1. A Similarity Evaluation Technique for Cooperative Problem Solving with a Group of Agents Seppo Puuronen, Vagan Terziyan Third International Workshop CIA-99 Cooperative Information Agents July 31 - August 2, 1999 Uppsala (Sweden)

2. 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 vagan@jytko.jyu.fi sepi@jytko.jyu.fi

3. Contents 4 The Research Goal 4 Basic Concepts 4 External Similarity Evaluation 4 An Example 4 Internal Similarity Evaluation 4 Conclusions

4. Goal 4 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 4 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: D is the set of problems D 1, D 2,..., D n in the VTE; C is the set of solutions C 1, C 2,..., C m, that are used to solve the problems; S is the set of agents S 1, S 2,..., S r, 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) ? 4 Distance between problems is used by agents to recognize nearest solved problems for any new problem 4 distance between solutions is necessary to compare and evaluate solutions made by different agents 4 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 Agents Problems Solutions

13. Deriving External Relation SC: Measures Agents Competence in the Area of Solutions 4 The value of the relation (S k,C j ) in a way represents the total support that the agent S k obtains selecting (refusing to select) the solution C j to solve all the problems.

14. Example of SC Relation Agents Problems Solutions

15. Deriving External Relation SD: Measures Agents Competence in the Problem’s Area 4 The value of the relation (S k,D i ) represents the total support that the agent S k receives selecting (or refusing to select) all the solutions to solve the problem D i.

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. Agent’s 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. 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

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 4 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. 4 The agents should define their selection of appropriate search machine for every search problem. 4 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 AltaVistaC 1 ExciteC 2 InfoseekC 3 LycosC 4 YahooC 5

24. S (agents) Set in the Example Agents Notation FoxS 1 WolfS 2 CatS 3 HareS 4

25. D (problems) Set in the Example

26. Selections Made for the Problem “Fishing in Finland” D 1 P(D,C,S) C 1 C 2 C 3 C 4 C 5 S 1 1-1-10-1 S 2 0 + -1 ** 0 ++ 1 * -1 *** S 3 00-110 S 4 1-1001 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” D 2 PC 1 C 2 C 3 C 4 C 5 S 1 -10-101 S 2 1-1-100 S 3 1-1011 S 4 -10010

28. Selections Made for the Problem “Artificial Intelligence” D 3 PC 1 C 2 C 3 C 4 C 5 S 1 101-10 S 2 010-11 S 3 -1-11-11 S 4 -1-11-11

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 setVia 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 Agents Solutions Problems

35. Conclusion 4 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 4 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