Improving convergence properties of a differential evolution algorithm

Knobloch, Roman; Mlýnek, Jaroslav; Srb, Radek

doi:10.1063/1.4968451

Cited by 6 publications

(10 citation statements)

References 3 publications

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“…This feature looks very good at the first sight but can lead to population stagnation in a local minimum in some situations. For details see article [4].…”

Section: Cdea Strong Points and Weaknessesmentioning

confidence: 99%

“…In article [4] we concentrate on the research of this algorithm and specifically on considerations concerning its ability to converge to the global minimum of the cost function. The conclusions of these investigations are:…”

Section: Cdea Strong Points and Weaknessesmentioning

confidence: 99%

“…In article [4] we compared the ability MDEA and CDEA to converge to the global minimum of the cost function. In this article we want to look at MDEA from a different point of view.…”

Section: Mdea and Random Sampling Comparisonmentioning

confidence: 99%

“…That is why this algorithm is titled as the classic differential evolution algorithm in [1]. For the details and more information on this algorithm see the book [1], or alternatively articles [2] or [4].…”

Section: Introductionmentioning

confidence: 99%

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Convergence rate of the modified differential evolution algorithm

Knobloch

Mlýnek

Srb³

2017

AIP Conference Proceedings

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Abstract. 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).

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“…This feature looks very good at the first sight but can lead to population stagnation in a local minimum in some situations. For details see article [4].…”

Section: Cdea Strong Points and Weaknessesmentioning

confidence: 99%

Section: Cdea Strong Points and Weaknessesmentioning

confidence: 99%

“…In article [4] we compared the ability MDEA and CDEA to converge to the global minimum of the cost function. In this article we want to look at MDEA from a different point of view.…”

Section: Mdea and Random Sampling Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Convergence rate of the modified differential evolution algorithm

Knobloch

Mlýnek

Srb³

2017

AIP Conference Proceedings

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“…The authors of the current article demonstrated (see [9]) that even the differential evolution algorithms as introduced in the original works of Price, Storn, and Lampien [16], [18] do not guarantee in general the convergence to the global minimum of the cost function. To be specific we focus on the classic differential evolution algorithm DE/rand/1/bin (further referenced to as CDEA) but our remarks apply mostly to all alternatives of the original differential evolution algorithms.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of the Convergence of the Differential Evolution Algorithm

Knobloch¹,

Mlýnek²

2020

NNW

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Differential evolution algorithms represent an efficient framework to tackle complicated optimization problems with many variables and involved constraints. Nevertheless, the classic differential evolution algorithms in general do not ensure the convergence to the global minimum of the cost function. Therefore, the authors of the article designed a modification of these algorithms that guarantees the global convergence in the asymptotic and probabilistic sense. The modification consists in adding a certain ratio of random individuals to each generation formed by the algorithm. The random individuals limit the premature convergence to the local minimum and contribute to more thorough exploration of the search space. This article concentrates specifically on the role of random individuals in the identification of the global minimum of the cost function. Besides, the paper also contains some useful estimates of the probability of finding the global minimum of the corresponding cost function.

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A differential evolution algorithm in the optimization task with a Lipschitz continuous cost function

Knobloch¹

2018

AIP Conference Proceedings

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Improving convergence properties of a differential evolution algorithm

Cited by 6 publications

References 3 publications

Convergence rate of the modified differential evolution algorithm

Convergence rate of the modified differential evolution algorithm

Probabilistic Analysis of the Convergence of the Differential Evolution Algorithm

A differential evolution algorithm in the optimization task with a Lipschitz continuous cost function

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