Influence maximization (IM) is a crucial optimization task related to analyzing complex networks in the real world, such as social networks, disease propagation networks, and marketing networks. Publications to date about the IM problem focus mainly on graphs, which fail to capture high-order interaction relationships from the real world. Therefore, the use of hypergraphs for addressing the IM problem has been receiving increasing attention. However, identifying the most influential nodes in hypergraphs remains challenging, mainly because nodes and hyperedges are often strongly coupled and correlated. In this paper, to effectively identify the most influential nodes, we first propose a novel hypergraph-independent cascade model that integrates the influences of both node and hyperedge failures. Afterward, we introduce genetic algorithms (GA) to identify the most influential nodes that leverage hypergraph collective influences. In the GA-based method, the hypergraph collective influence is effectively used to initialize the population, thereby enhancing the quality of initial candidate solutions. The designed fitness function considers the joint influences of both nodes and hyperedges. This ensures the optimal set of nodes with the best influence on both nodes and hyperedges to be evaluated accurately. Moreover, a new mutation operator is designed by introducing factors, i.e., the collective influence and overlapping effects of nodes in hypergraphs, to breed high-quality offspring. In the experiments, several simulations on both synthetic and real hypergraphs have been conducted, and the results demonstrate that the proposed method outperforms the compared methods.

翻译：影响力最大化是分析社交网络、疾病传播网络和营销网络等现实世界复杂网络的关键优化任务。当前关于影响力最大化问题的研究主要集中于图结构，然而图无法捕捉现实世界中的高阶交互关系。因此，利用超图解决影响力最大化问题日益受到关注。但由于节点与超边通常存在强耦合与相关性，如何在超图中识别最具影响力节点仍具挑战性。本文为有效识别最具影响力节点，首先提出一种新型超图独立级联模型，该模型融合了节点失效与超边失效的双重影响。继而引入遗传算法，利用超图集体影响力实现最具影响力节点的识别。在基于遗传算法的方法中，超图集体影响力被有效用于种群初始化，从而提升初始候选解的质量。所设计的适应度函数综合考虑节点与超边的联合影响，确保能够准确评估对节点与超边均具有最佳影响力的最优节点集。此外，通过引入超图中节点的集体影响力与重叠效应等因子，设计了新型变异算子以培育高质量子代。实验环节在合成超图与真实超图上开展了多项仿真验证，结果表明所提方法性能优于对比方法。