TY - JOUR

T1 - Genetic Stochastic Method of Global Extremum Search for Multivariable Function

AU - Ermakov, Sergej

AU - Vladimirova, Liudmila

AU - Rubtsova, Irina

AU - Rubanik, Alexey

N1 - Publisher Copyright: © 2022, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences. All rights reserved.

PY - 2022/6/2

Y1 - 2022/6/2

N2 - This article is devoted to the development of stochastic methods of global extremum search. The modification of the annealing simulation algorithm [Ermakov and Semenchikov, 2019] is combined with the covariance matrix adaptation method [Ermakov, Kulikov and Leora, 2017]. In this case, an effective computational approach [Ermakov and Mitioglova, 1977] is used for modeling the multivariate normal distribution. The special algorithms of covariance matrices adaptation are suggested to avoid the obtaining a local extremum instead of a global one. The methods proposed are successfully applied to the problem of nonlinear regression parameters calculation. This problem often arises in physics and mathematics and may be reduced to global extremum search. In particular case considered the extremum of ravine function of 14 variables was found.

AB - This article is devoted to the development of stochastic methods of global extremum search. The modification of the annealing simulation algorithm [Ermakov and Semenchikov, 2019] is combined with the covariance matrix adaptation method [Ermakov, Kulikov and Leora, 2017]. In this case, an effective computational approach [Ermakov and Mitioglova, 1977] is used for modeling the multivariate normal distribution. The special algorithms of covariance matrices adaptation are suggested to avoid the obtaining a local extremum instead of a global one. The methods proposed are successfully applied to the problem of nonlinear regression parameters calculation. This problem often arises in physics and mathematics and may be reduced to global extremum search. In particular case considered the extremum of ravine function of 14 variables was found.

KW - Genetic stochastics algorithms; Global extremum; Covariance matrics; Normfl distribution; Nonlinear regression

KW - Genetic stochastic algorithms; Global extremum; Covariance matrix; Normal distribution; Nonlinear regression

KW - Nonlinear regres-sion

KW - Normal distribution

KW - Global extremum

KW - Co-variance matrix

KW - Genetic stochastic algorithms

UR - https://www.mendeley.com/catalogue/c4a0e5eb-c70a-332d-a57e-14575fbe1551/

UR - http://www.scopus.com/inward/record.url?scp=85133225620&partnerID=8YFLogxK

U2 - 10.35470/2226-4116-2022-11-1-13-17

DO - 10.35470/2226-4116-2022-11-1-13-17

M3 - Article

VL - 11

SP - 13

EP - 17

JO - Cybernetics and Physics

JF - Cybernetics and Physics

SN - 2223-7038

IS - 1

M1 - 3

ER -