Self-Organized Service Management in Heterogeneous and Dynamic MAS

Outline System Definition Homophily-based Network Adaption Process Discussion Conclusions

Self–Organized Service Management inHeterogeneous and Dynamic MAS

M. Rebollo, E. del Val and V. Botti

Univ. Politecnica de Valencia (Spain)

9th European Workshop on Multi-Agent SystemsMaastricht, November 2011

@mrebollo UPVSelf–Organized Service Management in Heterogeneous and Dynamic MAS


Self–Organized Service Management

The ProblemAutomatic service self-adaption to the system demand withoutglobal knowledge

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Our Proposal

The challengeThe introduction of the homophily concept improves theperformance of greedy local search algorithms and it can be usedas individual adaption criteria.

What is needed. . .a network structure with small world characteristicsan efficient search algorithman adaptation mechanism to fit to the service demand



Outline

1 Outline

2 System Definition

3 Homophily-based Network

4 Structural Homophily as Local Self-Adaptive Method

5 Discussion

6 Conclusions



System Definition

Homophily based network

HomophilyTendency of individuals to associate and interact with similar ones

choice homophily: similarity measurevalue homophily: shared attributesstatus homophily: role

structural homophily: adaption to external conditions



System Definition

Network Model

Definition (System model)

(A, L), whereA = {a1, ..., an} is a finite set of autonomous agents andL ⊆ A× A is the set of links, where each link (ai , aj) ∈ Lindicates the existence of a direct relationship between agentai and aj .



System Definition

Network Model

Definition (Agent)

An agent ai ∈ A = (Ri ,Ni , sti , πi , ρi), where:Ri = {r1, . . . , rm} is the set of roles played by the agent;Ni is the set of neighbors of the agent,Ni = {ap, ..., aq} : ∀aj ∈ Ni ,∃(ai , aj) ∈ L, and |Ni | > 0.It is assumed that |Ni | � |A|;sti is the internal state of the agent;πi : sti → Ni , is the neighbor selection function that returnsthe most promising neighbor to provide a service;ρi : sti → Ψ is the adaptation selection function where Ψ isthe set of finite adaptation actions of the agent.



System Definition

Network Model

Definition (Role model)

A role ri ∈ Ri is defined by the tuple (φi ,Si) , where:φi is a semantic concept for the role;Si = {s1, . . . , sl} is the set of services associated to the role.Each service is defined by the tuple si = (Ii ,Oi ,Pi ,Efi), wherethe components are the set of inputs, outputs, preconditions,and effects of the services, respectively. All of them aresemantic concepts that can be defined in different ontologies.



Homophily-based Network

Value Homophily as Service Similarity

Definition (Value Homophily)

Hv (Si ,Sj) = α[β ∗WG ′I + (1− β)WG ′O

]+

(1− α)[β ∗WG ′P + (1− β)WG ′Eff

]=

= α

[β

∑wij∈E ′I

wij

max |Ii |, |Ij |+ (1− β)

∑wij∈E ′O

wij

max |Oi |, |Oj |

]+

+(1− α)

[β

∑wij∈E ′P

wij

max |Pi |, |Pj |+ (1− β)

∑wij∈E ′Ef

wij

max |Efi |, |Efj |

]




Value Homophily as Service Similarity

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DEFINITION 2: (Agent). An agent ai ∈ A is characterizedby a tuple of five elements (Ri, Ni, sti, πi, ρi) where:

• Ri = {r1, . . . , rm} is the set of roles played by the agent;• Ni is the set of neighbors of the agent, Ni = {ap, ..., aq} :∀aj ∈ Ni,∃(ai, aj) ∈ L, and |Ni| > 0. It is assumed that|Ni|� |A|;

• sti is the internal state of the agent;• πi : sti → Ni, is the neighbor selection function that

returns the most promising neighbor to provide a service;• ρi : sti → Ψ is the adaptation selection function where

Ψ is the set of finite adaptation actions of the agent.The organizational role of an agent is a semantic concept

that is defined in a common ontology shared in the system.The role is related to the services that can be offered by theagent.

DEFINITION 3: (Role). A role ri ∈ Ri is defined by thetuple (φi, Si) , where:

• φi is a semantic concept for the role;• Si = {s1, . . . , sl} is the set of services associated to

the role. Each service is defined by the tuple si =(Ii, Oi, Pi, Effi), where the components are the set ofinputs, outputs, preconditions, and effects of the services,respectively. All of them are semantic concepts that canbe defined in different ontologies.

Homophily is introduced to create s self-organized structurein which agents are linked to similar ones. Choice homophily(CH) is the factor that allows the agents to establish links withother agents and to redirect queries about services that theycannot offer. This homophily is based on the characterizationof the services that the agents provide and the roles that areplayed by them. Structural homophily (SH) refers to howthe structure in which the individuals are adapts itself toexternal conditions. The adaptation of each agent to the systemconditions makes the structure of the system more efficientin fulfilling the service demand. Also, choice homophily issubdivided into two types: (i) status homophily, which isrelated to the formal or informal status similarity of theindividuals (social status, status within an organization, orprofessional degree); and (ii) the value homophily, which isbased on the similarity of shared attributes (such as gender,age, geographical location, and so on).

Matching these concepts with the agency-related concepts,status homophily can be identified with the semantic descrip-tion of the role that an agent plays within an organization,whereas value homophily represents the individual character-istics of the agent.

DEFINITION 4: Choice homophily between two agentsai, aj ∈ A in the system is defined as the linear combinationof status and value homophily

CH(ai, aj) = ϕ ∗Hs(Ri, Rj) + (1− ϕ) ∗Hv(Si, Sj)

The ϕ parameter regulates the importance of the influence ofroles (status homophily) or services (value homophily) in thetotal homophily of the agent with its neighbors.

The value homophily function Hv(Si, Sj) calculates thedegree of matching between two set of services, where Si

and Sj are the sets of services provided by the agents ai andaj , respectively. In general, the level of matching between tosets of semantic concepts Ci and Cj is calculated through abipartite matching graph. Let G = (Ci, Cj , E) be a complete,weighted, bipartite graph that links each concept ci ∈ Ci toeach concept cj ∈ Cj . ωij represents the weight associatedto the arc ei = (ci, cj) ∈ E between ci and cj as thesemantic similarity between those concepts. Four degrees ofmatching can be identified: exact, subsumes, plug-in, andfail [18]. The match is considered as exact, if c1 ∈ Ci isequivalent to c2 ∈ Cj (c1 ≡ c2); subsumes, if c1 subsumesc2 (c1 ❂ c2); plug-in, if c1 is subsumed by c2 (c1 ❁ c2);and fail, otherwise. A value in the interval [0, 1] is assignedto each degree of matching, where 1 represents an exactmatching among the terms. The best match among conceptsis obtained by calculating the maximum weighted bipartitematching, G� = (Ci, Cj , E

�), where E� ⊆ E are the edgesthat have the maximal value.

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Fig. 1. Full connected Weighted Bipartite Graph G and resulting MaximumWeighted Matching Bipartite Graph G�

To calculate the value homophily, four bipartite graphs aredefined, one for each one of the components of service si:inputs, outputs, preconditions, and effects. Let’s explain thecase of the inputs. The rest of the components are treatedin the same way. Let Ii =

�si∈Si

Ii be the set formedby all the inputs of all the services si of the agent ai;GI = (Ii, Ij , E) the weighted bipartite graph among the inputsof all the services Si and Sj provided by agents ai and aj ;and let G�

I = (Ii, Ij , E�) be the maximum weighted bipartite

matching. Then WG�I

is defined as:

WG�I

=

�

ωij∈E�I

ωij

max |Ii|, |Ij |(1)

the normalized total weight of the maximum bipartite graphG�

I . WG�O

, WG�P

, and WG�Eff

are similarly defined for outputs,

Table with the values

ω15 = 0.5

ω25 = 0.75

ω36 = 0.75




Status Homophily as Role Similarity

Definition (Status Homophily)

Hs(Ri ,Rj) = maxri∈Ri ,rj∈Rj

(rmatch(φi , φj))

where (Fu et al. 2009)

rmatch(φi , φj) =

1 if path length = 0e(−λ(pl+pc)) ∗ δ if roles no siblingse(−λ(pl−d)) ∗ δ if roles siblings

andδ =

eγdp − e−γdpeγdp + e−γdp




Status Homophily as Role Similarity

Informative

Supplier

Leisure

Food Supplier

Seller CameraSeller

VehicleSeller

BookSeller

CarSeller

CycleSeller

Recommender

FilmRecommender

BookRecommender

MusicRecommender

Drink Supplier

pl = 7cp = 3d = 2superclasses = 3

Thing

superclasses = 4max depth = 6

TravelAgency

WeatherMan

LocationTouristInformation GeoInfo

LeisureOrganizer

HotelsManager

Work Occupational Information

Publication

Occupation

UniversityStaff

SciencePublisher

NovelPublisher

FoodProviderFreshFoodProvider

PreparedFoodProvider




Community Creation

Definition (Choice Homophily)

CH(ai , aj) = ϕ ∗ Hs(Ri ,Rj) + (1− ϕ) ∗ Hv (Si , Sj)

The ϕ parameter regulates the importance of the influence of roles(status homophily) or services (value homophily) in the totalhomophily of the agent with its neighbors.




Sample of Homophily-based Network Structure




Decentralized Service Search Algorithm

Neighbor selection function

πi(at) = argmaxaj∈Ni

Ps(aj , at)

Where the probability for a neighbor to be chosen depends on itssimilarity with the desired service (choice homophily) and its degree

Ps(aj , at) = 1−(1−

(CH(aj , at)∑

aj∈Ni CH(aj , at)

))|Nj |



Structural Homophily as Local Self-Adaptive Method

Structural Homophily

Relative importance of anagent based on the services ithas served and the queries ithas redirected as the valueassociated to the category ciof the most demanded servicesi ∈ Si :

SH(ai) = a · cbi

where

ci = argmaxx

a · xb

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0 2 4 6 8 10 12 14 16

Num

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of r

ecei

ved

quer

ies

Category of the received queries

agent trafficfitted power-law function a*x^b




Agent Self-DisconnectionEach agent decides

to leave the network if it is not important for the systemto replicate itself if it considers that it is relevant for thenetwork and it has received a significant increment in thenumber of queries that it receives; orto continue otherwise.

Probabilities for adaption function ρi

Pψ(leave) = 1− SH(ai)Pψ(continue) = Pψ(stay ∩ clone) = SH(ai)f (x)

Pψ(replicate) = Pψ(stay ∩ clone) = SH(ai)(1−f (x))




Link Decay

The utility of the links decaywith time if they are not usedfollowing a sigmoid function

dai (qi) = 1− 1

1 + l · e−(qi−m)

n 0

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0 10 20 30 40 50 60

Pro

babi

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to m

aint

ain

the

link

Number of queries that were forwarded to other links

n = 2n = 4n = 6



Discussion

Search Performance

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0 10 20 30 40 50 60 70 80 90 100

Num

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of p

aths

Path length

role-based EVNEVN

RandomDegree

Similarity

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0 10 20 30 40 50 60 70 80 90 100

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ber

of p

aths

Path length

role-based EVNEVN

RandomDegree

Similarity

Search performance without role information (left) and combiningservice and role information in the homophily calculation with

ϕ = 0.5 (right)



Discussion

Agent Self-Disconnection

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nts

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initial agents distributionagents distributionqueries distribution

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of p

aths

Path length

Original networkself-adapted network

With agents deciding to stay, leave or clone, the network adapts tothe demand (left) and the average path length is reduced (right)



Discussion

Link Decay

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nts

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initial agents distributionagents distributionqueries distribution

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Num

ber

of p

aths

Path length

Original networkself-adapted and rewired network

Including link decay, the network adapts to the demand (left) butwithout significant changes in the path length (right).



Conclusions

Conclusions

What we have done

network structure based on homophily as similarity criteriagreedy search algorithm with local informationadaption of the network without external coordination

agents decides to stay or to leave the systemlink decay

Ongoing work: Non-cooperative agentsTo include agents with different cooperation degree.

agents decide to remove links from non-cooperative agentsRF strategies to change the behavior to cooperate


Self-Organized Service Management in Heterogeneous and Dynamic MAS

Technology

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