Lower and upper bounds for linkage discovery

IEEE Transactions on Evolutionary Computation

Volumn 13, Issue 2, 2009, Pages 201-216

  Choi, Sung Soon ^a   Jung, Kyomin ^b   Moon, Byung Ro ^c  

^a Yonsei University   (South Korea)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Seoul National University   (South Korea)

Author keywords

Black box scenario; Complexity analysis; Linkage discovery; Linkage graph; Lower and upper bounds; Walsh analysis

Indexed keywords

BLACK BOX SCENARIO; COMPLEXITY ANALYSIS; LINKAGE DISCOVERY; LINKAGE GRAPH; LOWER AND UPPER BOUNDS; WALSH ANALYSIS;

CONTROL THEORY; GRAPH THEORY;

FUNCTION EVALUATION;

EID: 67349266615     PISSN: 1089778X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TEVC.2008.928499     Document Type: Article

References (40)

1. J. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor: Univ. Michigan Press, 1975.
2. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison Wesley, 1989.
3. T. N. Bui and B. R. Moon, "Genetic algorithm and graph partitioning," IEEE Trans. Comput., vol. 45, no. 7, pp. 841-855, Jul. 1996.
4. T. N. Bui and B. R. Moon, "GRCA: A hybrid genetic algorithm for circuit ratio-cut partitioning," IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 17, no. 3, pp. 193-204, Mar. 1998.
5. I. Hwang, Y. H. Kim, and B. R. Moon, "Multi-attractor gene reordering for graph bisection," in Proc. Genetic Evolut. Comput. Conf., 2006, pp. 1209-1216.
6. D. E. Goldberg, B. Korb, and K. Deb, "Messy genetic algorithms: Motivation, analysis, and first results," Complex Syst., vol. 5, no. 3, pp. 493-530, 1989.
7. D. E. Goldberg, K. Deb, and B. Korb, "Messy genetic algorithms revisited: Studies in mixed size and scale," Complex Syst., vol. 4, pp. 415-444, 1990.
8. D. E. Goldberg, K. Deb, H. Kargupta, and G. R. Harik, "Rapid accurate optimization of difficult problems using fast messy genetic algorithms," in Proc. 5th Int. Conf. Genetic Algorithms, 1993, pp. 56-64.
9. H. Kargupta, "The gene expression messy genetic algorithm," in Proc. Int. Conf. Evolut. Comput., 1996, pp. 814-819.
10. G. R. Harik and D. E. Goldberg, "Learning linkage," in Foundations of Genetic Algorithms. San Mateo, CA: Morgan Kaufmann, 1997, vol. 4, pp. 247-262.
11. R. P. Salustowicz and J. Schmidhuber, "Probabilistic incremental program evolution: Stochastic search through program space," in Machine Learning: ECML-97. New York: Springer-Verlag, 1997, vol. 1224, pp. 213-220.
12. G. R. Harik, F. G. Lobo, and D. E. Goldberg, "The compact genetic algorithm," in Proc. IEEE Conf. Evolut. Comput., 1998, pp. 523-528.
13. J. S. de Bonet, C. L. Isbell, Jr., and P. Viola, "MIMIC: Finding optima by estimating probability densities," in Advances in Neural Information Processing Systems. Cambridge, MA: The MIT Press, 1997, vol. 9, pp. 424-430.
14. M. Pelikan and H. Muhlenbein, "The bivariate marginal distribution algorithm," in Advances in Soft Computing - Engineering Design and Manufacturing. New York: Springer-Verlag, 1999, pp. 521-535.
15. M. Pelikan, D. E. Goldberg, and E. Cantú-Paz, "BOA: The Bayesian optimization algorithm," in Proc. Genetic Evolut. Comput. Conf., 1999, pp. 525-532.
16. M. Pelikan and D. E. Goldberg, "Hierarchical problem solving by the Bayesian optimization algorithm," in Proc. Genetic Evolut. Comput. Conf., 2000, pp. 267-274.
17. H. Mühlenbein and T. Mahnig, "FDA - A scalable evolutionary algorithm for the optimization of additively decomposed functions," Evolut. Comput., vol. 7, no. 1, pp. 45-68, 1999.
18. M. J. Streeter, "Upper bounds on the time and space complexity of optimizing additively separable functions," in Proc. Genetic Evolut. Comput. Conf., 2004, pp. 186-197.
19. A. H. Wright and S. Pulavarty, "On the convergence of an estimation of distribution algorithm based on linkage discovery and factorization," in Proc. Genetic Evolut. Comput. Conf., 2005, pp. 695-702.
20. S. Rana, R. B. Heckendorn, and D. Whitley, "A tractable walsh analysis of SAT and its implications for genetic algorithms," in Proc. l5th Nat. Conf. Artif. Intell., 1998, pp. 392-397.
21. A. Braunstein, M. Mézard, M. Weigt, and R. Zecchina, "Constraint satisfaction by survey propagation," CoRR, vol. cond-mat/0212451, 2002 [Online]. Available: http://arxiv.org/ abs/cond-mat/0212451
22. S. Droste, T. Jansen, and I. Wegener, "Upper and lower bounds for randomized search heuristics in black-box optimization," Theory Comput. Syst., vol. 39, no. 4, pp. 525-544, 2006.
23. R. B. Heckendorn and A. H. Wright, "Efficient linkage discovery by limited probing," in Proc. Genetic Evolut. Comput. Conf., 2003, pp. 1003-1014.
24. R. B. Heckendorn and A. H. Wright, "Efficient linkage discovery by limited probing," Evolut. Comput., vol. 12, no. 4, pp. 517-545, 2004.
25. H. Kargupta and B. Park, "Gene expression and fast construction of distributed evolutionary representation," Evolut. Comput., vol. 9, no. 1, pp. 1-32, 2001.
26. A. C. Yao, "Probabilistic computations: Toward a unified measure of complexity," in Proc. 18th Annu. IEEE Symp. Found. Comput. Sci., 1977, pp. 222-227.
27. J. B. Kruskal, R. Bellman, Ed., "The number of simplices in a complex," in Mathematical Optimization Techniques. Berkeley, CA: Univ. California Press, 1963, pp. 251-278.
28. G. O. H. Katona, "A theorem of finite sets," in Theory of Graphs P. Erdos and G. O. H. Katona, Eds. New York: Academic, 1968, pp. 187-207.
29. M. Pelikan and D. E. Goldberg, "Hierarchical BOA solves Ising spin glasses and MAXSAT," in Proc. Genetic Evolut. Comput. Conf., 2003, pp. 1271-1282.
30. S. H. Kim, Y. H. Kim, and B. R. Moon, "A hybrid genetic algorithm for the MAX CUT problem," in Proc. Genetic Evolut. Comput. Conf., 2001, pp. 416-423.
31. A. H. Wright, R. K. Thompson, and J. Zhang, "The computational complexity of NK fitness functions," IEEE Trans. Evolut. Comput., vol. 4, no. 4, pp. 373-379, Nov. 2000.
32. Y. Gao and J. Culberson, "Space complexity of estimation of distribution algorithms," Evolut. Comput., vol. 13, no. 1, pp. 125-143, 2005.
33. R. Motwani and P. Raghavan, Randomized Algorithms. Cambridge, U.K.: Cambridge Univ. Press, 1995.
34. M. Munetomo and D. E. Goldberg, "Identifying linkage groups by nonlinearity/non-monotonicity detection," in Proc. Genetic Evolut. Comput. Conf., 1999, pp. 433-440.
35. J. L. Walsh, "A closed set of orthogonal functions," Amer. J. Math. vol. 55, pp. 5-24, 1923.
36. R. B. Heckendorn and D. Whitley, "Predicting epistasis directly from mathematical models," Evolut. Comput., vol. 7, no. 1, pp. 69-101, 1999.
37. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, 2nd ed. Reading, MA: Addison Wesley, 1994.
38. L. Lovász, Combinatorial Problems and Exercises, 2nd ed. Amsterdam, The Netherlands: North-Holland, 1993.
39. S. S. Choi, Y. K. Kwon, and B. R. Moon, "Properties of symmetric fitness functions," IEEE Trans. Evolut. Comput., vol. 11, no. 6, pp. 743-757, Dec. 2007.
40. D. J. Coffin and C. D. Clack, "gLINC: Identifying composability using group perturbation," in Proc. Genetic Evolut. Comput. Conf., 2006, pp. 1133-1140.