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A Two-Stage Adaptive Differential Evolution Algorithm with Accompanying Populations

Author

Listed:
  • Chao Min

    (School of Science, Southwest Petroleum University, Xindu Road, Chengdu 610500, China
    Institute for Artificial Intelligence, Southwest Petroleum University, Xindu Road, Chengdu 610500, China
    National Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Xindu Road, Chengdu 610500, China)

  • Min Zhang

    (School of Science, Southwest Petroleum University, Xindu Road, Chengdu 610500, China)

  • Qingxia Zhang

    (School of Science, Southwest Petroleum University, Xindu Road, Chengdu 610500, China)

  • Zeyun Jiang

    (Institute for Artificial Intelligence, Southwest Petroleum University, Xindu Road, Chengdu 610500, China
    School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University, Riccarton Mains Road, Edinburgh EH14 4AS, Scotland, UK)

  • Liwen Zhou

    (School of Science, Southwest Petroleum University, Xindu Road, Chengdu 610500, China)

Abstract

Stochastic simulations are often used to determine the crossover rates and step size of evolutionary algorithms to avoid the tuning process, but they cannot fully utilize information from the evolutionary process. A two-stage adaptive differential evolution algorithm (APDE) is proposed in this article based on an accompanying population, and it has unique mutation strategies and adaptive parameters that conform to the search characteristics. The global exploration capability can be enhanced by the accompanying population to achieve a balance between global exploration and local search. This algorithm has proven to be convergent with a probability of 1 using the theory of Markov chains. In numerical experiments, the APDE is statistically compared with nine comparison algorithms using the CEC2005 and CEC2017 standard set of test functions, and the results show that the APDE is statistically superior to the comparison methods.

Suggested Citation

  • Chao Min & Min Zhang & Qingxia Zhang & Zeyun Jiang & Liwen Zhou, 2025. "A Two-Stage Adaptive Differential Evolution Algorithm with Accompanying Populations," Mathematics, MDPI, vol. 13(3), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:440-:d:1578939
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