Adaptive dimension-wise Cauchy perturbation for enhanced differential evolution optimization

Tae Jong Choi; Yeji An; Tae Jong Choi; Yeji An

doi:10.3934/math.2026032

AIMS Mathematics

2026, Volume 11, Issue 1: 734-766. doi: 10.3934/math.2026032

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Research article

Adaptive dimension-wise Cauchy perturbation for enhanced differential evolution optimization

Tae Jong Choi ¹,
Yeji An ^{2
,
,}

1.
Graduate School of Data Science, Chonnam National University, Gwangju 61186, Republic of Korea
2.
Department of Lifelong Education, Kyungil University, Gyeongsangbuk-do 38428, Republic of Korea

Received: 06 October 2025 Revised: 22 December 2025 Accepted: 25 December 2025 Published: 09 January 2026
MSC : 68T01, 68W50

We propose an adaptive dimension-wise Cauchy perturbation mechanism to enhance the performance of differential evolution (DE). While traditional Cauchy perturbation improves solution diversity, it uses a fixed jumping rate and fails to address dimension-specific premature convergence. To overcome these limitations, the proposed method dynamically estimates the convergence level of each dimension in every generation and adaptively adjusts the jumping rate accordingly. This dimension-specific adaptive perturbation, applied during the crossover phase, mitigates premature convergence and strengthens the algorithm's ability to locate high-quality solutions. The proposed method was embedded into the Linear population size reduction Success RaTe-based Differential Evolution (L-SRTDE) algorithm, winner of the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation (IEEE CEC) 2024 competition. Extensive experiments on challenging benchmark optimization problems from the IEEE CEC 2017 test suite demonstrate that our method significantly outperforms the original L-SRTDE and several state-of-the-art DE variants in both convergence speed and solution accuracy.
- artificial intelligence,
- evolutionary algorithms,
- evolutionary computation,
- differential evolution,
- mathematical optimization
Citation: Tae Jong Choi, Yeji An. Adaptive dimension-wise Cauchy perturbation for enhanced differential evolution optimization[J]. AIMS Mathematics, 2026, 11(1): 734-766. doi: 10.3934/math.2026032

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Abstract

We propose an adaptive dimension-wise Cauchy perturbation mechanism to enhance the performance of differential evolution (DE). While traditional Cauchy perturbation improves solution diversity, it uses a fixed jumping rate and fails to address dimension-specific premature convergence. To overcome these limitations, the proposed method dynamically estimates the convergence level of each dimension in every generation and adaptively adjusts the jumping rate accordingly. This dimension-specific adaptive perturbation, applied during the crossover phase, mitigates premature convergence and strengthens the algorithm's ability to locate high-quality solutions. The proposed method was embedded into the Linear population size reduction Success RaTe-based Differential Evolution (L-SRTDE) algorithm, winner of the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation (IEEE CEC) 2024 competition. Extensive experiments on challenging benchmark optimization problems from the IEEE CEC 2017 test suite demonstrate that our method significantly outperforms the original L-SRTDE and several state-of-the-art DE variants in both convergence speed and solution accuracy.

References

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