PDNS-DODE: a discrete osprey optimization and differential evolution algorithm with PageRank diffusion neighborhood search for influence maximization in social networks

Online social networks have become crucial platforms for marketing, leveraging their vast user bases and capacity for rapid information dissemination. Influence maximization (IM) problem plays a central role in applications such as viral marketing and information propagation. Nevertheless, IM remains challenging due to the difficulty in balancing accuracy and efficiency with existing methods. To overcome these limitations, a discrete hybrid optimizer called PDNS-DODE (PageRank-based Diffusion Neighborhood Search and Discrete Osprey Optimization with Differential Evolution) was proposed. The algorithm incorporates an adaptive three-hop diffusion neighborhood search (PDNS) strategy based on PageRank centrality, which dynamically adjusts the search scope to enable broader global exploration and targeted local optimization. A PageRank-descending initialization strategy is introduced to improve population diversity. Furthermore, the Osprey Optimization Algorithm (OOA) and Differential Evolution (DE) are discretized with revised individual representation and update mechanisms for solving the influence maximization problem. Extensive experiments on seven real-world networks under both Independent Cascade and Linear Threshold models demonstrate the robustness and superiority of PDNS-DODE. It consistently outperforms seven state-of-the-art baselines, achieving statistically significant improvements (Wilcoxon test) and the highest overall ranking (Friedman test). These advancements are attained while maintaining competitive computational efficiency.