🤖 AI Summary
This work proposes a reference-set-free adaptive convergence metric for multi-objective optimization that addresses the scalability limitations of existing indicators when the true Pareto front is unknown. By leveraging the Karush–Kuhn–Tucker (KKT) optimality conditions, the method integrates an entropy-inspired stationarity measure with a quantile normalization mechanism to enhance robustness against heterogeneous residual distributions. While preserving the intrinsic interpretability of KKT-based analysis, the proposed metric significantly improves stability and applicability in both many-objective and high-dimensional scenarios, thereby overcoming the scalability bottlenecks inherent in conventional convergence indicators.
📝 Abstract
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.