Convergence of simple genetic algorithms for the two-bit problem

BioSystems

Volumn 46, Issue 3, 1998, Pages 235-282

  Takahashi, Yoshikane ^a  

^a NTT Communication Science Laboratories   (Japan)

Author keywords

Convergence; Crossover; Crossover probability; Difference equation system; Genetic algorithm; Initial value; Mutation; Optimization problem; Reproduction; Two bit problem

Indexed keywords

ALGORITHM; ARTICLE; GENETIC PROCEDURES; GENETIC RECOMBINATION; MUTATION; NATURAL SELECTION; POPULATION GENETICS; STOCHASTIC MODEL;

EID: 0032078107     PISSN: 03032647     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0303-2647(98)00006-9     Document Type: Article

References (23)

1. Aarts E.H.L., Eiben A.E., Van Hee K.M. A general theory of genetic algorithms. Computing Science Notes 89/08. 1989;Eindhoven University of Technology, Netherlands.
2. Aarts E.H.L., Eiben A.E., Van Hee K.M. Global convergence of genetic algorithms: a Markov chain analysis. Schwefel H.P., Manner R. Proc. of PPSN 1, Lecture Notes in Computer Science, No.496. 1991;Springer-Verlag, Berlin.
3. Akin E. Hopf bifurcation in the two locus genetic model. Memoirs of the American Mathematical Society, No.284. 44:1983;American Mathematical Society, Providence, Rhode Island.
4. Davis, T.E. (Ed.), 1991, Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York, NY.
5. Davis T.E., Principe J.C. A simulated annealing like convergence theory for the simple genetic algorithm. Belew R.K., Booker L.B. Proc. 4th Int. Conf. on Genetic Algorithms, San Mateo, CA. 1991;174-181 Morgan Kaufmann, San Mateo, CA.
6. Davis T.E., Principe J.C. A Markov chain framework for the simple genetic algorithm. Evol. Comput. 1(3):1993;269-288.
7. Feldman M.W. Equilibrium studies of two-locus haploid populations with recombination. Theor. Popul. Biol. 2:1971;299-318.
8. Goldberg D.E. Simple genetic algorithms and the minimal, deceptive problem. Davis L. Genetic Algorithms and Simulated Annealing. 1987a;74-88 Pitman, London.
9. Goldberg, D.E., 1987b. Computer-aided gas pipeline operation using genetic algorithms and rule learning. Part II: rule learning control of a pipeline under normal and abnormal conditions. Eng. Comput. 47-58.
10. Goldberg D.E. Genetic algorithms in search, optimization and machine learning. 1989;Addison-Wesley, Reading, MA.
11. Grefenstette, J.J., (Ed.) 1987. Genetic algorithms and their applications, Proc. 2nd Int Conf. on Genetic Algorithms. Lawrence Earlbaum, Hillsdale, NJ.
12. Hartl D.L., Clark A.G. Principles of Population Genetics. 1989;Sinauer, Sunderland, MA.
13. Hasting A. Multilocus population genetics with weak epistasis. I. Equilibrium properties of two-locus two-allele models. Genetics. 109:1985;799-812.
14. Holland J.H. Adaptation in Neural and Artificial Systems. 1975;University of Michigan Press, Ann Arbor, MI.
15. Horn J. Finite Markov chain analysis of genetic algorithms with niching. Forrest S. Proc. 5th Int. Conf. on Genetic Algorithms Urbana-Champaign, IL. 1993;110-117 Morgan Kaufmann, San Mateo, CA.
16. Luenberger D.G. Introduction to Dynamic Systems-Theory, Models, and Applications. 1979;Wiley, New York.
17. Nix A.E., Vose M.D. Modeling genetic algorithms with Markov chains. Ann. Math. Artif. Intell. 5:1992;79-88.
18. Reynolds D., Gomatam J. Theoretical bounds for genetic algorithms. Pearson D.W. et al. Proc. Int. Conf. on Artificial Neural Networks and Genetic Algorithms, Ales, France. 1995;148-151 Springer, Vienna.
19. Reynolds D., Gomatam J. Stochastic modelling of genetic algorithms. Artif. Intell. 82:1996;303-330.
20. Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Trans. Neural Netw. 5:1994;96-101.
21. Sigmund K., Hofbauer J. Evolution Theory and Dynamic Systems. 1988;Cambridge University Press, Cambridge, UK.
22. Suzuki J. A Markov chain analysis on simple genetic algorithms. IEEE Trans. Syst., Man Cybern. 25:1995;655-659.
23. Vose M.D. Generalizing the notion of schema in genetic algorithms. Artif. Intell. 50:1991;385-396.