Variable-Length Evolutionary Search for Influence Maximization with Influence, Cost and Time

Influence maximization has been studied for social network analysis, such as viral marketing (advertising), rumor prevention, and opinion leader identification. However, most studies neglect the interplay between influence spread, cost efficiency, and temporal urgency. In practical scenarios such as viral marketing and information campaigns, jointly optimizing Influence, Cost, and Time is essential, yet remaining largely unaddressed in current literature. To bridge the gap, this paper proposes a new multi-objective influence maximization problem that simultaneously optimizes influence, cost, and time. We show the intuitive and empirical evidence to prove the feasibility and necessity of this multi-objective problem. We also develop an evolutionary variable-length search algorithm that can effectively search for optimal node combinations. The proposed EVEA algorithm outperforms all baselines, achieving up to 19.3% higher hypervolume and 25–40% faster convergence across four real-world networks, while maintaining a diverse and balanced Pareto front among influence, cost, and time objectives. We release the source code on GitHub: https://github.com/fmyzckj.