Download A Similarity Evaluation Technique for Cooperative Problem

Third International Workshop CIA-99
Cooperative Information Agents
A Similarity Evaluation Technique
for Cooperative Problem Solving
with a Group of Agents
Seppo Puuronen, Vagan Terziyan
July 31 - August 2, 1999
Uppsala (Sweden)
Authors
Seppo Puuronen
[email protected]
Vagan Terziyan
[email protected]
Department of Computer
Science and Information
Systems
University of Jyvaskyla
FINLAND
Department of Artificial Intelligence
Kharkov State Technical
University of Radioelectronics,
UKRAINE
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
 1,if the agent Sk selects solution C j

 to solve the problem Di ;
 1,if Sk refuses to select C j
P(Di ,C j ,Sk )  
 to solve Di ;
 0,if Sk does not select or refuse

 to select C j to solve Di .
Problem 1:
Deriving External Similarity Values
D
C
DCi,j
Di
Cj
SDk,i
SCk,j
S
Sk
External Similarity Values
D
C
DCi,j
Di
Cj
SDk,i
SCk,j
S
Sk
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
Di’’
D
Cj’’
C
DDi’,i’’
CCj’,j’’
Cj’
Di’
Sk’’
S
SSk’,k’’
Sk’
Internal Similarity Values
Di’’
D
Cj’’
C
DDi’,i’’
CCj’,j’’
Cj’
Di’
Sk’’
S
SSk’,k’’
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
r
DCi , j  CD j ,i   P ( Di , C j , S k ), Di  D, C j  C
k
Problems D
C
DCi,j=3
Di
Cj
1
S
Agents
Sk
3
Sk
2
Sk
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.
n
SCk , j  CS j ,k   DCi, j  P ( Di , C j , Sk ), Sk  S, C j  C
i
Example of SC Relation
CDj1 = -3
D1
CDj2 = 6
D2
D
Problems
C
CDj3 = 0
D3
D4
Cj
CDj4 = 1
Solutions
SCk,j=4
Agents
S
Sk
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.
m
SDk ,i  DSi,k   DCi, j  P( Di , C j , Sk ), Sk  S, Di  D
j
Example of SD Relation
D
Di
C
CD1i = -3
C1
CD2i = 5
C2
Problems
Solutions
SDk,i=2
S
Sk
Agents
Standardizing External
Relations to the Interval [0,1]
value - min( value )
standardizing value   value =
max(value) - min(value)
 DCi , j   CD j ,i 
 SC  k , j   CS  j , k 
 SD k ,i   DS i , k 
DCi , j  r
2r
SCk , j  n  (r  2)
2  n  (r  1)
SDk ,i  m  (r  2)
2  m  (r  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
n
1
Q ( Sk )    SD k ,i
n i
D
- 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
m
1
Q ( Sk )    SC
m j
C
k, j
- measure of the abilities of an agent in the area
of solutions from the support point of view
Quality Balance Theorem
Q ( Sk )  Q ( Sk )
D
C
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
1 n
Q ( Sk )    SD
n i
D
k ,i
1 n SDk ,i  m  ( r  2 )
 

n i
2  m  ( r  1)
m

n
1

n i
 ( DCi, j  P( Di , Cj , Sk ))  m  ( r  2 )
j

2  m  ( r  1)
...
n
...

m
1

m j
 ( DCi, j  P( Di , C j , Sk ))  n  ( r  2 )
i
2  n  ( r  1)
1 m SCk , j  n  (r  2) 1 m
 
    SC k , j  QC ( Sk )
m j
2  n  (r  1)
m j

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
Example
Solutions - search machines
AltaVista
Excite
Infoseek
Lycos
Yahoo
Notation
C1
C2
C3
C4
C5
S (agents) Set in the Example
Agents
Fox
Wolf
Cat
Hare
Notation
S1
S2
S3
S4
D (problems) Set in the
Example
Search problems with keywords
Fishing in Finland
D1
NOKIA prices
D2
Artificial intelligence
D3
Selections Made for the Problem
“Fishing in Finland”
P(D,C,S)
S1
S2
S3
S4
C1
1
0+
0
1
C2
-1
-1**
0
-1
D1
C3
-1
0 ++
-1
0
C4
0
1*
1
0
C5
-1
-1***
0
1
Agent 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”
P
S1
S2
S3
S4
C1
-1
1
1
-1
C2
0
-1
-1
0
D2
C3
-1
-1
0
0
C4
0
0
1
1
C5
1
0
1
0
Selections Made for the Problem
“Artificial Intelligence”
P
S1
S2
S3
S4
C1
1
0
-1
-1
C2
0
1
-1
-1
D3
C3
1
0
1
1
C4
-1
-1
-1
-1
C5
0
1
1
1
Result of Cooperative Problem
Solution Based on DC Relation
fishing in Finland
AltaVista, Lycos,
NOT Excite, NOT Infoseek
NOKIA prices
Lycos, Yahoo,
NOT Excite, NOT Infoseek
Artificial Intelligence
Infoseek, Yahoo,
NOT Lycos
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
Via one intermediate set
a)
A’
Set A
A”
A’
A’I
Set I
IA”
A’A”I
A”
Via two intermediate sets
A’I
b)
Set I
A’
IJ
Set A
A”
JA”
Set J
A’
A’A”IJ
A”
Internal Similarity for Agents:
Problems-based Similarity
Problems D
C
S’D
DS’’
S’
S’S’’D
S’’
S
' '' D
S  S, S  S  S S
'
''
Agents
 S D  DS
'
''
Internal Similarity for Agents:
Solutions-Based Similarity
Solutions
C
D
CS’’
S’C
S’
Agents
S’S’’C
S’’
S
' '' C
S  S, S  S  S S
'
''
 S C  CS
'
''
Internal Similarity for Agents:
Solutions-Problems-Based Similarity
Problems
Solutions
CD
C
D
S’
DS’’
S’C
S’S’’CD
S’’
S
' '' CD
S  S, S  S  S S
'
''
Agents
 S'C  CD  DS''
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