基于指标的多目标优化算法及其应用

 基于指标的多目标优化算法作为进化算法处理超多目标优化问题中的一类较新算法，具有搜索能力强的特点，能够巧妙地解决了大量非支配解所引起的低选择压力的问题。而在设计算法时，如何高效地平衡由算法所得解集的收敛性与多样性一直是备受关注的研究话题。另一方面，大量的研究也聚焦在如何高效地处理不同实际背景的多目标优化问题。本文针对基于指标的超多目标进化算法设计及其在不同场景下的应用这两方面，提出了相应的改进方法，工作内容和创新点可分为四个方面。

1. 在基于指标的多目标进化算法研究中，我们通过考虑支配解之间的支配关系来改进SDE，设计了一种更为通用的排序方法SDE⁺。充分利用SDE⁺的特点，我们在环境选择上设计了两种不同的策略，并提出了一种新的基于指标的多目标进化算法，即SDE⁺-MOEA。大量的实验研究表明，SDE⁺-MOEA在所比较的多目标进化算法中具有最佳的整体性能。
2. 在解决组合优化问题CARP中，我们提出了一种衡量决策空间多样性的新方法，同时设计有效的监测并提升解在决策变量空间的多样性，并应用于一个著名的算法DMAENS中，实验表明，使用我们的方法D-MAENS2能够有效地在目标空间中找到成本更低的高质量解。
3. 在解决航空发动机参数标定问题中，我们提出了具有简单框架的fSDE算法，该算法的实时性能方面优于前沿算法。同时，与经验丰富的人类工程师使用传统手动校准过程查找单个参数所需的时间相比，所提出的fSDE算法搜索到高质量的发动机参数所花费的时间少十倍。
4. 在提升机器学习模型公平性问题中，我们提出了一种新颖的多目标进化学习框架来减轻不公平性，该框架可以同时优化多个公平指标而不牺牲其中任何一个。并且基于此框架的集成方法能够自动实现准确性和多种公平性措施之间的权衡。

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