Fourier Analysis of Genetic Algorithms

Theoretical Computer Science

Volumn 229, Issue 1-2, 1999, Pages 143-175

  Kosters, Walter A ^a   Kok, Joost N ^a   Floréen, Patrik ^b  

^a LEIDEN UNIVERSITY   (Netherlands)

^b UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Fourier analysis; Genetic algorithms; Walsh products

Indexed keywords

EID: 0012205458     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(99)00092-4     Document Type: Article

References (25)

1. L. Altenberg, The evolution of evolvability in genetic programming, in: K.E. Kinnear, Jr. (Ed.), Advances in Genetic Programming, MIT Press, Cambridge, MA, 1994, pp. 47-74.
2. T. Bäck, D.B. Fogel, Z. Michalewicz, Handbook of Evolutionary Computation, Institute of Physics Publishing, Bristol, and Oxford University Press, Oxford, 1997.
3. A.D. Bethke, Genetic algorithms as function optimizers, Ph.D. Thesis, University of Michigan, 1981.
4. C.L. Bridges, D.E. Goldberg, The nonuniform Walsh-schema transform, in: G.J.E. Rawlins (Ed.), Foundations of Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1991, pp. 13-22.
5. B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan S.M. Watt, First Leaves: A Tutorial Introduction to Maple V, Springer, New York, 1992.
6. P. Floréen, J.N. Kok, Tracing the behavior of genetic algorithms using expected values of bit and Walsh products, in: Proc. 6th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Francisco, CA, 1995, pp. 201-208.
7. D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, MA, 1989.
8. D.E. Goldberg, Genetic algorithms and Walsh functions: Part I, A gentle introduction, Complex Systems 3 (1989) 129-152.
9. D.E. Goldberg, Genetic algorithms and Walsh functions: Part II, Deception and its analysis, Complex Systems 3 (1989) 153-171.
10. D.E. Goldberg, Construction of high-order deceptive functions using low-order Walsh coefficients, Ann. Math. Artif. Intell. 5 (1992) 35-47.
11. J.H. Holland, Adaptation in Natural and Artificial Systems, MIT Press, Cambridge, MA, 1992.
12. S. Khuri, Transform methods, in: T. Bäck, D.B. Fogel, Z. Michalewicz, Handbook of Evolutionary Computation, Institute of Physics Publishing, Bristol, and Oxford University Press, Oxford, 1997, B2.6: 1-10.
13. G.J. Koehler, S. Bhattacharyya, M.D. Vose, General cardinality genetic algorithms, Evolutionary Computation 5 (1998) 439-459.
14. G.E. Liepins, M.D. Vose, Polynomials, basis sets, and deceptiveness in genetic algorithms, Complex Systems 5 (1991) 45-61.
15. A.E. Nix, M.D. Vose, Modeling genetic algorithms with Markov chains, Ann. Math. Artif. Intell. 5 (1992) 79-88.
16. X. Qi, F. Palmieri, Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space; Part I: Basic properties of selection and mutation, IEEE Trans. Neural Networks 5 (1994) 102-119.
17. Y. Rabinovich, A. Wigderson, An analysis of a simple genetic algorithm, in: Proc. 4th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1991, pp. 215-221.
18. G. Rudolph, Convergence analysis of canonical genetic algorithms, IEEE Trans. Neural Networks 5 (1994) 96-101.
19. G. Rudolph, Convergence properties of evolutionary algorithms, Ph.D. Thesis, University of Dortmund, 1996.
20. M. Srinivas, L.M. Patnaik, Binomially distributed populations for modelling GAs, in: Proc. 5th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1993, pp. 138-145.
21. K. Takabatake, H. Miyauchi, S. Okada, Schema spectral analysis, in: Proc. 1996 IEEE Internat. Conf. on Evolutionary Computation, IEEE, New York, 1996, pp. 176-181.
22. M.D. Vose, Modeling simple genetic algorithms, in: L.D. Whitley (Ed.), Foundations of Genetic Algorithms, vol. 2, Morgan Kaufmann, San Mateo, CA, 1993, pp. 63-73.
23. M.D. Vose, G.E. Liepins, Punctuated equilibria in genetic search, Complex Systems 5 (1991) 31-44.
24. M.D. Vose, A.H. Wright, Simple genetic algorithms with linear fitness, Evolutionary Computation 2 (1995) 347-368.
25. D. Whitley, An executable model of a simple genetic algorithm, in: L.D. Whitley (Ed.), Foundations of Genetic Algorithms, vol. 2, Morgan Kaufmann, San Mateo, CA, 1993, pp. 45-62.