On one approach to hybridization in the multi-start method

Andrei Y. Gorchakov

Abstract


One of the approaches to hybridization and selection of parameters of minimization methods used in the multi-start method is proposed and experimentally tested. The approach consists in a combination of one-dimensional search methods depending on the values of the minimized function obtained in the calculation process. The multi-start method consists in repeatedly launching the methods of searching for a local minimum from various starting points. Therefore, we can assume that the problems of local minimization arising at each iteration of the method have similar characteristics. By using this feature of the multi-start method, it was possible to ensure the selection of parameters in the process of work. Numerical experiments were carried out to determine the dependence of the speed of local descent methods on the parameters and an algorithm was proposed for choosing the optimal parameter value. It has been experimentally shown that the interval of optimality of parameters has wide enough boundaries. Numerical experiments were carried out on the problem of finding the global minimum of the energy of a set of atoms of a fragment of a flat crystal lattice. To calculate the interatomic interaction energy, the Tersoff potential was used.


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References


Evtushenko Yu.G., Posypkin M.A. Versions of the method of nonuniform coverings for global optimization of mixed integer nonlinear problems.// Doklady Mathematics. –– Vol. 437. –– 2011.–– P. 168–172.

Antukh A.E., Karpenko A.P., Global optimization based on methods of particle swarm, mind evolution and clonal selection. // Engineering and computer technology.–– 2012.–– no. 08.

Hickernell Fred J, Yuan Ya-xiang. A simple multistart algorithm for global optimization.–– 1997.

Multi-start methods / Rafael Martí, Jose A Lozano, Alexan-der Mendiburu, Leticia Hernando // Handbook of Heuristics.––2016.–– P. 1–21.

Martí R, Moreno-Vega J Marcos, Duarte A. Advanced multi-startmethods // Handbook of metaheuristics.––Springer, 2010.–– P. 265–281.

Intelligent multi-start methods / Rafael Martí, Ricardo Aceves,Maria Teresa León et al. // Handbook of Metaheuristics.–– Springer,2019.–– P. 221–243.

Gorchakov A.Ju., Posypkin M.A. The effectiveness of local search methods in the problem of finding the minimum energy of a 2-D crystal.// Modern Information Technology and IT-education.–– 2017.–– Vol. 13, no. 2.

Two-dimensional materials from data filtering and abinitio calculations / Sébastien Lebègue, T Björkman, Mattias Klintenberg et al. //Physical Review X.–– 2013.–– Vol. 3, no. 3.–– P. 031002.

Tersoff JJPRB. Modeling solid-state chemistry: Interatomic potentialsfor multicomponent systems // Physical review B.–– 1989.–– Vol. 39,no. 8.–– P. 5566.

Posypkin Mikhail, Usov Alexander. Implementation and verificationof global optimization benchmark problems // Open Engineering.––2017.–– Vol. 7, no. 1.–– P. 470–478


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Abava  Absolutech Fruct 2020

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