Multi-objective Evolutionary Algorithms for Influence Maximization in Social Networks

Abstract

As the pervasiveness of social networks increases, new NPhard related problems become interesting for the optimization community. The objective of influence maximization is to contact the largest possible number of nodes in a network, starting from a small set of seed nodes, and assuming a model for information propagation. This problem is of utmost practical importance for applications ranging from social studies to marketing. The influence maximization problem is typically formulated assuming that the number of the seed nodes is a parameter. Differently, in this paper, we choose to formulate it in a multi-objective fashion, considering the minimization of the number of seed nodes among the goals, and we tackle it with an evolutionary approach. As a result, we are able to identify sets of seed nodes of different size that spread influence the best, providing factual data to trade-off costs with quality of the result. The methodology is tested on two real-world case studies, using two different influence propagation models, and compared against state-of-the-art heuristic algorithms. The results show that the proposed approach is almost always able to outperform the heuristics.

Improving Multi-objective Evolutionary Influence Maximization in Social Networks

“…Several metaheuristics and optimization algorithms have also been applied to the problem, ranging from simulated annealing [12] to genetic algorithms [6]. In [7], a Multi-Objective Evolutionary Algorithm (MOEA) [13] was proposed for influence maximization, where the two considered objectives were (i) maximizing the influence of a seed set and (ii) minimizing the number of nodes in the seed set. Intuitively, this produced a Pareto front of candidate solutions, each one a different compromise.…”

“…To improve upon the work presented in [7] and overcome the aforementioned limitations due to the method time consumption, we introduce here a seeding mechanism. In particular, we show that by seeding the initial population of the MOEA with the results of computationally cheap heuristics, the number of individual evaluations required to reach satisfying solutions drops dramatically.…”

“…In particular, we show that by seeding the initial population of the MOEA with the results of computationally cheap heuristics, the number of individual evaluations required to reach satisfying solutions drops dramatically. Another important difference with respect to the MOEA used in [7] concerns the algorithmic implementation: while that work was based a C++ open source customizable evolutionary tool [14], here we use inspyred 4 , a Python open source framework for creating biologically-inspired computational intelligence algorithms, including evolutionary computation, swarm intelligence, and immunocomputing. inspyred provides easy-to-modify canonical versions of several bio-inspired algorithms, among which the MOEA NSGA-II [15], that we use in the experiments presented in this paper.…”

“…In order to assess the proposed improvements for influence maximization, we selected three case studies among social network graphs available in the Network Repository 5 and SNAP 6 databases. Two of the selected social networks, ego-Facebook and ca-GrQc were also considered in [7], while soc-ePinions1 was not considered in the previous study. The selected benchmarks, with their respective features, are reported in Table 1.…”

“…As with many other NP-hard problem, evolutionary algorithms (EAs) where used to explore the vast search space of all possible subsets of nodes [6]. More recently, a multi-objective EA (MOEA), was used to maximize the influence I while concurrently minimizing the size of the seed set [7], providing users the necessary data to trade off between budget (the number of nodes that need to be influenced) and effect (the final influence over the whole network). This paper progresses on the same research line, showing how significant improvements can be attained by carefully initializing the initial population.…”