Fair Client Selection Method for Federated Learning Based on Discretized Firefly Algorithm

Federated Learning (FL) enables collaborative model training without exchanging sensitive local data, ensuring privacy and advancing distributed machine learning. However, in edge scenarios, FL faces challenges of data heterogeneity, device resource constraints, and fairness imbalance among small-data clients, making it difficult to balance performance, efficiency, and fairness. To tackle this, we propose the Discrete Firefly Algorithm (DFA) for fair client selection in FL, mapping clients to fireflies, retaining the brightness attraction"core while adapting to discrete selection. DFA quantifies brightness through data volume and historical contributions, optimizes efficiency with selective sampling, and guarantees fairness for small-data clients. Experiments on MNIST, Fashion-MNIST, and CIFAR-10 demonstrate DFA outperforms baselines: achieving 73.12\((%)\) accuracy on CIFAR-10 (2.56\((%)\) and 10.82\((%)\) higher than random selection and Power-of-Choice), with lower overhead, 2.4\((%)\) performance improvement for small-data clients, and compliance with the principle of contribution-matching benefit.