ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ebeling W. Nonlinear dynamics of mixed evolutionary strategies for solving optimization problems. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, iss. 3, pp. 22-27.

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(En):
PDF icon 1995no3p022.pdf
(downloads: 1)
Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
621.373

Nonlinear dynamics of mixed evolutionary strategies for solving optimization problems

Autors: 
Ebeling Werner, Humboldt University of Berlin
Abstract: 

Several elementary strategies of evolution are investigated and described by simple mathematical models, leading to a highdimensional system of coupled differential equations. The stationary states of the system correspond to relative optima and the stable attractor corresponds to the finai solution of the optimization problem. Special attention is devoted here to mixed Boltzmann - Darwin strategies modelling basic elements of thermodynamic and biological evolution respectively. A continous model leading to one p.d.e., the corresponding eigenvalue problem and several applications are discussed.

Key words: 
-
Reference: 
  1. Ebeling W, Feistel R. Physik der Selbstorganisation und Evolution. Berlin: Akademie-Verlag; 1982. 451 p. Feistel В, Ebeling W. Evolution of Complex Systems. Dordrecht: Kluwer Publ.; 1989. 242 p.
  2. Ebeling W, Peschel M, editors. Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems. Berlin: Akademie-Verlag; 1985. 271 p.
  3. Eigen M, Schuster P. The Hypercycle. Naturwissenschaften. 1978;65:341-369. DOI: 10.1007/BF00439699.
  4. Haken H, editor. Complex Systems - Operational Approaches in Neurobiology. Physics and Computers. Berlin Springer; 1985. 365 p. DOI: 10.1007/978-3-642-70795-7.
  5. Herzel H, Ebeling W, Schmitt AO. Entropies of biosequences. Phys. Rev. E. 1994;50(6):5061-5071. DOI: 10.1103/physreve.50.5061.
  6. Conrad M. Adaptability. N.Y.: Springer; 1983. 408 p. DOI: 10.1007/978-1-4615-8327-1.
  7. Klimontovich YuL. Turbulent Motion and the Structure of Chaos. Dordrecht: Springer; 1994. 401 p. DOI: 10.1007/978-94-011-3426-2.
  8. Rechenberg I. Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Stuttgart: Fromman-Verlag; 1973. 170 p.
  9. Schwefel H-P. Numerical Optimization of Computer Models. N.Y.: Wiley; 1981. 389 p.
  10. Agelmeyer T, Ebeling W, Rose Н. Smoothing representation of fitness landscapes — the genotype-phenotype map of evolution. Biosystems. 1996;39(1):63-76. DOI: 10.1016/0303-2647(95)01601-5.
  11. Ebeling W, Engel A. Models of evolutionary systems and their application to optimization problems. Syst. Anal. Моdеl. Sim. 1986;3:377-385.
  12. Ebeling W, Engel А, Mazenko VG. Modeling of selection processes with age-dependent birth and death rates. Biosystems. 1986;19(3):213-21. DOI: 10.1016/0303-2647(86)90040-7.
  13. Boseniuk T, Ebeling W, Engel A. Boltzmann and Darwin strategies in complex optimization. Phys. Lett. A. 1987;125(6-7):307-310.  DOI: 10.1016/0375-9601(87)90149-6. Boseniuk T, Ebeling W. Optimization of NP-Complete Problems by Boltzmann-Darwin Strategies Including Life-Cycles. Europhys. Lett. 1988;6(2):107. DOI: 10.1209/0295-5075/6/2/003.
  14. Muhlenbein H, Gorges-Schleuter M, Kramer O. New solutions to the mapping problem of parallel systems. Parallel Computing 1987;4(3):269-279.
  15. Acelmayer T, Ebeling W. Unified description of evolutionary strategies over continuous parameter spaces. Biosystems. 1997;41(3):167-178. DOI: 10.1016/s0303-2647(96)01671-1.
Received: 
19.10.1995
Accepted: 
25.02.1996
Published: 
05.04.1996
  • 47 reads