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A Similarity Evaluation Technique for Cooperative Problem Solving with a Group of Agents

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Third International Workshop CIA-99. Cooperative Information Agents. July 31 - August 2, 1999 ... proposals obtained from the agent Fox should be accepted if ... – PowerPoint PPT presentation

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Title: A Similarity Evaluation Technique for Cooperative Problem Solving with a Group of Agents


1
A Similarity Evaluation Technique for Cooperative
Problem Solving with a Group of Agents
Third International Workshop CIA-99 Cooperative
Information Agents
  • Seppo Puuronen, Vagan Terziyan

July 31 - August 2, 1999 Uppsala (Sweden)
2
Authors
Seppo Puuronen
sepi_at_jytko.jyu.fi
Vagan Terziyan
vagan_at_jytko.jyu.fi
Department of Computer Science and Information
Systems University of Jyvaskyla FINLAND
Department of Artificial Intelligence Kharkov
State Technical University of Radioelectronics,
UKRAINE
3
Contents
  • The Research Goal
  • Basic Concepts
  • External Similarity Evaluation
  • An Example
  • Internal Similarity Evaluation
  • Conclusions

4
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

5
Basic Concepts Virtual Training Environment (VTE)
  • VTE of a group of agents is a quadruple
  • ltD,C,S,Pgt
  • 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

6
Basic Concepts Semantic Predicate P
7
Problem 1 Deriving External Similarity Values
8
External Similarity Values
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)
9
Problem 2 Deriving Internal Similarity Values
10
Internal Similarity Values
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)
11
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.

12
Deriving External Relation DC How well solution
fits the problem
Solutions
Problems
Agents
13
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.

14
Example of SC Relation
Solutions
Problems
Agents
15
Deriving External Relation SD Measures Agents
Competence in the Problems 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.

16
Example of SD Relation
Problems
Solutions
Agents
17
Standardizing External Relations to the Interval
0,1
n is the number of problems m is the number of
solutions r is the number of agents
18
Agents Evaluation Competence Quality in Problem
Area
- measure of the abilities of an agent in the
area of problems from the support point of view
19
Agents Evaluation Competence Quality in
Solutions Area
- measure of the abilities of an agent in the
area of solutions from the support point of view
20
Quality Balance Theorem
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.
21
Proof
...
...
22
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.

23
C (solutions) Set in the Example
  • Solutions - search machines Notation
  • AltaVista C1
  • Excite C2
  • Infoseek C3
  • Lycos C4
  • Yahoo C5

24
S (agents) Set in the Example
  • Agents Notation
  • Fox S1
  • Wolf S2
  • Cat S3
  • Hare S4

25
D (problems) Set in the Example
26
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 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.
27
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

28
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

29
Result of Cooperative Problem Solution Based on
DC Relation
30
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
    ...

31
Deriving Internal Similarity Values
Via one intermediate set
Via two intermediate sets
32
Internal Similarity for Agents Problems-based
Similarity
Problems
Agents
33
Internal Similarity for Agents Solutions-Based
Similarity
Solutions
Agents
34
Internal Similarity for Agents Solutions-Problems
-Based Similarity
Problems
Solutions
Agents
35
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
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