一种自适应的基于KKT的收敛性指标用于多目标优化
An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization
AI总结：
本文提出了一种基于KKT条件的自适应收敛性指标，通过分位数归一化提高对异质分布残差的鲁棒性，以改进多目标优化的收敛性评估。
摘要：
性能指标是评估多目标优化算法收敛行为的重要工具，尤其是在真实Pareto前沿未知或难以近似的情况下。经典的基于参考点的指标如超体积和反向代际距离被广泛应用，但在多目标场景中可能面临可扩展性限制和参数选择敏感性的问题。基于Karush-Kuhn-Tucker（KKT）最优条件衍生的指标提供了一种内在替代方法，通过量化站定性而不依赖外部参考集。本文重新审视一种受熵启发的基于KKT的收敛性指标，并提出基于分位数归一化的稳健自适应改写方法。所提出的指标在保持原始公式站定性解释的同时，提高了对站定性残差异质分布的鲁棒性，这是多目标优化中反复出现的问题。
英文摘要：
Performance indicators are essential tools for assessing the convergence behavior of multi-objective optimization algorithms, particularly when the true Pareto front is unknown or difficult to approximate. Classical reference-based metrics such as hypervolume and inverted generational distance are widely used, but may suffer from scalability limitations and sensitivity to parameter choices in many-objective scenarios. Indicators derived from Karush--Kuhn--Tucker (KKT) optimality conditions provide an intrinsic alternative by quantifying stationarity without relying on external reference sets. This paper revisits an entropy-inspired KKT-based convergence indicator and proposes a robust adaptive reformulation based on quantile normalization. The proposed indicator preserves the stationarity-based interpretation of the original formulation while improving robustness to heterogeneous distributions of stationarity residuals, a recurring issue in many-objective optimization.
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