Influence maximization (IM) is a fundamental problem in complex network analysis, with a wide range of real-world applications. To date, existing approaches to influential node identification in IM have predominantly relied on standard graphs, failing to capture higher-order intrinsic interactions embedded in many real-world systems. Hypergraphs can be employed to better capture higher-order interactions. However, using hypergraphs may lead to an excessively large search space and increased complexity in modeling cascading dynamics, making it challenging to accurately identify influential nodes. Therefore, in this study, we propose a new hypergraph-modeled IM method, based on the Discrete Particle Swarm Optimization algorithm and the threshold model. In the proposed method, a particle (i.e., a candidate solution) represents the selection information of seed nodes, and the fitness function is designed to accurately and efficiently evaluate the influence of seed nodes via a two-layer local influence approximation. We also propose a degree-based initialization strategy to improve the quality of initial solutions and develop rules for updating particles' velocity and position, incorporated with a local search to drive particles toward better solutions. Experimental results demonstrate that the proposed method outperforms baseline methods on both synthetic and real-world hypergraphs. In addition, ablation studies validate the effectiveness of both the local search and the initialization strategies.

翻译：影响力最大化（IM）是复杂网络分析中的基本问题，具有广泛的现实应用。迄今为止，现有IM方法在识别关键节点时主要依赖标准图结构，未能捕捉许多现实系统中内嵌的高阶内在交互。超图能够更好地表征高阶交互，但可能导致搜索空间急剧扩大及级联动力学建模复杂性增加，给精准识别关键节点带来挑战。因此，本研究提出了一种基于离散粒子群优化算法与阈值模型的超图建模IM方法。在该方法中，粒子（即候选解）表征种子节点的选择信息；通过设计双层局部影响力近似机制，适应度函数可精准高效地评估种子节点影响力。我们同时提出了基于度数的初始化策略以提升初始解质量，并开发了融入局部搜索的粒子速度与位置更新规则，引导粒子趋近更优解。实验结果表明，该方法在合成超图与现实超图上均优于基线方法。此外，消融实验验证了局部搜索与初始化策略的有效性。