An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization

• URL: http://arxiv.org/abs/2603.04053v1
• Date: Wed, 04 Mar 2026 13:34:28 GMT
• Title: An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization
• Authors: Thiago Santos, Sebastiao Xavier,
• Abstract summary: This paper revisits an entropy-inspired convergence indicator and proposes a robust adaptive reformulation based on quantile normalization.<n>The proposed indicator preserves the stationarity-based interpretation of the original formulation while improving robustness to heterogeneous distributions of stationarity residuals.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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