Random heuristic search: Applications to GAs and functions of unitation

Computer Methods in Applied Mechanics and Engineering

Volumn 186, Issue 2-4, 2000, Pages 195-220

  Vose, Michael D ^a   Rowe, Jonathan E ^b  

^a University of Tennessee Knoxville   (United States)

^b DE MONTFORT UNIVERSITY   (United Kingdom)

Author keywords

Functions of unitation; Modeling evolutionary algorithms; Random heuristic search

Indexed keywords

FUNCTIONS; GENETIC ALGORITHMS; HEURISTIC METHODS; MATHEMATICAL MODELS; RANDOM PROCESSES;

EVOLUTIONARY ALGORITHMS; RANDOM HEURISTIC SEARCH;

COMPUTATION THEORY;

EID: 0033728867     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00384-9     Document Type: Article

References (33)

1. Akin E. The General Topology of Dynamical Systems. 1993;American Mathematical Society, Providence, RJ.
2. C. Bridges, D. Goldberg, An analysis of reproduction and crossover in a binary-coded genetic algorithm, in: J. Grefenstette (Ed.), Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, 1987, pp. 9-13.
3. Cox D., Little J., O'Shea D. Ideals, Varieties, and Algorithms. 1992;Springer, New York.
4. M. Eberlein, The GA heuristic generically has hyperbolic fixed points, Ph.D. Dissertation, The University of Tennessee, 1996.
5. Feller W. An Introduction to Probability Theory and Its Applications. 1968;Wiley, New York.
6. Gantmacher F.R. Matrix Theory. 1997;Chelsea, New York.
7. Goldberg D., Deb K., Clark J. Genetic algorithms, noise, and the sizing of populations. Complex Systems. 6:1992;333-362.
8. Holland J. Adaptation in Natural and Artificial Systems. 1975;The University of Michigan Press, Ann Arbor.
9. Juliany J., Vose M.D. The genetic algorithm fractal. Evolutionary Computation. 2(2):1994;165-180.
10. Koehler G. A proof of the vose-liepins conjecture. Annals of Mathematics and Artificial Intelligence. 10:1994;409-422.
11. Koehler G., Bhattacharyya S., Vose M.D. General cardinality genetic algorithms. Evolutionary Computation. 5(4):1997;439-459.
12. Lang S. Algebra. 1971;Addison-Wesley, Reading, MA.
13. M. Mitchell, J. Holland, S. Forrest, When will a genetic algorithm outperform hill climbing? in: S.J. Hensen, J.D. Cowan, C.L. Giles (Eds.), Advances in Neural Information Processing Systems 6, Morgan Kaufmann, San Mateo, CA, 1994.
14. Nix A., Vose M.D. Modeling genetic algorithms with markov chains. Annals of Mathematics and Artificial Intelligence. 5:1992;79-88.
15. Y. Rabinovich, A. Wigderson, An analysis of a simple genetic algorithm, in: R. Belew, L. Booker (Eds.), Proceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1991, 215-221.
16. Renyi A. Probability Theory. 1970;North-Holland, Amsterdam.
17. J.E. Rowe, Population fixed-points for functions of unitation, in: W. Bauzhaf, C. Reeves (Eds.), Foundations of Genetic Algorithms, vol. 5, Morgan Kaufmann, San Mateo, CA, 1999.
18. J. Shapiro, A. Prugel-Bennett, Maximum entropy analysis of genetic algorithm operators, in: Lecture Notes in Computer Science, vol. 993, Springer, Berlin, 1995, pp. 14-24.
19. J. Shapiro, A. Prugel-Bennett, M. Rattray, A statistical mechanical formulation of the dynamics of genetic algorithms, in: Lecture Notes in Computer Science, vol. 865, Springer, Berlin, 1994, pp. 17-27.
20. M. Srinivas, L. M. Patnaik, Binomially distributed populations for modeling GAs, in: S. Forrest (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1993, pp. 138-145.
21. van Nimwegen E., Crutchfield J., Mitchell M. Finite populations induce metastability in evolutionary search. Physics Letters A. 229:1997;144-150.
22. van Nimwegen E., Crutchfield J. Optimizing epochal evolutionary search: population-size indenpendent theory. Comput. Methods Appl. Mech. Engrg. 186:2000;171-194.
23. Vose M.D. A closer look at mutation in genetic algorithms. Annals of Mathematics and Artificial Intelligence. 10:1994;423-434.
24. M.D. Vose, Formalizing genetic algorithms, in: Proceedings of the IEEE workshop on Genetic Algorithms, Neural Nets, and Simulated Annealing Applied to Problems in Signal and Image Processing, Glasgow, UK, May 1990.
25. Vose M.D. Modeling simple genetic algorithms. Evolutionary Computation. 3(4):1995;453-472.
26. M.D. Vose, What are genetic algorithms? a mathematical perspective, in: L.D. Whitley, L.D. Davis, M.D. Vose, K. De Jong (Eds.), Evolutionary Algorithms, vol. 111, Springer, 1999.
27. Vose M.D. Logarithmic convergence of random heuristic search. Evolutionary Computation. 4(4):1996;395-404.
28. M.D. Vose, The Simple Genetic Algorithm: Foundations and Theory, MIT Press, Cambridge, MA, 1999.
29. M.D. Vose, Random Heuristic Search, University of Tennessee Technical Report, ut-cs-98-402 (1998).
30. Vose M.D., Liepins G. Punctuated equilibria in genetic search. Complex Systems. 5:1991;31-44.
31. Vose M.D., Wright A.H. Simple genetic algorithms with linear fitness. Evolutionary Computation. 2(4):1994;347-368.
32. Vose M.D., Wright A.H. The simple genetic algorithm and the walsh transform: Part I, Theory. Evolutionary Computation. 6(3):1998;253-273.
33. D. Whitley, An executable model of a simple genetic algorithm, in: D. Whitley (Ed.), Foundations Of Genetic Algorithms, vol. 2, Morgan Kaufmann, Los Altos CA, 1992, pp. 45-62.