An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization
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.
Keywords
Cite
@article{arxiv.2603.04053,
title = {An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization},
author = {Thiago Santos and Sebastiao Xavier},
journal= {arXiv preprint arXiv:2603.04053},
year = {2026}
}