  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.
