Differential evolution algorithms represent an efficient framework to solve complicated optimization tasks with many variables and complex constraints. Nevertheless, the classic differential evolution algorithm does not guarantee the convergence to the global minimum of the cost function. Therefore, the authors developed a modification of this algorithm that ensures asymptotic global convergence. The article provides a comparison of the ability to identify the global minimum of the cost function for the following three algorithms: the classic differential evolution algorithm, the above mentioned modified differential evolution algorithm and an algorithm of random sampling enhanced by a hill climbing procedure. We designed a series of numerical experiments to perform this comparison. The results indicate that the classic differential evolution algorithm is in general an extremely poor global optimizer (global minimum found in 2% of cases). On the other hand the performance of the modified differential evolution algorithm was considerably better (global minimum found in 83% of cases).

1.
K. V.
Price
,
R. M.
Storn
and
J. A.
Lampien
“Differential Evolution, A Practical Approach to Global Optimization”,
Springer-Verlag
,
Berlin Heidelberg
2005
2.
R. M.
Storn
and
K. V.
Price
Differential Evolution – A Simple and Efficient Heuristics for Global Optimization over Continuous Spaces
”,
Journal of Global Optimization
11
:
341
359
, ©
1997
Kluwer Academic Publishers
3.
J.
Mlynek
,
R.
Knobloch
and
R.
Srb
Mathematical Model of the Metal Mould Surface Temperature Optimization
”,
AIP Conference Proceedings
1690
,
020018
(
2015
)
4.
R.
Knobloch
,
J.
Mlynek
,
R.
Srb
Improving Convergence Properties of a Differential Evolution Algorithm
,
AIP Conference Proceedings
1789
,
030005
(
2016
)
5.
D.
Simon
“Evolutionary Optimization Algorithms, Biologically Inspired and Population-Based Approaches to Computer Intelligence”,
John Wiley & Sons, Inc
.,
Hoboken
,
New Jersey
2013
6.
R.
Knobloch
,
J.
Mlynek
,
R.
Srb
“The Classic Differential Evolution Algorithm and Its Convergence Properties”,
Applications of Mathematics
, Vol.
62
(
2017
), No.
2
,
published by Institute of Mathematics, Czech Academy of Sciences
, ISSN
This content is only available via PDF.