Fractal Dimension of Trajectory as Invariant of Genetic Algorithms

  • Authors:

  • Stefan Kotowski;Witold Kosiński;Zbigniew Michalewicz;Jakub Nowicki;Bartosz Przepiórkiewicz

  • Affiliations:

  • Faculty of Computer Science, Polish-Japanese Institute of Information Technology, Warszawa, Poland 02-008 and Institute of Fundamental Technological Research IPPT PAN, Warszawa, Poland 00-049;Faculty of Computer Science, Polish-Japanese Institute of Information Technology, Warszawa, Poland 02-008 and Institute of Environmental Mechanics and Applied Computer Science, Kazimierz Wielki Un ...;Faculty of Computer Science, Polish-Japanese Institute of Information Technology, Warszawa, Poland 02-008 and Adelaide University, Australia;Faculty of Computer Science, Polish-Japanese Institute of Information Technology, Warszawa, Poland 02-008;Faculty of Computer Science, Polish-Japanese Institute of Information Technology, Warszawa, Poland 02-008

  • Venue:
  • ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
  • Year:
  • 2006

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Abstract

Convergence properties of genetic algorithms are investigated. For them some measures are introduced. A classification procedure is proposed for genetic algorithms based on a conjecture: the entropy and the fractal dimension of trajectories produced by them are quantities that characterize the classes of the algorithms. The role of these quantities as invariants of the algorithm classes is presented. The present approach can form a new method in construction and adaptation of genetic algorithms and their optimization based on dynamical systems theory.