A gray wolf optimization algorithm with thinking and reflection mechanisms for influence maximization

Influence Maximization (IM) in social networks is a critical problem in social network analysis. The goal is to select a group of the most influential users from the network as initial spreaders, maximizing the influence propagation range under a specific diffusion model. The Gray Wolf Optimization (GWO) algorithm has gained attention due to its simplicity and efficiency; however, its effectiveness diminishes when tackling complex IM problems. The main issue lies in the lack of directional information, leading to an imbalance between exploration and exploitation and a tendency to fall into local optima. To overcome these challenges, this paper proposes a Gray Wolf Optimization algorithm with a dual-mode thinking — reflection mechanism (DTR-GWO). The algorithm introduces a dual-mode learning strategy — “intuitive thinking” for rapidly identifying high-impact regions in the solution space, and “deep thinking” for fine-grained local refinement — achieving a dynamic balance between exploration and exploitation. In addition, a reflection mechanism is incorporated, integrating self-reinforcement, elite-guided strategies, and knowledge preservation to improve solution quality, and effectively avoid premature convergence. Extensive experiments on real-world social networks demonstrate the superiority of the proposed approach. Results demonstrate the effectiveness of algorithm and improved the accuracy of the solution.