dynamic social knowledge: a comparative evaluation

Ma. Victoria Eyharabide 1

Dynamic Social Knowledge: A Comparative Evaluation

This paper presents a comparative evaluation, focused on the number of exchanged massages in the cooperation process, between:

• Contract Net Protocol• Coalition Based on Dependence • Dynamic Social Knowledge


Dynamic Social Knowledge: A Comparative Evaluation

The formalization of each of the considered strategies takes into account:

– The number of subtasks.

– The number of agents.

– The number of interaction cycles

involved in the cooperation process.

For each situation, there is a given goal g that defines a cooperative task J and this task can be split into l subtasks {j1, j2, ..., jl}. The cooperation involves n agents {a1,a2,...,an}


Contract Net Protocol

The agents involved into the cooperation process belong to a contract net and the execution of a task is decided through contracts established between agents.

Roles:– Manager– Contractor

Any agent can take on either role dynamically.


Contract Net Protocol The Cooperation Process

The cooperation process consists of four steps:

• Goal broadcast

• Announcement• Bidding• Awarding

A conflict is solved by opening successive contracts to perform the task, each one containing simpler subtasks having lower satisfaction degrees for the task execution.


Contract Net Protocol Formalizing the CNP

Best SituationFor each of the l subtasks, the first received bid has a satisfactory

grade and the contract is immediately awarded to its associated contractor.

tt

tt

a1

a2

a3

an

Goal broadcast

Announcement

Bidding

Awarding

. . .

. . .

. . .



Best SituationThe number of exchanged messages can be represented by the following expression:

MCNP, best = goal broadcast + announcement + bidding + awarding

= (n - 1) + (n - 1)L + L + L

= (n - 1) (L + 1) + 2L

The behaviour depends on:• The number of agents • The number of subtasks



Worst SituationFor each subtask ji, it is necessary to open wi modified contracts

searching for alternatives until a contractor is found to be awarded.

tt

tt

a1

a2

a3

an

Goal broadcast

Announcement

Bidding

Awarding

. . .

. . .

. . .



Worst SituationLet w be the mean value of w1, ..., wl

MCNP, worst = goal broadcast + announcement + bidding + awarding

= (n - 1) + (n - 1)Lw + (n - 1)Lw + L

= (n - 1) (2Lw + 1) + L

The value of MCNP, worst grows rapidly as the value of w increases.


Coalition Based on Dependence

The Coalition Based on Dependence uses the dependence relationship between agents to guide the formation of a coalition able to perform a collective task.

A negotiation strategy is used to solve conflicts about goals, plans and task allocation. Such negotiation strategy is a process by which a joint decision is made by two or more parties.


The cooperation process can be described in four steps:

• Goal broadcast

• Presentation

• Negotiation cycle

• Agreement

Coalition Based on Dependence The Cooperation Process


Coalition Based on Dependence Formalizing the CBD

Best SituationAfter the presentation, for each of the l subtasks, the agent

chooses another agent to do a coalition, sends one proposal and this agent agrees with it.

tt

tt

a1

a2

a3

an

Goal broadcast

Presentation

Negotiation

Agreement

. . .

. . .

. . .



Best Situation

MCBD, best = goal broadcast + presentation + negotiation + agreement

= (n - 1) + n(n - 1) + 2L + L

= (n2 - 1) + 3L

Because of the communication overhead represented by the presentation step, where the number of messages grows with the square of the number agents, the value of MCBD, best is always greater than the corresponding value of MCNP, best



Worst SituationFor each subtask ji, wi proposals are exchanged in the search for

alternatives or possible concessions in order to achieve an agreement.

tt

tt

a1

a2

a3

an

Goal broadcast

Presentation

Negotiation

Agreement

...

...

...



Worst Situation

MCBD, worst = goal broadcast + presentation + negotiation + agreement

= (n - 1) + n(n - 1) + 2nLw + L

= (n2 - 1) + L(2nw + 1)

For the same values of w, MCBD, worst lies always over MCNP, worst .


Dynamic Social Knowledge

• Split the task into subtasks.• Use contract announcements in order to find adequate contractors

to handle these subtasks.• if (no subset of the contracts satisfying the goal can be awarded)

– The information about the bids is stored in a knowledge base.

– Using this knowledge base, a rule-based system infers the best way for driving the cooperation process.


• Contract Frame: is a data structure designed to store all the information involved in the cooperation process.

It is composed by:

– One goal.– A group of agents.– A degree of satisfaction for the goal.– A deadline.– A set of possible contracts.

• Dynamic Social Knowledge Base: is a knowledge base built dynamically. It relates the information stored into the contract frame to the information available from the received bids.

Dynamic Social Knowledge


Dynamic Social Knowledge The Cooperation Process

For each cooperative task:– A contract frame is opened.– A contract process is opened for each member of the

contract set.– The involved agents will accept or refuse the subtask.

• If (the agent sent a proposal accepting)The proposal has a grade expressing how well the agent could perform the subtask.



– The agent keeps accepting proposals until one of the following situations occurs:

• Situation 1: A subset of contracts, able to satisfy the goal, has received satisfactory bids, so these contracts are awarded.

• Situation 2: The agent has received proposals to all the contract processes but no subset, able to satisfy the goal, has received satisfactory bids.

» The received proposals are used to build a DSK base.

• Situation 3: The deadline has expired.» The received proposals are used to build a DSK base.



In situations 2 and 3, according to:

• The knowledge in the DSK base

• Local agent knowledge

• A set of specially designed rules bases

The execution of a rule-based system may indicate:

1 .- A winner group that together can perform the subtasks needed.

2 .- The degree of satisfaction of the contract frame should be reduced, in such a way that a group of winners can be found.

3 .- A new contract set should be chosen and a new round of interaction should be open.

4 .- The cooperation process should be closed without awarding.


Dynamic Social Knowledge Formalizing the DSK

Best SituationThe best situation happens when there is a subset CS of the

contract set able to achieve the goal, and for all the ci in Cs, there is some bid able to be awarded with the respective contract.

tt

tt

a1

a2

a3

an

Goal broadcast

Announcement

Bidding

Awarding

. . .

. . .

. . .


Best SituationThe amount of exchanged messages can be given by the following expression, where LDSK = aL:

MDSK, best = goal broadcast + announcement + bidding + awarding

= (n - 1) + (n - 1) LDSK + LDSK + LDSK

= (n - 1) (aL + 1) + 2aL

Here the subtasks are not directly assigned to a contract like in CNP, they are first processed by a ruled-based system in order to generate the contract set. When J contains duplicate subtasks, the DSK strategy assigns only one contract to all duplicate subtasks, resulting in a < 1 and consequently MDSK, best < MCNP, best




Worst SituationThe worst case happens when none of the contracts allow the agents to achieve the goal, the DSK base is built and w negotiation rounds are necessary to conclude.

tt

tt

a1

a2

a3

an

Goal broadcast

Announcement

Bidding

Awarding

. . .

. . .

. . .



Worst Situation

MDSK, worst = goal broadcast + announcement + bidding + awarding

= (n - 1) + (n - 1) LDSK + (n - 1) LDSK + 2w + LDSK

= (n - 1) (2aL + 1) + 2w + aL

The number of repeated contracts, w, can be:

WDSK < WCNP

Because in DSK, eachcontract is generatedaccording to ruled-basedinferences, based onprevious contracts.

WDSK > WCNP

Because aech agent has more completeinformation about other agents, allowingmore efficient contract planning, but thisachieved through expensive presentationstep.


Conclusions

• The Dynamic Social Knowledge exposes a good balance between:– The amount of social knowledge used to drive the cooperation

strategy.

– The amount of interaction cycles involved in the cooperation process.

• The use of rule-based inference allows alternative ways to perform a given task to be searched in parallel, instead of sequentially, which is crucial to reduce:– The amount of exchanged messages.

– The cooperation convergence time.

dynamic social knowledge: a comparative evaluation

Documents

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n agents

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victoria eyharabidecoalition

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contract net protocolcoalition

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