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Differential evolution with exponential crossover: A survey
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DOI：10.1016/j.cosrev.2026.100990.png)
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Abstract
En 中文
Differential Evolution (DE) employs two primary crossover strategies: binomial crossover and exponential crossover. Most DE researchers consider variants with binomial crossover to be more effective for numerical optimization problems, while those with exponential crossover are better suited for problems with strong correlations between adjacent variables. However, recent studies have shown that, with appropriate tuning of the crossover rate CR and related control parameters, DE variants employing exponential crossover can outperform those using binomial crossover. Despite this promise, exponential crossover remains underexplored relative to binomial crossover in the DE literature. To address this gap, this paper presents a comprehensive review of DE variants employing exponential crossover. First, the behavioral characteristics of exponential crossover and binomial crossover are analyzed to enhance the understanding of these two crossover methods. Second, a classification framework is proposed to guide future research, dividing existing methods into three categories: traditional exponential crossover DE, improved exponential crossover DE, and hybrid crossover DE. Additionally, four advanced DE algorithms with exponential crossover and four advanced DE algorithms with binomial crossover are selected for comparative evaluation. Finally, the study summarizes the applications of exponential crossover DE across various domains and discusses key challenges and potential future directions. This review aims to draw greater attention to exponential crossover within the DE community, promoting further research and practical applications of related algorithms.
Keywords:
Differential Evolution
Exponential Crossover
Binomial Crossover
Numerical Optimization
Metaheuristic Algorithms
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