Adaptive Fairness Penalty Evolutionary Optimization with Entropy-Guided Constraint Control

Ensuring fairness in machine learning while maintaining predictive performance remains a fundamental challenge in data science. Most fairness-aware learning approaches rely on fixed penalty scalarization or static multi-objective formulations, which often lead to unstable trade-offs and sensitivity to manually tuned hyperparameters. In this paper, we propose SAFEA (Self-Adaptive Fairness Entropy Algorithm), a novel evolutionary optimization framework that dynamically regulates the fairness–accuracy trade-off using inequality-aware feedback mechanisms. SAFEA introduces two complementary measures: the Fairness Entropy Index (FEI), which captures the dispersion of group-level fairness violations, and the Gini Fairness Index, which quantifies disparity in prediction errors across protected groups. These measures guide an adaptive penalty update rule that autonomously adjusts the fairness coefficient during the evolutionary search process, eliminating the need for manual tuning. Theoretical analysis establishes boundedness and stability of the adaptive penalty under mild assumptions and discusses convergence properties under Lipschitz-continuous objectives. Experimental evaluation on benchmark datasets (Adult Income, COMPAS, and German Credit) demonstrates that SAFEA improves hypervolume by up to 12.4% compared to NSGA-II fairness formulations, reduces demographic parity difference by 18–25% relative to static penalty evolutionary methods, and achieves up to 3.1% higher F1-score than adversarial debiasing approaches while maintaining competitive accuracy. These results indicate that entropy-guided adaptive regulation leads to smoother fairness convergence and better Pareto front coverage. The proposed framework bridges inequality theory and evolutionary multi-objective optimization, providing a scalable and effective solution for fairness-aware learning in high-stakes applications.