The classic differential evolution algorithm and its convergence properties

Knobloch, Roman, Mlýnek, Jaroslav, and Srb, Radek. "The classic differential evolution algorithm and its convergence properties." Applications of Mathematics 62.2 (2017): 197-208. <http://eudml.org/doc/287964>.

@article{Knobloch2017,
abstract = {Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the classic differential evolution algorithm. This modification limits the possible premature convergence to local minima and ensures the asymptotic global convergence. We also introduce concepts that are necessary for the subsequent proof of the asymptotic global convergence of the modified algorithm. We test the classic and modified algorithm by numerical experiments and compare the efficiency of finding the global minimum for both algorithms. The tests confirm that the modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.},
author = {Knobloch, Roman, Mlýnek, Jaroslav, Srb, Radek},
journal = {Applications of Mathematics},
keywords = {optimization; cost function; global minimum; global convergence; local convergence; differential evolution algorithm; optimal solution set; convergence in probability; numerical testing},
language = {eng},
number = {2},
pages = {197-208},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The classic differential evolution algorithm and its convergence properties},
url = {http://eudml.org/doc/287964},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Knobloch, Roman
AU - Mlýnek, Jaroslav
AU - Srb, Radek
TI - The classic differential evolution algorithm and its convergence properties
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 197
EP - 208
AB - Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the classic differential evolution algorithm. This modification limits the possible premature convergence to local minima and ensures the asymptotic global convergence. We also introduce concepts that are necessary for the subsequent proof of the asymptotic global convergence of the modified algorithm. We test the classic and modified algorithm by numerical experiments and compare the efficiency of finding the global minimum for both algorithms. The tests confirm that the modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.
LA - eng
KW - optimization; cost function; global minimum; global convergence; local convergence; differential evolution algorithm; optimal solution set; convergence in probability; numerical testing
UR - http://eudml.org/doc/287964
ER -