The classic differential evolution algorithm and its convergence properties
| Autor: | Roman Knobloch, Radek Srb, Jaroslav Mlýnek |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization 02 engineering and technology Function (mathematics) Local convergence 020901 industrial engineering & automation Convergence of random variables Differential evolution Convergence (routing) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Convergence tests Compact convergence Premature convergence Mathematics |
| Zdroj: | APPLICATIONS OF MATHEMATICS. 62:197-208 |
| DOI: | 10.21136/am.2017.0274-16 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|