在多目标问题 (LeadingOnes,TrailingZeros) 上对进化多样性优化的运行时间分析
Denis Antipov1, Aneta Neumann2, Frank Neumann3
1LIP6, CNRS, Sorbonne Université, Paris, 75252, France denis.antipov@lip6.fr.
Evolutionary computation
|December 4, 2025
概括
进化多样性优化 (EDO) 算法有效地找到多样化的解决方案. 本研究分析了LOTZk基准的EDO,证明GSEMOD在总不平衡方面实现了最佳多样性,比在排序不平衡向量方面更快.
科学领域:
- 优化算法的优化算法
- 进化计算的演变
- 多目标优化多目标优化
背景情况:
- 多样性优化寻求一组多样化的高质量解决方案.
- 进化算法通常用于此目的,称为进化多样性优化 (EDO).
- 分析EDO在基准问题上的表现对于理解其效率至关重要.
研究的目的:
- 分析进化多样性优化 (EDO) 算法的性能.
- 评估GSEMOD的运行时间,以在LOTZk基准上实现最佳多样性.
- 为了比较不同的多样性措施的理论界限与经验结果.
主要方法:
- 对GSEMO和GSEMOD算法的理论分析.
- 使用帕雷托最佳和多样化解决方案的预期代进行运行时分析.
- 关于三目标LOTZk基准函数的实证研究.
- 评估两种多样性指标:总不平衡和排序不平衡向量.
主要成果:
- GSEMO将所有帕雷托最佳解决方案计算在预期的代中.
- GSEMOD优化了在O ((kn2log n) 期望代中的总不平衡,比找到帕雷托最佳解决方案更快.
- 对于优化排序不平衡向量,GSEMOD的上限是O(k2n3log n) 的预期代.
- 经验结果与理论分析一致,表明总不平衡的严格界限和不平衡向量的悲观界限.
结论:
- 该GSEMOD算法证明了多样性优化的高效融合.
- 理论边界为不同的多样性指标提供了对算法性能的见解.
- 该研究验证了EDO的有效性,并确定了在理论分析中进一步改进的领域.
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