Genetic Stochastic Method of Global Extremum Search for Multivariable Function

Abstract

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 of 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.