The Influence Maximization (IM) problem seeks to discover the set of nodes in a graph that can spread the information propagation at most. This problem is known to be NP-hard, and it is usually studied by maximizing the influence (spread) and, optionally, optimizing a second objective, such as minimizing the seed set size or maximizing the influence fairness. However, in many practical scenarios multiple aspects of the IM problem must be optimized at the same time. In this work, we propose a first case study where several IM-specific objective functions, namely budget, fairness, communities, and time, are optimized on top of the maximization of influence and minimization of the seed set size. To this aim, we introduce MOEIM (Many-Objective Evolutionary Algorithm for Influence Maximization) a Multi-Objective Evolutionary Algorithm (MOEA) based on NSGA-II incorporating graph-aware operators and a smart initialization. We compare MOEIM in two experimental settings, including a total of nine graph datasets, two heuristic methods, a related MOEA, and a state-of-the-art Deep Learning approach. The experiments show that MOEIM overall outperforms the competitors in most of the tested many-objective settings. To conclude, we also investigate the correlation between the objectives, leading to novel insights into the topic. The codebase is available at https://github.com/eliacunegatti/MOEIM.

翻译：影响力最大化（IM）问题旨在发现图中能够最大程度传播信息传播的节点集合。该问题已知为NP难问题，通常通过最大化影响力（传播）并可选地优化第二目标（如最小化种子集规模或最大化影响力公平性）进行研究。然而，在许多实际场景中，IM问题的多个方面必须同时优化。本文提出首个案例研究，在最大化影响力和最小化种子集规模的基础上，同时优化多个IM特定目标函数，即预算、公平性、社区和时间。为此，我们提出MOEIM（基于多目标演化算法的影响力最大化方法），这是一种基于NSGA-II的多目标演化算法（MOEA），集成了图感知算子与智能初始化。我们在两个实验设置中比较MOEIM，涉及九个图数据集、两种启发式方法、一种相关MOEA以及一种前沿深度学习方法。实验表明，在大多数测试的多目标设定中，MOEIM整体上优于对比方法。最后，我们研究了目标之间的相关性，得出了该课题的新见解。代码库见https://github.com/eliacunegatti/MOEIM。