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Despite rapid progress, federated learning still faces several unsolved challenges. Specifically, communication costs and system heterogeneity, such as nonidentical data distribution, hinder federated learning's progress. Several approaches have recently emerged for federated learning involving heterogeneous clients with varying computational capabilities (namely, heterogeneous federated learning). However, heterogeneous federated learning faces two key challenges: optimising model size and determining client selection ratios. Moreover, efficiently aggregating local models from clients with diverse capabilities is crucial for addressing system heterogeneity and communication efficiency. This paper proposes an evolutionary multiobjective optimisation framework for heterogeneous federated learning (MOHFL) to address these issues. Our approach elegantly formulates and solves a biobjective optimisation problem that minimises communication cost and model error rate. The decision variables in this framework comprise model sizes and client selection ratios for each Q client cluster, yielding a total of 2\u00a0\u00a0Q optimisation parameters to be tuned. We develop a partition\u2010based strategy for MOHFL that segregates clients into clusters based on their communication and computation capabilities. Additionally, we implement an adaptive model sizing mechanism that dynamically assigns appropriate subnetwork architectures to clients based on their computational constraints. We also propose a unified aggregation framework to combine models of varying sizes from heterogeneous clients effectively. Extensive experiments on multiple datasets demonstrate the effectiveness and superiority of our proposed method compared to existing approaches.<\/jats:p>","DOI":"10.1049\/cit2.70090","type":"journal-article","created":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T12:40:57Z","timestamp":1764938457000},"page":"1-14","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi\u2010Objective Optimisation Framework for Heterogeneous Federated Learning"],"prefix":"10.1049","volume":"11","author":[{"given":"Jamshid","family":"Tursunboev","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence Kyungpook National University  Daegu South Korea"}]},{"given":"Vikas","family":"Palakonda","sequence":"additional","affiliation":[{"name":"Department of Mathematics Kyungpook National University  Daegu South Korea"}]},{"given":"Il\u2010Min","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering Queen's University  Kingston Ontario Canada"}]},{"given":"Sunghwan","family":"Moon","sequence":"additional","affiliation":[{"name":"Department of Mathematics Kyungpook National University  Daegu South Korea"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-8181-5994","authenticated-orcid":false,"given":"Jae\u2010Mo","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence Kyungpook National University  Daegu South Korea"}]}],"member":"265","published-online":{"date-parts":[[2025,12,5]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10115\u2010022\u201001664\u2010x"},{"key":"e_1_2_10_3_1","first-page":"374","volume-title":"Proceedings of the Conference on Machine Learning Systems (MLSys)","author":"Bonawitz K.","year":"2019"},{"key":"e_1_2_10_4_1","first-page":"1273","volume-title":"Artificial Intelligence and Statistics","author":"McMahan B.","year":"2017"},{"key":"e_1_2_10_5_1","volume-title":"Advances in Neural Information Processing Systems (NeurIPS) Workshops","author":"Horvath S.","year":"2021"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2021.07.098"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/msp.2020.2975749"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1910.03581"},{"key":"e_1_2_10_9_1","volume-title":"Advances in Neural Information Processing Systems","author":"Alistarh D.","year":"2017"},{"key":"e_1_2_10_10_1","article-title":"Communication\u2010efficient Distributed SGD With Sketching","volume":"32","author":"Ivkin N.","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2004.12088"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICC.2019.8761315"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2002.10619"},{"key":"e_1_2_10_14_1","volume-title":"Advances in Neural Information Processing Systems","author":"Smith V.","year":"2017"},{"key":"e_1_2_10_15_1","volume-title":"Advances in Neural Information Processing Systems","author":"Khodak M.","year":"2019"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2008.03371"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2010.01264"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.3390\/fi15060209"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2025.3567387"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2024.07.046"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3676968"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/4235.996017"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1561\/2200000083"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1812.07210"},{"issue":"1","key":"e_1_2_10_25_1","first-page":"1929","article-title":"Dropout: A Simple Way to Prevent Neural Networks From Overfitting","volume":"15","author":"Srivastava N.","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/lwc.2022.3149783"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/GLOBECOM46510.2021.9685710"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2020\/288"},{"key":"e_1_2_10_29_1","volume-title":"Evolutionary Algorithms for Solving Multi\u2010Objective Problems","author":"Coello C. 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