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Traditional federated learning faces challenges such as high communication costs, structural heterogeneity,and insufficient privacy protection. To address these issues, this paper proposes a federated learning evolutionary algorithm that applies sparse evolutionary training algorithm to reduce communication costs and integrates local differential privacy protection for participants’ privacy. Additionally, it utilizes the NSGA-Ⅲ algorithm to optimize the network structure and sparsity of the global federated learning model, adjusting the relationship between data availability and privacy protection. This achieves a balance between the effectiveness, communication costs, and privacy of the global federated learning model. Experimental results under unstable communication environments demonstrate that, on the MNIST and CIFAR-10 datasets, compared to the solution with the lowest error rate using the FNSGA-Ⅲ algorithm, the proposed algorithm improves communication efficiency by 57. 19% and 52. 17%, respectively. The participants also achieved（3. 46, 10-4） and（6. 52, 10-4）-local differential privacy. This algorithm can effectively reduce communication costs and protect participant privacy without significantly compromising the accuracy of the global model. [ABSTRACT FROM AUTHOR]