A Two-Stage Adaptive Differential Evolution Algorithm with Accompanying Populations

Chao Min (), Min Zhang, Qingxia Zhang, Zeyun Jiang and Liwen Zhou
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Chao Min: School of Science, 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
Liwen Zhou: School of Science, Southwest Petroleum University, Xindu Road, Chengdu 610500, China

Mathematics, 2025, vol. 13, issue 3, 1-28

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.

Keywords: differential evolution; optimization algorithms; staged evolution; accompanying populations; adaptive parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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