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An adaptive Cauchy differential evolution algorithm for global numerical optimization.

Choi TJ, Ahn CW, An J - ScientificWorldJournal (2013)

Bottom Line: Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem.The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution.Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Engineering, Sungkyunkwan University (SKKU), 2066 Seobu-ro, Suwon, Republic of Korea.

ABSTRACT
Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems.

Show MeSH
Adaptive Cauchy DE.
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Related In: Results  -  Collection


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alg1: Adaptive Cauchy DE.

Mentions: Similarly, the CRi is adapted by the Cauchy distribution with the average parameter value. After that, the CRi is truncated to 0 or 1 if the CRi is less than 0 or greater than 1. The adaptation of the crossover rate is given as follows:(14)CRi,G+1=C(0,γCR)+CRavg,G,where CRavg,G is the average parameter value of the accumulated information in the CR_Memory as the location parameter of the Cauchy distribution. The γF is scaling factor of the equation and is assigned 0.1. Algorithm 1 describes the pseudocode of the proposed algorithm.


An adaptive Cauchy differential evolution algorithm for global numerical optimization.

Choi TJ, Ahn CW, An J - ScientificWorldJournal (2013)

Adaptive Cauchy DE.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3713346&req=5

alg1: Adaptive Cauchy DE.
Mentions: Similarly, the CRi is adapted by the Cauchy distribution with the average parameter value. After that, the CRi is truncated to 0 or 1 if the CRi is less than 0 or greater than 1. The adaptation of the crossover rate is given as follows:(14)CRi,G+1=C(0,γCR)+CRavg,G,where CRavg,G is the average parameter value of the accumulated information in the CR_Memory as the location parameter of the Cauchy distribution. The γF is scaling factor of the equation and is assigned 0.1. Algorithm 1 describes the pseudocode of the proposed algorithm.

Bottom Line: Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem.The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution.Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Engineering, Sungkyunkwan University (SKKU), 2066 Seobu-ro, Suwon, Republic of Korea.

ABSTRACT
Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems.

Show MeSH