{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T13:34:20Z","timestamp":1776692060971,"version":"3.51.2"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T00:00:00Z","timestamp":1653264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"General Program of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61871388"],"award-info":[{"award-number":["61871388"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Federated learning (FL) can tackle the problem of data silos of asymmetric information and privacy leakage; however, it still has shortcomings, such as data heterogeneity, high communication cost and uneven distribution of performance. To overcome these issues and achieve parameter optimization of FL on non-Independent Identically Distributed (non-IID) data, a multi-objective FL parameter optimization method based on hierarchical clustering and the third-generation non-dominated sorted genetic algorithm III (NSGA-III) algorithm is proposed, which aims to simultaneously minimize the global model error rate, global model accuracy distribution variance and communication cost. The introduction of a hierarchical clustering algorithm on non-IID data can accelerate convergence so that FL can employ an evolutionary algorithm with a low FL client participation ratio, reducing the overall communication cost of the NSGA-III algorithm. Meanwhile, the NSGA-III algorithm, with fast greedy initialization and a strategy of discarding low-quality individuals (named NSGA-III-FD), is proposed to improve the convergence efficiency and the quality of Pareto-optimal solutions. Under two non-IID data settings, the CNN experiments on both MNIST and CIFAR-10 datasets show that our approach can obtain better Pareto-optimal solutions than classical evolutionary algorithms, and the selected solutions with an optimized model can achieve better multi-objective equilibrium than the standard federated averaging (FedAvg) algorithm and the Clustering-based FedAvg algorithm.<\/jats:p>","DOI":"10.3390\/sym14051070","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T05:12:27Z","timestamp":1653455547000},"page":"1070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Optimizing Multi-Objective Federated Learning on Non-IID Data with Improved NSGA-III and Hierarchical Clustering"],"prefix":"10.3390","volume":"14","author":[{"given":"Jialin","family":"Zhong","sequence":"first","affiliation":[{"name":"Science and Technology on Information System Engineering Laboratory, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yahui","family":"Wu","sequence":"additional","affiliation":[{"name":"Science and Technology on Information System Engineering Laboratory, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wubin","family":"Ma","sequence":"additional","affiliation":[{"name":"Science and Technology on Information System Engineering Laboratory, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Su","family":"Deng","sequence":"additional","affiliation":[{"name":"Science and Technology on Information System Engineering Laboratory, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haohao","family":"Zhou","sequence":"additional","affiliation":[{"name":"Science and Technology on Information System Engineering Laboratory, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ribeiro, M., Grolinger, K., and Capretz, M. 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