gdist(i, X) X {Q, O, P, R} i δ (i, X)

gdist(i, Q) = 1 δ (i, Q)= 0.58 gdist(i, O) = 1 δ (i, O)= 0.55 gdist(i, P ) = 1 δ (i, P )= 0.47 gdist(i, R) = 1 δ (i, R) = 0.4

ginf(i, X) X {Q, O, P, R} i N (i, X)

X ginf(i, Q) = 1 N (i, Q) + 1 = 0.5 ginf(i, O) = 1 N (i, O) + 1 = 0.4 ginf(i, P ) = 1 N (i, P ) + 1 = 0.7 ginf(i, R) = 1 N (i, R) + 1 = 1

greli(i, X) X {Q, O, P, R} i f (i, X)

X

greli(i, Q) = 1− f (i, Q) = 0.6

greli(i, O) = 1− f (i, O) = 0.5

greli(i, P ) = 1− f (i, P ) = 0.4

greli(i, R) = 1− f (i, R) = 0.9

i −→ Vij = (1,−1) −→ Vik= (−1, 2) −→ Vil= (−2, −1) −−→ Vim= (1, 1) −→ Fij = (0.8_{− 0.5)} 0.5 . −→ Vij √ 2 = 0.42∗ −→ Vij = (0.42,−0.42) −→ Fik= (0.9_{− 0.5)} 0.5 . −→ Vik √ 5 = 0.35∗ −→ Vik= (−0.35, 0.7) −→ Fil= (1_{− 0.5)} 0.5 . −→ Vil √ 5 = 0.44∗ −→ Vil= (−0.88, −0.44) −−→ Fim= (0.1_{− 0.5)} 0.5 . −−→ Vim √ 2 =−0.56 ∗ −−→ Vim= (−0.56, −0.56) − → Fi −→ Fij−→Fik−→Fil−−→Fim − → Fi=−→Fij+−→Fik+−→Fil+−−→Fim= (−1.37, −0.72) 1 2 3 4 5 6 7 8 9 10 11 j m i k l 1 2 3 4 5 6 7 8 9 10 i

F

F

ij ik

F

im

F

il

F

(3,7.5) O (2.3, 3.9) Q (5.6, 9.4) P (11, 6.2) R i

− →_F i − →_F i −−→ViX X

j

m

i

k

l

i

F

(3,7.5)

O

(2.3, 3.9)

Q

(5.6, 9.4)

P

(11, 6.2)

R

− → Fi O, P, Q, R O(3, 7.5) Q(2.3, 3.9) P (5.6, 9.4) R(11, 6.2) −→ ViO= (x0− xi, y0− yi) = (3− 5, 7.5 − 5) = (−2, 2.5) −→ ViQ= (xQ− xi, yQ− yi) = (2.3− 5, 1.3.9 − 5) = (−2.7, −1.1) −→ ViP = (xP − xi, yP− yi) = (5.6− 5, 7.9.4 − 5) = (0.6, 4.4) −→ ViR= (xR− xi, yR− yi) = (11− 5, 1.6.2 − 5) = (5.9, 1.2) gagent(i, O) = x−→_F i.x−−→ViO+ x−−→ViO.x−F→i  x2 −−→ ViO + y2 −−→ ViO = (−1.37) ∗ (−2) + 2.5 ∗ (−0.72)√ 4 + 6.25 = 0.29 gagent(i, Q) = x−_F→ i.x−−→ViQ+ x−−→ViQ.x−→Fi x2 −−→ ViQ+ y 2 −−→ ViQ = (−1.37) ∗ (−2.7) + (−1.1) ∗ (−0.72)√ 7.29 + 1.21 = 1.54

gagent(i, P ) = x−→_F i.x−−→ViP+ x−−→ViP.x−→Fi  x2 −−→ ViP + y2 −−→ ViP =(−1.37) ∗ 0.6 + 4.4 ∗ (−0.72)√ 0.36 + 19.36 =−0.5 gagent(i, R) = x−→ Fi.x−−→ViR+ x−−→ViR.x−→Fi  x2 −−→ ViR+ y 2 −−→ ViR =(−1.37) ∗ 11 + 6.2 ∗ (−0.72)√ 121 + 38.44 =−1.55

gagent(i, Q) > gagent(i, O) > gagent(i, P ) > gagent(i, R) −→Fi −iQ→

− → Fi−iO→ −→Fi−iO→ F→−i−iP→ −→Fi −iP→ − → Fi −iR→ i Q g (i, Q) = 0.25.0.58 0.58+ 0.25. 0.5 1 + 0.25. 0.6 0.9+ 0.25. 1.54 1.54= 0.785 g (i, O) = 0.25.0.55 0.58+ 0.25. 0.4 1 + 0.25. 0.5 0.9+ 0.25. 0.29 1.54 = 0.52 g (i, P ) = 0.25.0.47 0.58+ 0.25. 0.7 1 + 0.25. 0.4 0.9+ 0.25. (_−0.5) 1.54 = 0.4 g (i, R) = 0.25. 0.4 0.58+ 0.25. 1 1 + 0.25. 0.9 0.9+ 0.25. (−.1.55) 1.54 = 0.42 w1= w2= w3= w4= 0.25 positiont+1(i) = Q i j i i i j

90%

9 9 10

p (i) = _n 1

δ (Xcurr, Xnext)

δ (Xcurr, Xnext) Xcurr i i

Xnext i X

1

preli(i, j) = Tij

pdur(i, j) = min



△tij

avg{△t′

ik}k∈Acom(i)

, 1  △tij= t−t′ij i j t t′ ij i j △t′ ik= t′ik−t′′ik i k k i (k_{∈ A}com(i)) t′ik i k t′′ ik t′′ik= 0 i k avg{△t′

ik}k∈Acom(i) △t

′

ij i

i

j i

pdur(i, j) = min

 t_{− t}′ ij t′ ij− t′′ij , 1  i m n △t′ ik △t′ ik △tik avg{△t′ ik} i m n

pdur(i, m) = min

 △tim avg{△t′ ik} , 1  = min 7 27, 1  = 7 27 pdur(i, n) = min

 △tin avg_{△t′ ik} , 1  = min 10 27, 1  = 10 27 i n

pdur(i, n) = min △t in △t′ in , 1  = 1 1 t > avg_{△t′ ik}

j pnew(i, j) = 1 2.  nj

max (nk)k∈At−1com(i)

+nj n′ j  pnew(i, j) i j t nj j t− 1 n′ j j t− 1

max (nk)k∈At−1com(i)

i t− 1 i j k l m pnew(x, y) 5 10 pnew(i, j) = 1 2. 5 10+ 5 10 = 0.5 5 20 pnew(i, k) = 12. 5 10+ 5 20 = 0.375 10 10 pnew(i, l) = 1 2. 10 10+ 10 20 = 0.75 1 1 pnew(i, m) = 12. 1 10+ 1 1 = 0.55 max_k∈At−1 com(i)(nk) = 10 At−1 com(i) ={j, k, l, m} i _{{j, k, l, m}}

p (i, j) = w5.preli(i, j) + w6.pdur(i, j) + w7.pnew(i, j)

w5+ w6+ w7= 1

w5 w6 w7

w5

w6

p (i, j, Di(X)) = Tii Di(X) i X j Tii i 1 p (i, j, IN Di(X)) = f (i, X) IN Di(X) i X f (i, X) X i

t Xcurr Xnext At−1 com(i) i t_{− 1 A}com(i) i i j i p(i)_← 1 n √ δ(Xcurr,Xnext) f lip(p(i)) = 1 avg(∆′_t i)← ∆′ti k i j i preli(i, j)← Tij

pdur(i, j) = min

 tij avg{t′ ik}k∈Acom(i) , 1  pnew(i, j) = 1₂.  nj max(nk)_k∈At−1 com (i) +nj n′ j 

p (i, j)_{← w}5.preli(i, j) + w6.pdur(i, j) + w7.pnew(i, j)

f lip(p(i, j)) = 1

X i

f lip(Tii) = 1 Di(X) j

X i

i ^LJƐƚğŵĞĚĞĐŽŵŵƵŶŝĐĂƚŝŽŶ ^LJƐƚğŵĞĚĞĐŽůůĞĐƚĞĚ͛ŝŶĨŽƌŵĂƚŝŽŶ ^LJƐƚğŵĞĚĞĐŽŶĨŝĂŶĐĞ

KƌŐĂŶŝƐĂƚŝŽŶ^ŽĐŝĂůĞ

KƌŐĂŶŝƐĂƚŝŽŶ^ƉĂƚŝĂůĞ

ŽƵĐůĞƐĚĞ ƌĠƚƌŽĂĐƚŝŽŶ ŽƵĐůĞƐĚĞ ƌĠƚƌŽĂĐƚŝŽŶ levelreli= n 1δ (Di(X) , Dj(X)) n n δ (Di(X) , Dj(X)) i j X δ (Di(X) , Dj(X)) =  1 −1 Di(X) = Di(X) Di(X)= Dj(X) 

levelnew= pnew(i, j)− 0.5 = 1 2.  nj max(nk)k∈At com(i) +nj n′ j  − 0.5 − → Fi − → Fi i j −→ Fij= (Tij− 0.5) 0.5 . −→ Vij δ(i, j) i −→Fij j j j t −→ Fij = μij. −→ Vij δ(i, j) μij =  w8. (Tij− 0.5)

0.5 + w9.levelreli+ w10.levelnew  =  w8. (Tij− 0.5) 0.5 + w9. n 1δ (Di(X), Dj(X)) n + w10.  1 2.  nj max(nk)k∈At com(i) +nj n′ j  − 0.5  w8+ w9+ w10= 1 − → Fi −→Fik

gagent(i, X) = cos(−→Fi,V−−→iX).|−→Fi| =

− → Fi.−−→ViX

|−−→ViX|

g(i, X) = w1. gdist(i, X)

maxZ∈Pf ront(i)(gdist(i, Z))

+ w2. ginf(i, X)

maxZ∈Pf ront(i)(ginf(i, Z))

+w3. greli(i, X)

maxZ∈Pf ront(i)(greli(i, Z))

+ w4. gagent(i, X)

maxZ∈Pf ront(i)(gagent(i, Z))

positiont+1(i) i

positiont+1(i) = M tel que g(i, M ) = maxZ∈Pf ront(i)(ginf(i, Z))

w8

w10

i Xcurr i i Xcurr i i Xcurr p(i)← 1 n √ δ(Xcurr,Xnext) f lip(p(i)) = 1 avg(∆′_t i)← ∆′ti k i j i preli(i, j)← Tij

pdur(i, j)← min

 tij avg{t′ ik}k∈Acom(i) , 1  pnew(i, j)← 12.  nj max(nk)_k∈At−1 com (i) +nj n′ j 

p (i, j)_{← w}5.preli(i, j) + w6.pdur(i, j) + w7.pnew(i, j)

f lip(p(i, j)) = 1 X i f lip(Tii) = 1 Di(X) j X i f lip(f (i, X)) = 1 IN Di(X) j Xcurr Xnext i X i

gdist(i, X)← n√_δ(i,X)1

ginf(i, X)← _n√ 1 N(i,X)+1

greli(i, X)← 1 − f (i, X)

j i

leveltrust(i, j)← Tij_0.5−0.5

levelreli(i, j)← n

1δ(Di(X),Dj(X))

0.5

levelnew(i, j)← 12∗

 _n j max(nk)+ nj n′ j  − 0.5 gagent(i, X)← − → Fi.−−→ViX |−−→ViX| X i

g (i, X)_{← w}1._maxz gdist(i,X)

∈Pfront(i)(gdist(i,Z))+ w2.

ginf(i,X)

max_zfront(i)(ginf(i,Z))+

w3._max greli(i,X)

zfront(i)(greli(i,Z))+ w4.

gagent(i,X)

maxz_∈Pfront(i)(gagent(i,Z))

^LJƐƚğŵĞ^

ŽƵĐůĞƐĚĞ ƌĠƚƌŽĂĐƚŝŽŶ

^ϭ

^LJƐƚğŵĞ ;ZğŐůĞƐ Ϳ ^LJƐƚğŵĞ ;ZğŐůĞƐ Ϳ ^LJƐƚğŵĞ ;ZğŐůĞƐ Ϳ ͙͙͘ ^LJƐƚğŵĞĐŽŶƚƌƀůĞ ;ZğŐůĞƐ Ϳ ^LJƐƚğŵĞĐŽŶƚƌƀůĞ ;ZğŐůĞƐ Ϳ {S1, S2, ..., Sn} {Sn+1, Sn+2, ..., Sn′} n m = n(n−1)₂ S =_{S1, S2, ..., Sn′} n′= n +n(n−1) 2 Si Ri={ri1, ri2, .., rik} rij wij ∈ [0, 1] Si k j=0 wij = 1,∀i : 0 ≤ i ≤ n′ R ={R1∪ R2...∪ Rn...∪ R′n} n m k (n + m)_{∗ k} (n + m)_{∗ k} v v(n+m)∗k n = 3 m = n(n−1)₂ = 3 k = 5 v = 100 100(3+3)∗5 _{= 10}60

r1, r2...rz z {w1, w2, ..., wz} w1 wz (w1, w2, ..., wz) (x1, x2, ..., xz) (x1, x2, ..., xz) (w1, w2, ..., wz) wi= xi  rj∈Rkxj ,_{∀i : r}i∈ Rk wi ∈ [0, 1] rj∈Rkwj = 1 k (w1, w2, ..., wz) z_{∗ n} n xi x1 xz

1

w1 w2 w3 w4

w5 w6 w7

S1 S2

A 150

70

150 A 30 B 10

-robot [ ] : Robot -zone : Zone GIS Environement -obstacle [ ] : Obstacle Zone 1 *

-niveau de danger : int Obstacle 1 0..1 +capture_Env() +mettre_à_jour() +communiquer() +déplacer() -couleur : string -vitesse : int -rayon_perception : int -rayon_communication : int -trustset : TrustSet Robot 1 * déployé sur +capture_Env() : Obstacle -couleur : string = bleu

Robot fiable

+capture_Env() : Obstacle -couleur : string = rouge

Robot défectueux -trustT : TrustTable -trustG : TrustGraph TrustSet 1 1 TrustGraph TrustTable +pas() : int -Environnement SIG Simulation 1 * 1 1 1 1

SENSEUR

Communication

Module de

mise à jour

2

5

IND

i

D

i

Carte

i

TT

i

TG

i

6

Déplacement

3

D

i

,I

N

D

i

,T

G

i

D

i

D

j

,IND

j

,TG

j

TERRAIN

D

j

,IND

j

,TG

j

Carte

i

,TT

i

6

8

informations

internes

6

informations communicables

4

7

informations

ENVIRONNEMENT

ROBOT i

ROBOT j

1

i

WĞƌĐĞǀŽŝƌ

ů͛ĞŶǀŝƌŽŶŶĞŵĞŶƚ

ŽŵŵƵŶŝƋƵĞƌ

DĞƚƚƌĞăũŽƵƌůĞƐ

ďĂƐĞƐĚĞĚŽŶŶĠĞƐ

^Ğ

_{ĚĠƉůĂĐĞƌ}

width 200 height 200 random f alse nRobot 50 nLiar 20 nObstact 200 stop All strategy 4 rp 20 rc 10 speed 5 N I 5 ρstab 0.2 U pp 0.6 Low 0.4 Tinit 0.5 μ 0.05

400 400 200 50

Ϭ ϱϬϬ ϭϬϬϬ ϭϱϬϬ ϮϬϬϬ ϮϱϬϬ Ϭ͘ϯ Ϭ͘ϱ Ϭ͘ϲ Ϭ͘ϳ Ϭ͘ϴ Ϭ͘ϵ dĞŵ Ɖ Ɛ ŵ Ž LJ ĞŶ Ě ĞƐ ŝŵ Ƶ ůĂ ƚŝŽ Ŷ  >ĞƉŽƵƌĐĞŶƚĂŐĞ ĚĞƐƌŽďŽƚƐ ĚĠĨĞĐƚƵĞƵdž DŽĚğůĞĚĞŝĂ DŽĚğůĞĚĞ<ŝŵΘ^ĞŽ DŽĚğůĞĚĞEŐƵLJĞŶĞƚĂů͘;dƌƵƐƚ^ĞƚĂǀĞĐƚĞŶĚĂŶĐĞƐͿ DŽĚğůĞĚĞ^ĐŚŝůůŽĞƚĂů͘ ŵŽŶĂƉƉƌŽĐŚĞ A B B DTAB A B AgtsB TAX = Told AX∗ TAA+ DTAB∗ TBX TAA+ DTAB X∈ AgtsB TAXold A X 30% 70% 50%

Ϭ ϱϬϬ ϭϬϬϬ ϭϱϬϬ ϮϬϬϬ ϮϱϬϬ Ϭ͘ϯ Ϭ͘ϱ Ϭ͘ϲ Ϭ͘ϳ Ϭ͘ϴ Ϭ͘ϵ dĞŵ Ɖ Ɛ ŵ Ž LJ ĞŶ Ě Ğ Ɛŝŵ Ƶ ůĂ ƚŝŽ Ŷ  >ĞƉŽƵƌĐĞŶƚĂŐĞ ĚΖĂŐĞŶƚƐ ĚĠĨĞĐƚƵĞƵdž ƵĐƵŶĞĐŽŵŵƵŶŝĐĂƚŝŽŶ ŽŵŵƵŶŝĐĂƚŝŽŶƐĂŶƐůĞƐƵƉƉŽƌƚĚĞĐŽŶĨŝĂŶĐĞ ŽŵŵƵŶŝĐĂƚŝŽŶĂǀĞĐdƌƵƐƚ^ĞƚƐ;ƵƚŝůŝƐĂƚŝŽŶĚĞƐƐĞƵŝůƐͿ DŽĚğůĞĚĞƌĠƉƵƚĂƚŝŽŶ DŽĚğůĞĚĞŝĂ DŽĚğůĞĚĞ<ŝŵΘ^ĞŽ DŽĚğůĞĚĞEŐƵLJĞŶĞƚĂů͘;dƌƵƐƚ^ĞƚĂǀĞĐƚĞŶĚĂŶĐĞƐͿ DŽĚğůĞĚĞ^ĐŚŝůůŽĞƚĂů͘ ŵŽŶĂƉƉƌŽĐŚĞ Ϭ ϮϬϬϬϬ ϰϬϬϬϬ ϲϬϬϬϬ ϴϬϬϬϬ ϭϬϬϬϬϬ ϭϮϬϬϬϬ ϭϰϬϬϬϬ ϭϲϬϬϬϬ ϭϴϬϬϬϬ Ϭ͘ϯ Ϭ͘ϱ Ϭ͘ϲ Ϭ͘ϳ Ϭ͘ϴ Ϭ͘ϵ s Ž ůƵ ŵ Ğ Ě Ζŝ Ŷ ĨŽ ƌ ŵ Ă ƚŝ Ž Ŷ Ɛ Ě ŝƌ Ğ Đ ƚĞ Ɛ ƌĞ Đ Ƶ Ğ ŝů ůŝ Ğ Ɛ WŽƵƌĐĞŶƚĂŐĞ ĚĞƌŽďŽƚƐ ĚĠĨĞĐƚƵĞƵdž ƵĐƵŶĞĐŽŵŵƵŶŝĐĂƚŝŽŶ ŽŵŵƵŶŝĐĂƚŝŽŶƐĂŶƐůĞƐƵƉƉŽƌƚĚĞĐŽŶĨŝĂŶĐĞ ŽŵŵƵŶŝĐĂƚŝŽŶĂǀĞĐdƌƵƐƚ^ĞƚƐ;ƵƚŝůŝƐĂƚŝŽŶĚĞƐƐĞƵŝůƐͿ ŽŵŵƵŶŝĐĂƚŝŽŶĂǀĞĐdƌƵƐƚdĂďůĞƐ DŽĚğůĞĚĞŝĂ DŽĚğůĞĚĞ<ŝŵΘ^ĞŽ DŽĚğůĞĚĞEŐƵLJĞŶĞƚĂů͘;dƌƵƐƚ^ĞƚĂǀĞĐƚĞŶĚĂŶĐĞƐͿ DŽĚğůĞĚĞ^ĐŚŝůůŽĞƚĂů͘ ŵŽŶĂƉƉƌŽĐŚĞ 50% 0.3 0.9

Ϭ ϱϬϬ ϭϬϬϬ ϭϱϬϬ ϮϬϬϬ ϮϱϬϬ Ϭ͘ϯ Ϭ͘ϱ Ϭ͘ϲ Ϭ͘ϳ Ϭ͘ϴ Ϭ͘ϵ dĞŵ Ɖ Ɛ ŵ Ž LJ ĞŶ Ě ĞƐŝŵ Ƶ ůĂ ƚŝŽ Ŷ  WŽƵƌĐĞŶƚĂŐĞ ĚĞƌŽďŽƚƐŝŶƚĞƌŵŝƚƚĞŶƚƐ ƵĐƵŶĞĐŽŵŵƵŶŝĐĂƚŝŽŶ ŽŵŵƵŶŝĐĂƚŝŽŶƐĂŶƐůĞƐƵƉƉŽƌƚĚĞĐŽŶĨŝĂŶĐĞ ŽŵŵƵŶŝĐĂƚŝŽŶĂǀĞĐdƌƵƐƚ^ĞƚƐ;ƵƚŝůŝƐĂƚŝŽŶĚĞƐƐĞƵŝůƐͿ ŽŵŵƵŶŝĐĂƚŝŽŶĂǀĞĐdƌƵƐƚdĂďůĞƐ DŽĚğůĞĚĞŝĂ DŽĚğůĞĚĞ<ŝŵΘ^ĞŽ DŽĚğůĞĚĞEŐƵLJĞŶĞƚĂů͘;dƌƵƐƚ^ĞƚĂǀĞĐƚĞŶĚĂŶĐĞƐͿ DŽĚğůĞĚĞ^ĐŚŝůůŽĞƚĂů͘ ŵŽŶĂƉƉƌŽĐŚĞ 50 1 45

0, 8

0, 25 0, 45

1, 8 751

E Ž ŵ ď ƌĞ Ě Ζŝ Ŷ ĨŽ ƌ ŵ Ă ƚŝ Ž Ŷ Ɛ WĂƐĚĞƐŝŵƵůĂƚŝŽŶ EŽŵďƌĞĚΖŝŶĨŽƌŵĂƚŝŽŶƐƚƌĂŝƚĠĞƐ EŽŵďƌĞĚΖŝŶĨŽƌŵĂƚŝŽŶƐƌĞĕƵĞƐ E Ž ŵ ď ƌĞ Ě Ζŝ Ŷ ĨŽ ƌ ŵ Ă ƚŝ Ž Ŷ Ɛ WĂƐĚĞƐŝŵƵůĂƚŝŽŶ EŽŵďƌĞĚΖŝŶĨŽƌŵĂƚŝŽŶƐƚƌĂŝƚĠĞƐ EŽŵďƌĞĚΖŝŶĨŽƌŵĂƚŝŽŶƐƌĞĕƵĞƐ 400 400 200 50 20 10 1.0 0.5 1.0

s

Ă

ůĞ

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Ě

Ğ

ů

ΖĂ

Ƶ

ƚŽͲ

ĐŽŶ

Ĩŝ

Ă

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ĐĞ

Ğƚ

Ě

Ğ

ů

Ă



ƌĠƉ

Ƶ

ƚĂ

ƚŝ

ŽŶ

WĂƐĚĞƐŝŵƵůĂƚŝŽŶ

ZĠƉƵƚĂƚŝŽŶĚĞƐƌŽďŽƚƐĚĠĨĞĐƚƵĞƵdž ƵƚŽĐŽŶĨŝĂŶĐĞĚĞƐƌŽďŽƚƐĚĠĨĞĐƚƵĞƵdž ZĠƉƵƚĂƚŝŽŶĚĞƐƌŽďŽƚƐĨŝĂďůĞƐ ƵƚŽĐŽŶĨŝĂŶĐĞĚĞƐƌŽďŽƚƐĨŝĂďůĞƐ ϮϱƌŽďŽƚƐ ĨŝĂďůĞƐ ϮϱƌŽďŽƚƐĚĠĨĞĐƚƵĞƵdž



Ƶ

ƚŽ

ͲĐ

Ž

Ŷ

Ĩŝ

Ă

Ŷ

Đ

Ğ

Ě

Ƶ

ƌ

Ž

ď

Ž

ƚ

ZĠƉƵƚĂƚŝŽŶĚƵƌŽďŽƚ

ϮϱƌŽďŽƚƐĨŝĂďůĞƐ

ϮϱƌŽďŽƚƐĚĠĨĞĐƚƵĞƵdž

M (robots f iables) = 0.9319482 M (robots d´ef ectueux) = 0.3569736 p < .001 M (robots f iables) = 0.867583 M (robots d´ef ectueux) = 0.349114 p < .001

0.2 0.4 0.6 0.8 1.0 Mo y enne de la réputation Robots fiables Robots défectueux 0.3 0.5 0.7 0.9 Mo y enne de la confiance Robots fiables Robots défectueux M (explorateur) = 52207 M (autres) = 22076 p < 0.001

20000 40000 60000 Mo y enne de z ones détectées explorateurs autres w1 = 0.1, w2 = 0.1, w3 = 0.1, w4 = 0.7 w4

w5 = 0.8, w6 = 0.1, w7 = 0.1 w5 w8 = w9 = w10 = 1/3 w8 w9 w10 ƌŽďŽƚϮϭϬ ƌŽďŽƚϮϮϴ ƌŽďŽƚϮϯϳ ƌŽďŽƚϮϰϳ ƌŽďŽƚϮϯϴ ƌŽďŽƚϮϭϯ ƌŽďŽƚϮϭϭ ƌŽďŽƚϮϮϲ ƌŽďŽƚϮϭϱ ƌŽďŽƚϮϭϮ ƌŽďŽƚϮϬϯ ƌŽďŽƚϮϯϬ ƌŽďŽƚϮϬϳ ƌŽďŽƚϮϯϰ ƌŽďŽƚϮϯϲ ƌŽďŽƚϮϯϱ ƌŽďŽƚϮϱϮ ƌŽďŽƚϮϰϬ ƌŽďŽƚϮϰϭ ƌŽďŽƚϮϰϰ ƌŽďŽƚϮϰϮ ƌŽďŽƚϮϮϳ ƌŽďŽƚϮϯϭ ƌŽďŽƚϮϮϱ ƌŽďŽƚϮϮϮ ƌŽďŽƚϮϭϴ ƌŽďŽƚϮϰϵ ƌŽďŽƚϮϮϬ ƌŽďŽƚϮϮϭ ƌŽďŽƚϮϮϯ ƌŽďŽƚϮϰϴ ƌŽďŽƚϮϯϮ ƌŽďŽƚϮϯϯ ƌŽďŽƚϮϱϬ ƌŽďŽƚϮϱϭ ƌŽďŽƚϮϰϲ ƌŽďŽƚϮϬϱ ƌŽďŽƚϮϬϵ ƌŽďŽƚϮϭϰ ƌŽďŽƚϮϬϲ ƌŽďŽƚϮϮϰ ƌŽďŽƚϮϬϰ ƌŽďŽƚϮϭϵ ƌŽďŽƚϮϯϵ ƌŽďŽƚϮϭϳ ƌŽďŽƚϮϮϵ ƌŽďŽƚϮϰϯ ƌŽďŽƚϮϭϲ ƌŽďŽƚϮϰϱ ƌŽďŽƚϮϬϴ

ůƵƐƚĞƌ

ůƵƐƚĞƌ

WĂƐĚĞƐŝŵƵůĂƚŝŽŶ ϱϬϬ Ϭ ϭϬϬ ϮϬϬ ϯϬϬ ϰϬϬ E Ƶ ŵ Ġ ƌ Ž Ě Ğ ƌ Ž ď Ž ƚ w6 = 0.1, w7 = 0.1

50% 25 25

M (envoi) = 71.657 M (r´eception) = 51.300

p < .001

EŽŵďƌĞĚΖŝŶĨŽƌŵĂƚŝŽŶƐĞŶǀŽLJĠĞƐ

E

Žŵ

ď

ƌĞ

Ě

ΖŝŶ

ĨŽƌ

ŵ

Ă

ƚŝŽŶ

Ɛƌ

Ğ

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Ğ

Ɛ

ƌ

Ž

ď

Ž

ƚƐ

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ůĞƐ

ƌ

Ž

ď

Ž

ƚƐ

Ě

ĠĨ

ĞĐ

ƚƵ

ĞƵ

dž

50 55 60 65 70

Quantités de données échangées

émission

réception

80 85 90 95

Quantités de données échangées

émission

0 20 40 60 80 100 0 40 80 120 160 200 240 280 320 360 400 440 480

Nombre d'informati

o

ns

WĂƐĚĞƐŝŵƵůĂƚŝŽŶ

Nombre d'informations indirectes envoyées par des robots fiables Nombre d'informations directes envoyées par des robots fiables Nombre d'informations directes envoyées par des robots défectueux Nombre d'informations indirectes envoyées par des robots défectueux

0 10 20 30 40 50 60 70 80 90 0 40 80 120 160 200 240 280 320 360 400 440 480

Nombre d'i

n

formations

WĂƐĚĞƐŝŵƵůĂƚŝŽŶ

Nombre d'informations indirectes reçues par des robots fiables Nombre d'informations directes reçues par des robots fiables Nombre d'informations indirectes reçues par des robots défectueux Nombre d'informations directes reçues par des robots défectueux

M (inf ormations directes) = 42.230 M (inf ormations indirectes) = 28.814 p < 0.001

M (inf ormations directes) = 21.771 M (inf ormations indirectes) = 23.492 p < 0.001

30

35

40

Quantités de données échangées

information directe information indirecte 21 22 23 24

Quantités de données échangées

information directe

information indirecte

{wi} w1 = w2 = w3 = 0.3 w4 = 0.1 w1 w2 w3 w1= w2= w3= 0.1 w4= 0.7 w4 wi = 13, i = 5..10 20000 40000 60000 La quantité de z ones détectées exploration communication 10 20 30 40 50 60 La quantité d’inf or mations échangées exploration communication M (exploration) = 48102 M (comunication) = 42459 p < .04 M (exploration) = 30.34 M (communication) = 35.78 p < .05 w1, w2, w3, w4

{w1, w2, .., w10} w1 w10 10 w1w2, w10 w1w2, w10 x1x2 x10 xi∈ [0, 15] 4 xi wi wi=_x1+x2x+xi 3+x4, i = 1..4 wj= _x5+xxj6+x7, j = 5..7 wk= _x8+xx9k+x10, k = 8..10 w1+ w2+ w3+ w4 = 1 w5+ w6+ w7 = 1 w8+ w9+ w10 = 1 w1w2, w10 40 10 xi 4 xi 10 xi 24∗10 > 1 f (i) = Datai ti Datai i ti 68 5 7% 10

30 30 15 30 30 10% 3 40 10 5 30 30 3 5 68 30 α 10% 10e ₃₀e 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 G1 G3 G5 G7 G9 G11 G13 G15 G17 G19 G21 G23 G25 G27 G29

V

ale

urs d'utilités

Générations

moyenne des individus sélectionnés

moyenne de toute la population

10 wi

wi wi

30

w5 w6 w7 w10 w8 w9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 G0 G2 G4 G6 G8 G10 G12 G14 G16 G18 G20 G22 G24 G26 G28 G30 w1 w2 w3 w4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 G0 G2 G4 G6 G8 G10 G12 G14 G16 G18 G20 G22 G24 G26 G28 G30 w5 w6 w7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 G0 G2 G4 G6 G8 G10 G12 G14 G16 G18 G20 G22 G24 G26 G28 G30 w8 w9 w10 wi wi wi wi wi 50 100 150 200 250 300

w1 0, 55 0, 60 w2 0, 30 0, 35 w3 0, 10 w4 0, 01 w4 w6 0, 40 w5 w7 0, 30 w10 0, 40 w9 w9 0, 35 w8 0, 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 50 100 150 200 250 300

nombre d'individus choisis

w1 w2 w3 w4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 50 100 150 200 250 300

nombre d'individus choisis

w5 w6 w7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 50 100 150 200 250 300 nombre d'individus choisis

w8 w9 w10 wi w4 w4 w4 8e 9e 10e 8e ₉e ₁₀e w8−w10 w8−w10 w8−w10 w8− w10 M (avec) = 1, 27 M (sans) = 1, 23 p_{− value < 0, 001} w4

s

Ă

ůĞ

Ƶ

ƌƐ

Ě

ΖƵ

ƚŝ

ůŝ

ƚĠ

Ɛ

ĂǀĞĐtϴͲtϭϬ

ƐĂŶƐtϴͲtϭϬ

1.20 1.25 1.30 1.35 1.40 V aleurs d’utilités avec w8−w10 sans w8−w10 w8− w10 20% 40% 60% 7% 5 68 wi 30 wi w1 w4 w2 w3 w2 w3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7% 20% 40% 60% 80% % des agents non fiables dans le système

w1 w2 w3 w4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7% 20% 40% 60% 80% % des agents non fiables dans le système

w5 w6 w7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7% 20% 40% 60% 80% % des agents non fiables dans le système

w8 w9 w10 wi w5 w6 w7 7% 60% w6 w5 w7 60% w5 w5 w8 w9 w10 40% w9 w10 {wi} 40% 60% w3 w2 w9 80% w5 w6

t A

(x, y) A t + 1

−− −−

−− −−

−− −−

−− −−

−− −−

− −

− −

−− −− −− −− −− −− −− −− i. i j i j

−− −−

−− −−

−− −−

−− −−