Differential evolution (DE) generally requires parameter control methods (PCMs) for the scale factor and crossover rate. Although a better understanding of PCMs provides a useful clue to designing an efficient DE, their effectiveness is poorly understood in mixed-integer black-box optimization. In this context, this paper benchmarks PCMs in DE on the mixed-integer black-box optimization benchmarking function (bbob-mixint) suite in a component-wise manner. First, we demonstrate that the best PCM significantly depends on the combination of the mutation strategy and repair method. Although the PCM of SHADE is state-of-the-art for numerical black-box optimization, our results show its poor performance for mixed-integer black-box optimization. In contrast, our results show that some simple PCMs (e.g., the PCM of CoDE) perform the best in most cases. Then, we demonstrate that a DE with a suitable PCM performs significantly better than CMA-ES with integer handling for larger budgets of function evaluations. Finally, we show how the adaptation in the PCM of SHADE fails.

翻译：差分进化（DE）通常需要针对尺度因子和交叉率采用参数控制方法（PCM）。尽管对PCM的深入理解能为设计高效DE提供有益线索，但在混合整数黑箱优化中，其有效性尚未得到充分认识。在此背景下，本文采用组件化方式，在混合整数黑箱优化基准函数（bbob-mixint）套件上对DE中的PCM进行基准测试。首先，我们证明最优PCM显著依赖于变异策略与修复方法的组合。尽管SHADE的PCM在数值黑箱优化中处于前沿水平，但我们的结果表明其在混合整数黑箱优化中表现欠佳。相反，部分简单PCM（如CoDE的PCM）在多数情况下表现最优。其次，我们发现采用合适PCM的DE在较大函数评估预算下显著优于集成整数处理的CMA-ES。最后，我们揭示了SHADE的PCM中自适应机制失效的原因。