New global optima results for the Kauffman NK model: Handling dependency

Mathematical Programming

Volumn 108, Issue 2-3, 2006, Pages 475-494

  Kaul, Hemanshu ^a   Jacobson, Sheldon H ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Concentration of measure; Dependency graph; Equitable coloring of graphs; NK model; Order statistics; Stochastic combinatorial optimization

Indexed keywords

GRAPH THEORY; LARGE SCALE SYSTEMS; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING;

CONCENTRATION OF MEASURE; DEPENDENCY GRAPH; EQUITABLE COLORING OF GRAPHS; NK MODEL; ORDER STATISTICS; STOCHASTIC COMBINATORIAL OPTIMIZATION;

MATHEMATICAL MODELS;

EID: 33745712302     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0719-3     Document Type: Article

References (37)

1. Alon, N., Spencer, J.H.: The probabilistic method 2nd edn. John Wiley & Sons, (2000)
2. Arnold, B.C., Groeneveld, R.A. : Bounds on expectations of linear systematic statistics based on dependent samples. Ann. Statist. 7 (1), 220-223 (1979)
3. Balakrishna, N., Rao, C.R.: Order Statistics - An Introduction. In: N. Balakrishna, C.R Rao (eds.), Order Statistics - Theory and Methods, Elsevier Science B.V., 1998
4. David, H.A.: Order statistics 2nd edn. John Wiley & Sons, 1981
5. Derrida, B.: Random-energy model - An exactly solvable model of disordered systems. Phys. Rev. B, Condensation Matter 24, 2613-2626 (1981)
6. Durrett, R., Limic, V.: Rigorous results for the N K model. Ann. Probab. 31 (4), 1713-1753 (2003)
7. Evans, M., Hastings, N., Peacock, J.B.: Statistical Distributions, 3rd edn. Wiley, 2000
8. Evans, S.N., Steinsaltz, D.: Estimating some features of NK fitness landscapes. Ann. Appl. Prob. 12, 1299-1321 (2002)
9. Flyvbjerg, H., Lautrup, B.: Evolution in a rugged landscape. Phys. Rev. A, At. Mol. Opt. Phys. 46, 6714-6723 (1992)
10. Frieze, A.: On random symmetric travelling salesman problems. Math. Oper. Res. 29, 878-890 (2004)
11. Gao, Y., Culberson, J.: An analysis of phase transition in NK landscapes. J. Artificial Intelligence Res. 17, 309-332 (electronic) (2002)
12. Gascuel, O., Caraux, G.: Bounds on expectations of order statistics via extremal dependences. Statist. Probab. Lett. 15 (2), 143-148 (1992)
13. Geard, N., Wiles, J., Halliman, J., Tonkes, B., Skellet, B.: A comparison of neutral landscapes - NK, NKp, NKq. Preprint, University of Queensland, Brisbane, Australia, 2003
14. Hajnal, A., Szemerédi, E.: Proof of a conjecture of P. Erdös. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfüred, 1969), North-Holland, (1970), pp. 601-623
15. Hastings, C.: Approximations for digital computers. Princeton University Press, 1955
16. Hill, S., O'Riordan, C.: Genetic Algorithms, their Operators and the NK Model. Preprint, National University of Ireland, Galway, 2001
17. Hill, S., O'Riordan, C.: Analysis of the performance of Genetic Algorithms and their Operators using Kauffman's NK Model. Preprint, National University of Ireland, Galway, 2002
18. Kauffman, S.A.: The Origins of Order. Oxford University Press, Oxford, 1993
19. Kauffman, S.A., Levin, S.: Towards a general theory of adaptive walks on rugged landscapes. J. Theor. Biol. 128, 11-45 (1987)
20. Kauffman, S.A., Weinberger, E.D., Perelson, A.S. : Maturation of the immune response via adaptive walks on affinity landscapes. In : A. S Perelson (ed.), Theoretical Immunology, Part I, SFI studies in the Sciences of Complexity, Addison-Wesley, 1988, pp 349-382
21. Kaul, H., Jacobson, S.H.: Global optima results for the Kauffman NK model. Mathematical Programming 106, 318-319 (2006)
22. Levinthal, D.A.: Adaptation on rugged landscapes. Management Sci. 43, 934-950 (1997)
23. Limic, V., Pemantle, R.: More rigorous results on the Kauffman-Levin model of evolution. Ann. Proba. 32, 2149-2178 (2004)
24. Macken, C.A., Hagan, P.S., Perelson, A.S.: Evolutionary walks on rugged landscapes. SIAM J. Appl. Math. 51, 799-827 (1991)
25. Martin, O.C., Monasson, R., Zecchina R.: Statistical mechanics methods and phase transitions in optimization problems. Theoretical Comp. Sci. 265, 3-67 (2001)
26. McDiarmid, C.: Concentration. In: M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, B. Reed (eds.), Probabilistic Methods for Algorithmic Discrete Mathematics, Springer, New York, 1998, pp 195-248
27. Patel, J.K., Read, C.B.: Handbook of the normal distribution. 2nd edn. Marcel Dekker, 1996
28. Pemmaraju, S.: Equitable coloring extends Chernoff-Hoeffding bounds. Proceedings of the 5th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM 2001), Berkeley, California, 2001, pp 285-296
29. Percus, A.G., Martin, O.C.: The stochastic traveling salesman problem. J. Stat. Phys. 94, 739-758 (1999)
30. Perelson, A.S., Macken, C.A.: Protein evolution on partially correlated landscapes. Proc. National Academy of Science USA 92, 9657-9661 (1995)
31. Slepian, D.: The one-sided barrier problem for Gaussian noise. Bell System Tech. J. 41, 463-501 (1962)
32. Solow, D., Burnetas, A., Tsai, M., Greenspan, N.S.: On the expected performance of systems with complex interactions among components. Complex Systems 12, 423-456 (2000)
33. Solow, D., Vairaktarakis, G., Pideritt, S., Tsai, M.: Managerial insights into the effects of interactions on replacing members of a team. Management Sci. 48, 1060-1073 (2002)
34. van Zwet, W.R.: Convex transformations of random variables. Mathematical Centre, Amsterdam, 1964
35. Weinberger, E.D.: A more rigorous derivation of some properties of uncorrelated fitness landscapes. J. Theoretical Biol. 134, 125-129 (1988)
36. Weinberger, E.D. : Local properties of Kauffman's NK model: A tunably rugged energy landscape. Phys. Rev. A, At. Mol. Opt. Phys. 44, 6399-6413 (1991)
37. West, D.B.: Introduction to graph theory, 2nd edn. Prentice-Hall, 2000