## 2 Materials and Methods
### Developing the Improved Federated RHLP Algorithm for Efficient Client Selection
Furthermore, we aim to dynamically adjust client participation in each round, considering factors such as fluctuating client participation ratios and local training epochs. This adjustment will be based on the influence of global model tuning and the contributions of client groups in each communication round, optimizing the efficiency of the global model. Conceptualization, P.S., N.P. and K.T. ; methodology, P.S. and N.P. ; software, P.S. ; validation, P.S., N.P. and K.T. ; formal analysis, P.S., N.P. and K.T. ; investigation, P.S., N.P. and K.T. ; resources, P.S., N.P. and K.T. ; data curation, P.S., N.P. and K.T. ; writing--original draft preparation, P.S. ; writing--review and editing, P.S., N.P. and K.T. ; visualization, P.S. and K.T. ; supervision, P.S. and K.T. ; project administration, P.S. and K.T. ; funding acquisition, K.T. All authors have read and agreed to the published version of the manuscript. This research was funded by Naresuan University (NU) and National Science, Research and Innovation Fund (NSRF), grant number 180613. Data Availability Statement: Data are contained within the article. We thank [PERSON], Lecturer (Special Knowledge and Abilities), Faculty of Medical Science, Naresuan University, Thailand for carefully checking the general format of the manuscript. The authors declare no conflicts of interest. ## References

* (1) [PERSON]; [PERSON] Multi-Criterion Client Selection for Efficient Federated Learning. In Proceedings of the AAAI Symposium Series, Stanford, CA, USA, 20 May 2024; Volume 3, pp. 318-322. * (2) [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Adaptive client selection with personalization for communication efficient Federated Learning. _Ad Hoc Netw._**2024**, _157_, 103462. [CrossRef]
* (3) [PERSON]; [PERSON]; [PERSON]; [PERSON] Understanding and improving model averaging in federated learning on heterogeneous data. _IEEE Trans. Mob. Comput._**2024**, _23_, 12131-12145. [CrossRef]
* (4) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Communication-efficient learning of deep net-works from decentralized data. In Proceedings of the 20 th International Conference on Artificial Intelligence and Statistics, Fort Lauderdale, FL, USA, 20-22 April 2017; PMLR: Birmingham, UK, 2017; pp. 1273-1282. * (5) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] ACS: Accuracy-based client selection mechanism for federated industrial IoT. _Internet Things_**2023**, _21_, 100657. [CrossRef]
* (6) [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Federated learning: Challenges, SoTA, performance improvements and application do-mains. _IEEE Open J. Commun. Soc._**2024**, \(5\), 5933-6017. [CrossRef]
* (7) [PERSON]; [PERSON]; [PERSON] A multi-agent reinforcement learning approach for efficient client selection in federated learning. In Proceedings of the AAAI Conference on Artificial Intelligence, Pittsburgh, PA, USA, 28 June 2022; Volume 36, pp. 9091-9099. * (8) [PERSON]; [PERSON]; [PERSON]; [PERSON] On the Convergence of Heterogeneous Federated Learning with Arbitrary Adaptive Online Model Pruning. _arXiv_**2022**, arXiv:2201.11803. * (9) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] FedProc: Prototypical contrastive federated learning on non-IID data. _Future Gener. Comput. Syst._**2023**, _143_, 93-104. [CrossRef]
* (10) [PERSON]; [PERSON]; [PERSON] Client selection in federated learning: Convergence analysis and power-of-choice se-lection strategies. _arXiv_**2020**, arXiv:2010.01243. * (11) [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON] A Client Selection Method Based on Loss Function Optimization for Federated Learning. _Comput. Model. Eng. Sci._**2023**, _137_, 1047-1064. [CrossRef]
* (12) [PERSON]; [PERSON] Fed-RHLP: Enhancing Federated Learning with Random High-Local Performance Client Selection for Improved Convergence and Accuracy. _Symmetry_**2024**, _16_, 1181.