A further result on the Markov chain model of genetic algorithms and its application to a simulated annealing-like strategy

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 28, Issue 1, 1998, Pages 95-102

  Suzuki, Joe ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

Genetic algorithms; Markov chain; Simulated annealing

Indexed keywords

MARKOV PROCESSES; MATHEMATICAL MODELS; PROBABILITY; SIMULATED ANNEALING;

ERGODICITY;

GENETIC ALGORITHMS;

EID: 0031996991     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/3477.658583     Document Type: Article

References (33)

1. G. J. Koehler, S. Bhattacharyya, and M. D. Vose, "General cardinality genetic algorithms," in Decisions and Information Sciences. Gainesville, FL: Univ. Florida Press, 1995.
2. U," Complex Syst., vol. 8, pp. 227-256, 1994.
3. A. D. Bethke, "Genetic algorithms as function optimizers," Ph.D. dissertation, Univ. Michigan, Ann Arbor, 1981.
4. T. E. Davis, "Toward an extrapolation of the simulated annealing convergence theory onto the simple genetic algorithm," Ph.D. dissertation, Univ. Florida, Gainesville, 1991.
5. T. E. Davis and J. C. Principe, "A simulated annealing like convergence theory for the simple genetic algorithm," in Proc. 4th Int. Conf. Genetic Algorithms'91. San Mateo, CA: Morgan Kaufmann, 1991, pp. 174-181.
6. K. A. De Jong, "An analysis of the behavior of a class of genetic adaptive systems," Ph.D. dissertation, Univ. Michigan, Ann Arbor, 1975.
7. A. E. Eiben, E. H. L. Aarts, and K. M. Van Hee, "Global convergence of genetic algorithms: A Markov chain analysis," in Parallel Problem Solving from Nature, H. P. Schwefel and R. Männer, Eds. Berlin, Germany: Springer, 1990, pp. 4-12.
8. L. J. Eshelman, R. A. Caruana, and J. D. Schaffer, "Biases in the crossover landscape," in Proc. Int. Conf. Genetic Algorithms'89. San Mateo, CA: Morgan Kaufmann, 1989, pp. 10-19.
9. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, Nov. 1984.
10. D. E. Goldberg and P. Segrest, "Finite Markov chain analysis of genetic algorithms," in Proc. Int. Conf. Genetic Algorithms'87, J. J. Grefenstette, Ed. Hillsdale, NJ: Lawrence Erlbaum, 1987.
11. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley, 1989.
12. _, "Genetic algorithm and Walsh functions: Part I, a gentle introduction, Part II: Deception and its analysis," Complex Syst., vol. 3, pp. 129-171, 1990.
13. _, "A note on Boltzmann tournament selection for genetic algorithms and population-oriented simulated annealing," Complex Syst., vol. 4, pp. 445-460, 1990.
14. J. H. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor, MI: Univ. Michigan Press, 1975.
15. M. Iosifescu, Finite Markov Processes and Their Applications. Chichester, U.K.: Wiley, 1980.
16. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecci, "Optimization by simulated annealing," Science, vol. 220, pp. 671-680, May 1983.
17. S. W. Mahfoud and D. E. Goldberg, "A genetic algorithm for parallel simulated annealing," in Parallel Problem Solving from Nature, 2, R. Männer and B. Manderick, Eds. Amsterdam, The Netherlands: North-Holland, 1992, pp. 302-310.
18. _, "Parallel recombinative simulated annealing: A genetic algorithm," Parallel Computing, vol. 21, pp. 1-28, 1995.
19. F. Romeo and A. Sangiovanni-Vincentelli, "A theoretical framework for simulated annealing," Algorithm, vol. 6, pp. 302-345, 1991.
20. G. Rudolph, "Convergence analysis of canonical genetic algorithms," IEEE Trans. Neural Networks, vol. 5, pp. 96-101, Jan. 1994.
21. E. Seneta, Non-Negative Matrices and Markov Chains. New York: Springer-Verlag, 1981.
22. W. M. Spears and K. A. DeJong, "On the virtues of parametrized uniform crossover," in Proc. 4th Int. Conf. Genetic Algorithms'91. San Mateo, CA: Morgan Kaufmann, 1991, pp. 230-236.
23. J. Suzuki, "A Markov chain analysis on a genetic algorithm," in Proc. 5th Int. Conf. Genetic Algorithms'93, S. Forest, Ed. San Mateo, CA: Morgan Kaufmann, 1993, pp. 146-153.
24. _, "A Markov chain analysis on a simple genetic algorithm," IEEE Trans. Syst., Man, Cybern., vol. 25, pp. 655-659, Apr. 1995.
25. G. Syswerda, "Uniform crossover in genetic algorithms," in Proc. Int. Conf. Genetic Algorithms'89, J. D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, 1989, pp. 2-9.
26. E. A. Nix and M. D. Vose, "Modeling genetic algorithms with Markov chains," Ann. Math. Artif. Intell., vol. 5, pp. 79-88, 1992.
27. M. D. Vose and G. E. Liepins, "Punctuated equilibria in genetic search," Complex Syst., vol. 5, pp. 31-44, 1991.
28. M. D. Vose, "Advanced GA theory," ICGA-95 tutorial, p. 8, 1995.
29. Proc. Int. Conf. Genetic Algorithms'89, J. D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, 1989.
30. Proc. 4th Int. Conf. Genetic Algorithms'91, R. K. Belew and L. B. Booker, Eds. San Mateo, CA: Morgan Kaufmann, 1991.
31. Proc. 5th Int. Conf. Genetic Algorithms'93, S. Forest, Ed. San Mateo, CA: Morgan Kaufmann, 1993.
32. Parallel Problem Solving from Nature, H. P. Schwefel and R. Männer, Eds. Berlin, Germany: Springer, 1990.
33. Parallel Problem Solving from Nature, 2, R. Männer and B. Manderick, Eds. Amsterdam, The Netherlands: North-Holland, 1992.