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

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,,

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.


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/

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-


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


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