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Differential privacy (DP), as a promising privacy-preserving model, has attracted great interest from researchers in recent years. At present, research on the combination of deep learning and DP is active. In contrast, another widely used artificial intelligence technique, swarm intelligence (SI), has received little attention in the context of DP even though it also triggers privacy concerns. For this reason, this paper attempts to combine DP and SI for the first time and proposes a general differentially private swarm intelligence algorithm framework (DPSIAF). By utilizing the exponential mechanism, this framework can easily develop existing SI algorithms into the private versions. As examples, we apply it to four popular SI algorithms, and the related analyses demonstrate the effectiveness of our DPSIAF. More importantly, our private algorithms also exhibit some interesting experimental phenomena. In some cases, their performance is not strictly affected by the privacy budget, and one of them even outperforms its non-private version. These findings are different from the conventional cognition, which indicates DP owns the potential to serve as an optimization tool for some SI algorithms. Our study may provide a new perspective on DP and promote the synergy between metaheuristic optimization community and privacy computing community. [ABSTRACT FROM AUTHOR]