One of the primary challenges in distributed systems, such as cloud computing, lies in ensuring that data objects are accessible within a reasonable timeframe. To address this challenge, the data objects are replicated across multiple servers. Estimating the minimum quantity of data replicas and their optimal placement is considered an NP-complete optimization problem. The primary objectives of the current research include minimizing data processing costs, reducing the quantity of replicas, and maximizing the applied algorithms’ reliability in replica placement. This paper introduces a hybrid chaos-based swarm approach using the modified shuffle-frog leaping algorithm with a new local search strategy for replicating data in distributed systems. Taking into account the algorithm’s performance in static settings, the introduced method reduces the expenses associated with replica placement. The results of the experiment conducted on a standard data set indicate that the proposed approach can decrease data access time by about 33% when using approximately seven replicas. When executed several times, the suggested method yields a standard deviation of approximately 0.012 for the results, which is lower than the result existing algorithms produce. Additionally, the new approach’s success rate is higher in comparison with existing algorithms used in addressing the problem of replica placement.