A Similarity Evaluation Technique for Cooperative Problem Solving with a Group of Agents Seppo Puuronen, Vagan Terziyan Third International Workshop CIA-99.

A Similarity Evaluation Technique for Cooperative Problem Solving

with a Group of Agents

Seppo Puuronen, Vagan Terziyan

Third International Workshop CIA-99Cooperative Information Agents

July 31 - August 2, 1999Uppsala (Sweden)

Authors

Department of Computer Science and Information Systems

University of Jyvaskyla FINLAND

Seppo Puuronen

Vagan Terziyan

Department of Artificial Intelligence

Kharkov State Technical University of Radioelectronics,

UKRAINE

[email protected]

[email protected]

Contents

The Research Goal Basic Concepts External Similarity Evaluation An Example Internal Similarity Evaluation Conclusions

Goal

The goal of this research is to develop simple similarity evaluation technique to be used for cooperative problem solving based on opinions of several agents

Problem solving here is finding of an appropriate solution for the problem among available ones based on opinions of several agents

Basic Concepts:Virtual Training Environment (VTE)

VTE of a group of agents is a quadruple:

<D,C,S,P>• D is the set of problems D1, D2,..., Dn in the VTE;

• C is the set of solutions C1, C2,..., Cm , that are used to solve the problems;

• S is the set of agents S1, S2,..., Sr , who selects solutions to solve the problems;

• P is the set of semantic predicates that define relationships between D, C, S

Basic Concepts:Semantic Predicate P

P(D ,C ,S )

,if the agent S selects solution C

to solve the problem D ;

,if S refuses to select C

to solve D ;

,if S does not select or refuse

to select C to solve D .

i j k

k j

i

k j

i

k

j i

1

1

0

Problem 1:Deriving External Similarity Values

DC

S

DiCj

Sk

SDk,i

DCi,j

SCk,j

External Similarity Values

DC

S

DiCj

Sk

SDk,i

DCi,j

SCk,j

External Similarity Values (ESV): binary relations DC, SC, and SD between the elements of (sub)sets of D and C; S and C; and S and D.

ESV are based on total support among all the agents for voting for the appropriate connection (or refusal to vote)

Problem 2:Deriving Internal Similarity Values

D C

S

Di’

SSk’,k’’

DDi’,i’’ CCj’,j’’

Di’’

Cj’

Cj’’

Sk’

Sk’’

Internal Similarity Values

D C

S

Di’

SSk’,k’’

DDi’,i’’ CCj’,j’’

Di’’

Cj’

Cj’’

Sk’

Sk’’

Internal Similarity Values (ISV): binary relations between two subsets of D, two subsets of C and two subsets of S.

ISV are based on total support among all the agents for voting for the appropriate connection (or refusal to vote)

Why we Need Similarity Values (or Distance Measure) ? Distance between problems is used by agents to

recognize nearest solved problems for any new problem

distance between solutions is necessary to compare and evaluate solutions made by different agents

distance between agents is useful to evaluate weights of all agents to be able to integrate them by weighted voting.

Deriving External Relation DC:How well solution fits the problem

DC CD P D C S D D C Ci j j i i j k i jk

r

, , ( , , ), ,

DC

S

DiCj

Sk2

DCi,j=3

Sk1

Sk3

Agents

Problems Solutions

Deriving External Relation SC: Measures Agents Competence in the Area of Solutions

The value of the relation (Sk,Cj) in a way represents the total support that the agent Sk obtains selecting (refusing to select) the solution Cj to solve all the problems.

SC CS DC P D C S S S C Ck j j k i j i j ki

n

k j, , , ( , , ), ,

Example of SC Relation

DC

SSk

Cj

D2

SCk,j=4

D1

D4

D3

CDj1 = -3

CDj2 = 6

CDj3 = 0

CDj4 = 1

Agents

Problems Solutions

Deriving External Relation SD: Measures Agents Competence in the Problem’s Area

The value of the relation (Sk,Di) represents the total support that the agent Sk receives selecting (or refusing to select) all the solutions to solve the problem Di.

SD DS DC P D C S S S D Dk i i k i j i j kj

m

k i, , , ( , , ), ,

Example of SD Relation

DC

SSk

Di

C1

SDk,i=2

C2

CD1i = -3

CD2i = 5

ProblemsSolutions

Agents

Standardizing External Relations to the Interval [0,1]

standardizing value value =value value

max(value) - min(value)

-min( )

DC CDDC r

ri j j ii j

, ,,

2

SC CSSC n r

n rk j j kk j

, ,, ( )

( )

2

2 1

SD DSSD m r

m rk i i kk i

, ,, ( )

( )

2

2 1

n is the number of problems

m is the number of solutions

r is the number of agents

Agent’s Evaluation:Competence Quality in Problem Area

Q Sn

SDDk k i

i

n( ) , 1

- measure of the abilities of an agent in the area of problems from the support point of view

Agent’s Evaluation:Competence Quality in Solutions’ Area

- measure of the abilities of an agent in the area of solutions from the support point of view

Q Sm

SCCk k j

j

m( ) , 1

Quality Balance Theorem

Q S Q SDk

Ck( ) ( )

The evaluation of an agent competence (ranking, weighting, quality evaluation) does not depend on the competence area “virtual world of problems” or “conceptual world of solutions” because both competence values are always equal.

Proof

Q Sn

SDn

SD m r

m rD

k k ii

nk i

i

n( )

( )

( ),,

1 1 2

2 1

1

2

2 1n

DC P D C S m r

m r

i j i j kj

m

i

n( ( , , )) ( )

( )

,

1

2

2 1m

DC P D C S n r

n r

i j i j ki

n

j

m( ( , , )) ( )

( )

,

...

...

1 2

2 1

1

m

SC n r

n r mSC Q S

k j

j

m

k jj

mC

k,

,

( )

( )( )

An Example

Let us suppose that four agents have to solve three problems related to the search of information in WWW using keywords and search machines available.

The agents should define their selection of appropriate search machine for every search problem.

The final goal is to obtain a cooperative result of all the agents concerning the “search problem - search machine” relation.

C (solutions) Set in the ExampleSolutions - search machines Notation

AltaVista C1

Excite C2

Infoseek C3

Lycos C4

Yahoo C5

S (agents) Set in the Example

Agents Notation

Fox S1

Wolf S2

Cat S3

Hare S4

D (problems) Set in the Example

S e a r c h p r o b l e m s w i t h k e y w o r d s

D 1F i s h i n g i n F i n l a n d

D 2N O K I A p r i c e s

D 3A r t i f i c i a l i n t e l l i g e n c e

Selections Made for the Problem “Fishing in Finland”

D1

P(D,C,S) C1 C2 C3 C4 C5

S1 1 -1 -1 0 -1

S2 0+ -1** 0 ++ 1* -1***

S3 0 0 -1 1 0

S4 1 -1 0 0 1Agent Wolf prefers to select Lycos* to find information about “Fishing in Finland” and it refuses to select Excite** or Yahoo***. Wolf does not use or refuse to use the AltaVista+ or Infoseek++.

Selections Made for the Problem “NOKIA Prices”

D2

P C1 C2 C3 C4 C5

S1 -1 0 -1 0 1

S2 1 -1 -1 0 0

S3 1 -1 0 1 1

S4 -1 0 0 1 0

Selections Made for the Problem “Artificial Intelligence”

D3

P C1 C2 C3 C4 C5

S1 1 0 1 -1 0

S2 0 1 0 -1 1

S3 -1 -1 1 -1 1

S4 -1 -1 1 -1 1

Result of Cooperative Problem Solution Based on DC Relation

AltaVista, Lycos,NOT Excite, NOT Infoseekfishing in Finland

Lycos, Yahoo,NOT Excite, NOT Infoseek

NOKIA prices

Infoseek, Yahoo,NOT LycosArtificial Intelligence

Results of Agents’ Competence Evaluation (based on SC and SD sets)

… Selection proposals obtained from the agent Fox should be accepted if they concern search machines Infoseek and Lycos or search problems related to “Fishing in Finland” and “Artificial Intelligence”, and these proposals should be rejected if they concern AltaVista or “NOKIA Prices”. In some cases it seems to be possible to accept selection proposals from the agent Fox if they concern Excite and Yahoo. All four agents are expected to give an acceptable selection concerning “Artificial Intelligence” related search and only suggestion of the agent Cat can be accepted if it concerns “NOKIA Prices” search ...

Deriving Internal Similarity Values

Set A Set I

A’

A”

A’I

IA”

A’A”I

A’

A”

a)

Set A

Set I

A’

A”

A’I

JA”

A’A”IJ

A’

A”

b)

Set J

IJ

Via one intermediate set Via two intermediate sets

Internal Similarity for Agents:Problems-based Similarity

D C

SS’S’’D

S’’

S’DS’’

S’D

S S S S S S S D DSD' '' ' '' ' '',

Problems

Agents

Internal Similarity for Agents:Solutions-Based Similarity

D C

SS’S’’C

S’’

S’

CS’’

S’C

S S S S S S S C CSC' '' ' '' ' '',

Solutions

Agents

Internal Similarity for Agents:Solutions-Problems-Based Similarity

D C

SS’S’’CD

S’’

S’DS’’S’C

CD

S S S S S S S C CD DSCD' '' ' '' ' '',

Agents

SolutionsProblems

Conclusion

Discussion was given to methods of deriving the total support of each binary similarity relation. This can be used, for example, to derive the most supported solution and to evaluate the agents according to their competence

We also discussed relations between elements taken from the same set: problems, solutions, or agents. This can be used, for example, to divide agents into groups of similar competence relatively to the problems-solutions environment