Many differential evolution (DE) algorithms with various parameter control methods (PCMs) have been proposed. However, previous studies usually considered PCMs to be an integral component of a complex DE algorithm. Thus, the characteristics and performance of each method are poorly understood. We present an in-depth review of 24 PCMs for the scale factor and crossover rate in DE and a large-scale benchmarking study. We carefully extract the 24 PCMs from their original, complex algorithms and describe them according to a systematic manner. Our review facilitates the understanding of similarities and differences between existing, representative PCMs. The performance of DEs with the 24 PCMs and 16 variation operators is investigated on 24 black-box benchmark functions. Our benchmarking results reveal which methods exhibit high performance when embedded in a standardized framework under 16 different conditions, independent from their original, complex algorithms. We also investigate how much room there is for further improvement of PCMs by comparing the 24 methods with an oracle-based model, which can be considered to be a conservative lower bound on the performance of an optimal method.

中文翻译：

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差分进化中参数控制方法的回顾和基准测试


人们已经提出了许多具有各种参数控制方法（PCM）的差分进化（DE）算法。然而，之前的研究通常认为 PCM 是复杂 DE 算法的一个组成部分。因此，人们对每种方法的特征和性能知之甚少。我们对 DE 中的比例因子和交叉率的 24 个 PCM 进行了深入审查，并进行了大规模基准测试研究。我们仔细地从原始、复杂的算法中提取出 24 个 PCM，并按照系统的方式描述它们。我们的审查有助于理解现有代表性 PCM 之间的异同。在 24 个黑盒基准函数上研究了具有 24 个 PCM 和 16 个变分算子的 DE 的性能。我们的基准测试结果揭示了哪些方法在 16 种不同条件下嵌入到标准化框架中时表现出高性能，独立于其原始的复杂算法。我们还通过将 24 种方法与基于预言机的模型进行比较，研究了 PCM 的进一步改进空间有多大，该模型可以被认为是最佳方法性能的保守下限。