Lévy flights as an underlying mechanism for global optimization algorithms

• Autorzy: Gutowski M.
• Języki publikacji: EN

Abstrakty

EN

In this chapter we propose and advocate the use of the so called Lévy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reason overlooked until now, is - in the author's opinion - very relevant to our need for an algorithm which is capable of generating trial steps of very different length in the search space. The required balance between short and long steps can be easily and fully controlled. A simple example of the approximated Lévy distribution, implemented in FORTRAN 77, is given. We also discuss the physical grounds of presented methods.

Słowa kluczowe

EN

global optimization; stochastic optimization; stochastic algorithm; Lévy flights

PL

optymalizacja globalna; optymalizacja stochastyczna; algorytm stochastyczny; loty Lévy'ego

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Elektronika
• Rocznik: 2002
• Tom: z. 139
• Strony: 175--184
• Opis fizyczny: Bibliogr. 5 poz., tab., wykr.

Twórcy

autor

Gutowski M.

• Institute of Physics, Polish Academy of Sciences, 02-668 Warszawa, Al. Lotników 32/46, Poland

Bibliografia

• 1. Klafter J., Shlesinger M.F., Zumofen G.: Beyond Browanian Motion, Physics Today, 1996, 33-39.
• 2. The exact from of the Levy distribution is rarely quoted in the literature, we have found it in: Rosario N. Mantegna and H. Eugene Stanley: Stochastic Process with ?Ultraslow Convergence to a Gaussian: The Truncated Levy Flight, Phys. Rev. Lett., vol. 73, no 22, 1994, 2946-2947.
• 3. Bergstrom H.: Arkiv. Gur Matematik, vol. 2, 1952, 375.
• 4. Bardou F.: Cooling gases with Levy flights: using the generalized central limit theorem in physics, in O. Barndorff-Nielsen S.E. Craversen and T. Mikosch (eds.), mini proceedings of Conference on Levy processes: theory and applications, Aarhus, 1999, MaPhyusto Publication (Miscellanea no. 11, ISSN 1398-5957), also available at URL: http://arXiv.org/abs/physics/0012049.
• 5. Galar R., Kopciuch R.: Impatience and polarization in evolutionary processes, 2nd National Conference Evolutionary algorithms and global optimization, Potok Złoty (Poland), 1999, 115-122, (in Polish).