сравнительное исследование генетических алгоритмов и

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vladimirzvonkov802@yandex.ru
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: , , , Abstract
The most perspective and developing global optimization methods are competing methods, such
as genetic algorithm (and its varieties) and particle swarm optimization algorithms at the modern
stage of global optimization methods development of multiextremal functions, nondifferentiable
functions, ravine surface functions and other complex criterion functions (functional, quality criteria, algorithmically and table of predefined functions) for classical methods optimization. The
particle swarm optimization algorithms are studied to a lesser extent than genetic algorithms,
many questions of tuning and the use of this approach are still remain uninvestigated, which is
very important and the author of this research is interesting in this approach, as well as, probably,
scientific community. In this scientific research two competing methods are compared and the
correlation of some parameters of PSO and numerical efficiency criteria is obtained by author.
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[1] Holland J. H. Adaptation in Natural and Artificial Systems / J.H. Holland - Ann Arbor: The University of
Michigan Press, 1975.–228 p.
[2] Goldberg D. E. Genetic algorithms in search, optimization, and machine learning / D.E. Goldberg. - Reading, MA: Addison-Wesley, 1989.
[3] 8
, . @ , " " : ;. . M..
8". / 8
., ; !., 8
F – !.: < – , 2006. –
452 .: .
[4] 8", F.B. & — 9, > . . . 33 (1978), . 3–16.
[5] Schwefel H. P. Numerical optimization of computer models. Chichester: Wiley, 1981.
[6] '"
, B.&. & " " / B.&. '"
, .'. < // M9 " . - | 3. - 2007.
[7] , .M. M " "
:
Q. / .M. , '.<. M
– Q9: Q<BQ, 1999. – 105 .
[8] *
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". / .&. *
, .!. : // 9 - :MM-2008: 3- . - !.: URSS, 2008 .
157-161.
[9] *
, B.. 8 " " "
% . . .9.-.. , 2000.
[10] :
, B.:. K
# " % 9 / B.:.
:
, 8.M. // M
%. - |4. – 2009 . 74-79.
[11] :
, F.<. ; # " " "" " / F.<.
:
// 9 - :MM-2008: 3- . - !.: URSS, 2008 c. 242-245.
[12] :, .!. @ "
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.!. :, .&. :% // 9 - :MM-2008: 3- . .1 - !.: URSS, 2008 . 179-191.
[13] F
, !.. K
" " # / !..
F
, B.. &9
// M
%. - |4. – 2009 c. 53-64.
[14] Khloudova M. Classification of scheduling algorithms for real-time systems // Proc. of International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering. – 1999. – Vol.
3687. – P. 228-231.
[15] Hallam N., Kendall G., and Blanchfield P. Solving Multi-objective Optimization Problems Using the Potential Pareto Regions Evolutionary Algorithm, in T.P. Runarsson et al (Eds.): Parallel problem solving
from nature (PPSN IX: 9th international conference), LNCS 4193, pp. 503-512, Springer-Verlag Berlin
Heidelberg 2006.
796
[16] Jurgen Branke, Kalyanmoy Deb, Henning Dierolf, and Matthias Osswald. Finding Knees in Multi-objective
Optimization, in X. Yao et al. (Eds.): Parallel problem solving from nature (PPSN VIII: 8th international
conference), LNCS 3242, pp. 722-731, Springer-Verlag Berlin Heidelberg 2004.
[17] Kennedy, J. Particle swarm optimization / J. Kennedy, R. Eberhart // in Proc. of IEEE International Conference on Neural Networks. – Piscataway, 1995. – P. 1942 – 1948.
[18] Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization // P. N. Suganthan, N. Hansen, J. J. Liang et al. / Technical Report, Nanyang Technological University, Singapore And KanGAL Report Number 2005005 (Kanpur Genetic Algorithms Laboratory, IIT Kanpur), May 2005 - 50 p.
[19] L
.'. 8 IT-SAGA % , " % " > / .'. L
/ M ": . & ! % , (
;
, 1-6 # 2011 ".). – : M-
" "
" "
, 2011 – . 183-195.
[20] Michalewicz, Z. Evolutionary algorithms for constrained parameter optimization problems / Z. Michalevicz, M. Schouenauer // Evolutionary Computation. - 4. - 1996. - P. 1 – 32.
[21] Michalewicz, Z. Evolutionary algorithms for constrained engineering problems / Z. Michalewicz, D. Dasgupta, Riche Le, M. R. and M. Schoenauer // Computers & Industrial Engineering Journal - 30, 1996. – P.
851 – 870.
[22] Zitzler E., Thiele L. Multiobjective evolutionary algorithms: A comparative case study and the strength
Pareto approach // IEEE Transactions on Evolutionary Computation, Vol. 3, No. 4, pp. 257-271, 1999.
[23] &" 8.'. B
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Biography
Zvonkov Vladimir B. Bachelor's degree of engineering and technology of "System analysis and
control" (2011 year, honours degree diploma), undergraduate student of institute of informatics and
telecommunication, system analysis and operations research department of Siberian state aerospace
university named after academician M.F. Reshetnev (responsible attitude to learning, self-education
and excellent knowledge of disciplines). I published over 25 scientific researches. Field of scientific
interests is complex systems modelling and optimization, evolutionary algorithms, artificial neural
networks, particle swarm optimization, committees of intelligent algorithms. The program system ITSAGA was awarded with 2nd rank in the nomination of "Research and experimental programs» as
well as with absolute 2nd rank in the All-Russia student's competition of computer programs (taken
part in Vologda, 2010 year). The author was awarded with the President of the Russian Federation
Prize for the talented youth (order of the Ministry of education and science of the Russian Federation
dated October 15, 2010, N 1031). The author is a laureate of the 3rd degree in a competition "Eureka2011" (taken part in Novocherkassk). The author has received 5 diplomas of the I-st degree, 4 diplomas of the II-nd degree, 1 diploma of III-th degree in the full-time different conferences. E-mail: vladimirzvonkov802@yandex.ru. Phone number: +7-913-585-69-35.
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