A Multi-Granularity Fireworks Algorithm with Collaboration and Competition for Solving the Influence Maximization Problem

The Influence Maximization (IM) problem in social networks has been extensively studied, with greedy algorithms providing accurate and reliable solutions. However, their high computational cost renders them impractical for large-scale networks. Conversely, structure-based heuristic methods reduce computational complexity but often yield suboptimal solutions. To address these challenges, this paper proposes a novel cooperative and competitive multi-granularity fireworks algorithm (CCFWA). Unlike traditional point-based optimization algorithms, CCFWA employs spherical fireworks of varying granularity to enhance the search process. By distributing fireworks of different scales throughout the solution space, the algorithm effectively distinguishes between critical and less significant regions. Fine-granularity fireworks conduct detailed searches in key areas, while coarse-granularity fireworks enable rapid exploration of less important regions. This multi-granularity representation balances global exploration and local exploitation, improving both accuracy and efficiency in solving the IM problem. Experiments on four real-world social networks demonstrate that CCFWA consistently outperforms six state-of-the-art algorithms in terms of computational efficiency and solution quality.