An adaptive differential evolution algorithm with exponential crossover based on a learning strategy within the difference vector

Junpeng Chen

doi:10.1016/j.swevo.2025.102247

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An adaptive differential evolution algorithm with exponential crossover based on a learning strategy within the difference vector

2025-12-04

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Junpeng Chen

Zhenyu Meng *

DOI：10.1016/j.swevo.2025.102247

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Abstract

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Most Differential Evolution (DE) researchers tend to adopt the binomial crossover operation in tackling optimization problems. However, we find that the DE variants using exponential crossover can also achieve superior performance to those using binomial crossover, as long as appropriate parameter control strategies are applied. Therefore, this paper proposes a new DE algorithm, an adaptive Differential Evolution algorithm with exponential crossover based on Learning Strategy within Difference vector (DLS-DE), to fill the gap in this field. The main contributions of this work are summarized as follows: First, a two-phase parameter control strategy is designed to regulate the scale factor F for balancing exploration and exploitation. In addition, considering the dispersion of effective parameter values, an adaptive σF strategy is proposed to adjust the sampling distribution and enhance parameter adaptability. Second, a differential vector learning strategy is developed to identify and incorporate promising difference vector information during an individual’s stagnation, enabling the search direction to adapt based on its past performance. Finally, the algorithm employs exponential crossover, where the crossover rate CR is automatically generated, and a fitness-independent parameter weight update mechanism is adopted to mitigate premature convergence. The performance of DLS-DE is evaluated on 88 benchmark functions from the CEC2013, CEC2014, and CEC2017 test suites. Statistical analyses, including the Friedman test and the Wilcoxon rank-sum test, demonstrate its effectiveness and competitiveness compared with ten state-of-the-art algorithms. In addition, DLS-DE is applied to an Economic Load Dispatch (ELD) problem in a power system with 40 generating units, achieving satisfactory results.

Keywords:

Differential evolution

Differential vector

Exponential crossover

Parameter control