An information-theoretic analysis on the interactions of variables in combinatorial optimization problems

Evolutionary Computation

Volumn 15, Issue 2, 2007, Pages 169-198

  Seo, Dong Il ^a   Moon, Byung Ro ^a  

^a Seoul National University   (South Korea)

Author keywords

Combinatorial optimization; Entropic epistasis; Entropy; Linkage; Mutual information; Variable interaction

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BIOLOGY; EVOLUTION; GENETIC EPISTASIS; INFORMATION SCIENCE; STATISTICAL MODEL;

ALGORITHMS; COMPUTATIONAL BIOLOGY; EPISTASIS, GENETIC; EVOLUTION; INFORMATION THEORY; MODELS, GENETIC; MODELS, STATISTICAL;

EID: 34447544454     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/evco.2007.15.2.169     Document Type: Article

References (31)

1. Bethke, A. D. (1981). Genetic Algorithms as Function Optimizers. Ph.D. thesis, University of Illinois, Urbana, IL.
2. Boese, K. D., Kahng, A. B., and Muddu, S. (1994). A new adaptive multi-start technique for combinatorial global optimizations. Operations Research Letters, 16(2):101-113.
3. Bui, T. N. and Moon, B. R. (1994). A new genetic approach for the traveling salesman problem. In Michalewicz, Z. et al., editors, Proc. IEEE Conference on Evolutionary Computation, pages 7-12, IEEE Press, Piscataway, NJ.
4. Chiu, D., Wong, A., and Cheung, B. (1991). Information discovery through hierarchical maximum entropy discretization and synthesis. In Piatetsky-Shapiro, G. and Frawley, W. J., editors, Knowledge Discovery in Databases. The MIT Press, Cambridge, MA.
5. Cover, T. and Thomas, J. (1991). Elements of Information Theory. John Wiley & Sons, New York.
6. Davidor, Y. (1990). Epistasis variance: Suitability of a representation to genetic algorithms. Complex Systems, 4(4):369-383.
7. Forrest, S. and Mitchell, M. (1993). Relative building-block fitness and the buildingblock hypothesis. In Whitley, L. D., editor, Foundations of Genetic Algorithms 2, pages 109-126, Morgan Kaufmann Publishers, San Francisco, CA.
8. Garey, M. R. and Johnson, D. S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York.
9. Goldberg, D. E. (1987). Simple genetic algorithms and the minimal deceptive problem. In Davis, L., editor, Genetic Algorithms and Simulated Annealing, pages 74-88, Morgan Kaufmann Publishers, San Francisco, CA.
10. Goldberg, D. E. (1989a). Genetic algorithms and Walsh functions: Part I, a gentle introduction. Complex Systems, 3:129-152.
11. Goldberg, D. E. (1989b). Genetic algorithms and Walsh functions: Part II, deception and its analysis. Complex Systems, 3:153-171.
12. Heckendorn, R. B. and Wright, A. H. (2004). Efficient linkage discovery by limited probing. Evolutionary Computation, 12(4):517-545.
13. Holland, J. (1992). Adaptation in Natural and Artificial Systems. The MIT Press, Cambridge, MA.
14. Horn, J. and Goldberg, D. E. (1995). Genetic algorithm difficulty and the modality of fitness landscapes. In Whitley, L. D. and Vose, M. D., editors, Foundations of Genetic Algorithms 3, pages 243-270, Morgan Kaufmann Publishers, San Francisco, CA.
15. Jones, T. and Forrest, S. (1995). Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In Eshelman, L. J., editor, Proceedings International Conference on Genetic Algorithms, pages 184-192, Morgan Kaufmann Publishers, San Francisco, CA.
16. Kargupta, H. (1995). Signal-to-noise, crosstalk, and long range problem difficulty in genetic algorithms. In Eshelman, L. J., editor, Proceedings International Conference on Genetic Algorithms, pages 193-200, Morgan Kaufmann Publishers, San Francisco, CA.
17. Kauffman, S. A. (1989). Adaptation on rugged fitness landscapes. In Stein, D. L., editor, Lectures in the Sciences of Complexity, pages 527-618. Addison-Wesley, Reading, MA.
18. Larrañaga, P. and Lozano, J. A. (2002). Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Boston, MA.
19. Lin, S. and Kernighan, B. (1973). An effective heuristic algorithm for the traveling salesman problem. Operations Research, 21(2):498-516.
20. Munetomo, M. and Goldberg, D. E. (1999). Linkage identification by non-monotonicity detection for overlapping functions. Evolutionary Computation, 7(4):377-398.
21. Pelikan, M., Goldberg, D. E., and Lobo, F. (2002). A survey of optimization by building and using probabilistic models. Computational Optimization and Applications, 21(1):5-20.
22. Rana, S., Heckendorn, R. B., and Whitley, D. (1998). A tractable Walsh analysis of SAT and its implications for genetic algorithms. In Rich, C. and Mostow, J., editors, Proceedings National Conference on Artificial Intelligence, pages 392-397, AAAI Press, Menlo Park, CA.
23. Reeves, C. R. and Wright, C. C. (1995a). An experimental design perspective on genetic algorithms. In Whitley, L. D. and Vose, M. D., editors, Foundations of Genetic Algorithms 3, pages 7-22, Morgan Kaufmann Publishers, San Francisco, CA.
24. Reeves, C. R. and Wright, C. C. (1995b). Epistasis in genetic algorithms: An experimental design perspective. In Eshelman, L. J., editor, Proceedings International Conference on Genetic Algorithms, pages 217-224, Morgan Kaufmann Publishers, San Francisco, CA.
25. Seo, D. L., Kim, Y. H., and Moon, B. R. (2003a). New entropy-based measures of gene significance and epistasis. In Cantú-Paz, E. et al., editors, Genetic and Evolutionary Computation Conference, pages 1345-1356, Springer-Verlag, Berlin, Germany.
26. Seo, D. I. and Moon, B. R. (2002). Voronoi quantized crossover for traveling salesman problem In Langdon, W. B. et al., editors, Genetic and Evolutionary Computation Conference, pages 544-552, Springer-Verlag, Berlin, Germany.
27. Seo, D. I. and Moon, B. R. (2003). A survey on chromosomal structures and operators for exploiting topological linkages of genes. In Cantú-Paz, E. et al., editors, Genetic and Evolutionary Computation Conference, pages 1357-1368, Springer-Verlag, Berlin, Germany.
28. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27:379-423, 623-656.
29. Streeter, M. J. (2004). Upper bounds on the time and space complexity of optimizing additively separable functions. In Deb, K. et al., editors, Genetic and Evolutionary Computation Conference, pages 186-197, Springer-Verlag, Berlin, Germany.
30. Theil, H. (1972). Statistical Decomposition Analysis. North-Holland Publishing Company, Amsterdam, Netherlands.
31. Weinberger, E. D. (1996). NP completeness of Kauffman's NK model, a tunable rugged fitness landscape. Technical report 96-02-003, Santa Fe Institute, Santa Fe, NM.