Node deletion sequences in influence diagrams using genetic algorithms

Statistics and Computing

Volumn 14, Issue 3, 2004, Pages 181-198

  Gomez M ^a   Bielza, C ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

decision making under uncertainty; genetic algorithms; influence diagrams; node deletion sequence; NP hard problems; statistical analysis

Indexed keywords

EID: 3843058989     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:STCO.0000035300.39728.03     Document Type: Article

References (41)

1. Alander J.T. 1992. On optimal population size of genetic algorithms. In: Proc. CompEuro 1992, Comput. Sys. and Soft. Engineer., 6th Annual European Computer Conf., pp. 65-70.
2. Amir E. 2001. Efficient approximation for triangulation of minimum treewidth, In: Koller D. and Breese J. (Eds.). Proc. 17th Conf. on Uncertainty in Artificial Intelligence, San Francisco, CA, Morgan Kaufmann, pp. 7-15.
3. Arnborg S., Corneil D., and Proskurowski, A. 1987. Complexity of finding embeddings in a k-tree. SIAM Journal Algebraic Discrete Methods 8:277-284.
4. Bielza C., Gómez M., Ríos-Insua S., and Fernández del Pozo J.A. 2000. Structural, elicitation and computational issues faced when solving complex decision problems with influence diagrams. Computers and Operations Research 27(7/8):725-740.
5. Bielza C. and Shenoy P.P. 1999. A comparison of graphical techniques for asymmetric decision problems. Management Science 45(11): 1552-1569.
6. Cano A. and Moral S. 1994. Heuristic algorithms for the triangulation of graphs. In: Proc. 5th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge Based Systems (IPMU), Vol. 1, pp. 166-171.
7. Chew E.P., Ong C.J., and Lim K.H. 2002. Variable period adaptive genetic algorithm. Computers & Industrial Engineering 42(2-4):353-360.
8. Clemen R.T. 1996. Making Hard Decisions: An Introduction to Decision Analysis, 2nd edition. Duxbury, Belmont, CA.
9. Cooper G.F. 1988. A method for using belief networks as influence diagrams. In: Proc. Workshop on Uncertainty in Artificial Intelligence, Minneapolis, Minnesota, pp. 55-63.
10. Cooper G.F. 1990. The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence 42:393-405.
11. De Jong K.A. 1975. An analysis of the behavior of a class of genetic adaptive systems. PhD. Diss., University of Michigan.
12. Ezawa K.J. 1986. Efficient evaluation of influence diagrams. PhD. Diss., Dept. of Engineering-Economic Systems, Stanford University, Stanford, CA.
13. Fogarty T.C. 1989. Varying the probability of mutation in the genetic algorithm. In: Proc. Third Int. Conf. on Genetic Algorithms, pp. 104-109.
14. Gómez, M. 2002. IctNeo: A decision support system for neonatal jaundice treatment. PhD. Diss., Dept. of Artificial Intelligence, Technical University of Madrid, Spain.
15. Henrion M. 1989. Some practical issues in constructing belief networks. Uncertainty in Artificial Intelligence 3:161-173.
16. Holland J. 1975. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.
17. Howard R.A. and Matheson J.E. 1984. Influence diagrams. In: Howard R. and Matheson J. (Eds.), The Principles and Applications of Decision Analysis, Vol. II, Menlo Park, CA, Strategic Decisions Group, pp. 719-762.
18. Hsu J.C. 1996. Multiple Comparisons: Theory and Methods. Chapman & Hall, London.
19. Jensen F.V. 2001. Bayesian Networks and Decision Graphs. Springer, New York.
20. Jensen F., Jensen F.V., and Dittmer S.L. 1994. From influence diagrams to junction trees. In: Mantaras R.L. and Poole D. (Eds.), Proc. 10th Conf. on Uncertainty in Artificial Intelligence, San Mateo, CA, Morgan Kaufmann, pp. 367-373.
21. Kirkwood C.W. 1997. Strategic Decision Making. Multiobjective Decision Analysis with Spreadsheets, Duxbury, Belmont, CA.
22. Kjaerulff U. 1992. Optimal decomposition of probabilistic networks by simulated annealing. Statistics and Computing 2:7-17.
23. Kong A. 1986. Multivariate belief functions and graphical models. Ph.D. Diss., Dept. of Statistics, Harvard University, Cambridge, MA.
24. Larrañaga P., Kuijpers C.M.H., Poza M., and Murga R.H. 1997. Decomposing Bayesian networks: triangulation of the moral graph with genetic algorithms. Statistics and Computing 7(1):19-34.
25. Larrañaga P., Kuijpers C.M.H., Murga R.H., Inza I., and Dizdarevic S. 1999. Genetic algorithms for the travelling salesman problem: A review of representations and operators. Artificial Intelligence Review 13:129-170.
26. Madsen A.L. and Jensen F.V. 1999. Lazy evaluation of symmetric Bayesian decision problems. In: Laskey K.B. and Prade H. (Eds.), Proc. 15th Conf. on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, pp. 382-390.
27. Mahfoud S.W. 1995. Niching methods for genetic algorithms. Ph.D. Diss., University of Illinois, Champaigne, IL.
28. Mellouli K. 1987. On the propagation of beliefs in networks using the Dempster-Shafer theory of evidence. PhD. Diss., School of Business, University of Kansas, Lawrence, KS.
29. Michalewicz Z. 1992. Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin.
30. Mitchell M. 1998. An Introduction to Genetic Algorithms. MIT Press, Cambridge, MA.
31. Nielsen T.D. and Jensen F.V. 1999. Welldefined decision scenarios. In Laskey K.B. and Prade H. (Eds.), Proc. 15th Conf. on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, pp. 502-511.
32. Shachter R.D. 1986. Evaluating influence diagrams. Operations Research 34(6):871-882.
33. Shachter R.D., Andersen S.K., and Poh K.L. 1990. Directed reduction algorithms and decomposable graphs. In: Bonissone P., Henrion M., Kanal L., and Lemmer J. (Eds.), Proc. 6th Conf. on Uncertainty in Artificial Intelligence. Elsevier, New York, NJ, pp. 237-244.
34. Shachter R.D., Andersen S.K., and Szolovits P. 1994. Global conditioning for probabilistic inference in belief networks. In: López de Mántaras R. and Poole D. (Eds.), Proc. 10th Conf. on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, pp. 514-522.
35. Shachter R.D. and Ndilikilikesha P. 1993. Using potential influence diagrams for probabilistic inference and decision making. In: Heckerman D. and Mamdani A. (Eds.), Proc. 9th Conf. on Uncertainty in Artificial Intelligence, pp. 383-390.
36. Shenoy P.P. 1992. Valuation-based systems for Bayesian decision analysis. Operations Research 40(3):463-484.
37. Shoikhet K. and Geiger D. 1997. A practical algorithm for finding optimal triangulations. In: Proc. 14th Nat. Conf. on Artificial Intelligence. AAAI Press, Menlo Park, CA, pp. 185-190.
38. Tatman J.A. and Shachter R.D. 1990. Dynamic programming and influence diagrams. IEEE Transactions on Systems, Man and Cybernetics 20(2):365-379.
39. Venables W. and Ripley B. 1994. Modern Applied Statistics with S-Plus. Springer, New York.
40. Zhang N.L. 1993. Studies on hypergraphs I: hyperforests. Discrete Applied Mathematics 42:95-112.
41. Zhang N.L. 1998. Probabilistic inference in influence diagrams. In: Cooper G.F. and Moral S. (Eds.), Proc. 14th Conf. on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, pp. 514-522.