Presentations : Resonant nature of setting the control parameters of the optimization of the differential evolution algorithm

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Presentations

Kurkov V.A.¹, Shkirina U.A.², Chesalin D.D., Pishchalnikov R.Y.

Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilova street, 38, V.K27@yandex.ru, rpishchal@kapella.gpi.ru

Differential evolution is one of the most widely used evolutionary

optimization methods, the heuristic nature of which allows it to be applied to

a wide range of tasks, without going into the nuances and details of the model under study.

We have developed a software in which you can use

as an optimized function any pre-set mathematical

function. Also, narrowly focused procedures for calculating

semi-classical quantum parameters necessary for the calculation of optical

properties of organic pigments and crystals [1-3]. In this paper, we investigated

the convergence of the algorithm on a set of test functions (both for unimodal and

multimodal), which represent an unsolvable problem for classical

optimization methods, such as gradient descent or the method of least

squares. As a result, the resonant nature of the increase

in the convergence rate of differential evolution was found when the two main

parameters of the algorithm were varied: F (weight coefficient) and Cr (crossover verticality).

This feature of the algorithm should always be kept in mind, since the

non-optimal selection of F and Cr can significantly reduce the efficiency

of optimization up to a complete lack of convergence.

Literature

1. Pishchalnikov R. Application of differential evolution for modeling the linear

optical response of photosynthetic pigments // Journal of Computational Physics, volume 372,

2018, pp. 603-615, doi:10.1016/j.jcp.2018.06.040.

2. Pishchalnikov, R.Yu.; Yaroshevich, I.A.; Zlenko, D.V.; Tsoraev, G.V.; Osipov, E.M.;

Lazarenko V.A.; Parshina E.Yu.; Chesalin D.D.; Sluchanko N.N.; Maksimov E.G.

The role of the local environment in the structural heterogeneity of beta-ion rings of carotenoids

// Investigation of photosynthesis, volume 156, November 1, 2022, pp. 3-17, doi:10.1007/s11120-022-

00955-2.

3. Chesalin, D.D.; Kulikov, E.A.; Yaroshevich, I.A.; Maksimov, E.G.; Selishcheva, A.A.;

Pishchalnikov R.Yu. Differential evolution reveals the influence of polar and nonpolar

solvents on carotenoids: an example of modeling the optical response of astaxanthin // Swarm

and evolutionary calculations, 75, 2022, 101210, doi:10.1016/j.swevo.2022.101210