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Lithium-ion batteries (LIBs) experience aging degradation during long-term operation. Accurate prediction of the remaining useful life (RUL) in advance is crucial to ensure continuous and reliable energy supply of the battery management system (BMS). Aiming at the problem of limited robustness of deep extreme learning machine (DELM) in RUL prediction for LIBs, an improved multi-objective arithmetic optimization algorithm (MOAOA) is proposed to enhance the prediction ability of DELM. Firstly, in order to overcome the limitations of the traditional single-objective optimization algorithm in terms of model stability, MOAOA is introduced to optimize the parameter selection of the DELM model, which effectively solved the problems of low efficiency and poor stability of parameter selection. Secondly, four health indexes (HIs) are extracted from the charging and discharging process, and their correlation ability was verified using Pearson, Spearman and Kendall correlation coefficient. Finally, the MOAOA-DELM method is fully validated using the NASA battery dataset, and the prediction results are compared with traditional methods and other multi-objective algorithms. The results show that the MOAOA-DELM method has small prediction error, strong state tracking fitting ability, good generalization ability and robustness.