Many-Objective Evolutionary Influence Maximization: Balancing Spread, Budget, Fairness, and Time

TL;DR

This work introduces MOEIM (Many-Objective Evolutionary Algorithm for Influence Maximization), a Multi-Objective Evolutionary Algorithm based on NSGA-II incorporating graph-aware operators and a smart initialization, and compares MOEIM in two experimental settings.

Abstract

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.

Figures (3)

• Figure 1: Graphical representation of the IC and WC models (left), and LT model (right). The top row shows activated nodes (green circles) and non-activated nodes (dashed red circles) at timestep $t_{i-1}$. The bottom row shows the nodes that can be activated at timestep $t_i$.
• Figure 2: Non-dominated solutions found MOEIM and DeepIM ling2023deep. For MOEIM, we provide the worst, median and best sets of non-dominated solutions found across $10$ runs. To allow for a direct comparison with the results reported in ling2023deep, the x-axis and y-axis show, respectively, the seed set size $\mathcal{S}^{\downarrow}$ and the final influence $\mathcal{I}^{\uparrow}$, both normalized w.r.t. the size of each network, $|\mathcal{V}|$. For DeepIM, we show the results available in the original paper, where they are reported separately for each value of $\mathcal{S}^{\downarrow}$/$|\mathcal{V}|$.
• Figure 3: Pearson correlation among the objectives ($\mathcal{I}^{\uparrow}$: Influence; $\mathcal{S}^{\downarrow}$: Seed set size; $\mathcal{C}^{\uparrow}$: Communities; $\mathcal{F}^{\uparrow}$: Fairness; $\mathcal{B}^{\downarrow}$: Budget; $\mathcal{T}^{\downarrow}$: Time). This correlation has been computed over the results of the 10 runs available for the "MOEIM (all)" setting (see \ref{['tab:results']} for details). Top row: IC model, bottom row: WC model.