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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.04053 |
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| _version_ | 1866915833980125184 |
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| author | Santos, Thiago Xavier, Sebastiao |
| author_facet | Santos, Thiago Xavier, Sebastiao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04053 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization Santos, Thiago Xavier, Sebastiao Optimization and Control Neural and Evolutionary Computing 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. |
| title | An Adaptive KKT-Based Indicator for Convergence Assessment in Multi-Objective Optimization |
| topic | Optimization and Control Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2603.04053 |