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.

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In the context of social networks, maximizing influence means contacting the largest possible number of nodes starting from a set of seed nodes, and assuming a model for influence propagation. The real-world applications of influence maximization are of uttermost importance, and range from social studies to marketing campaigns. Building on a previous work on multi-objective evolutionary influence maximization, we propose improvements that not only speed up the optimization process considerably, but also deliver higher-quality results. State-of-the-art heuristics are run for different sizes of the seed sets, and the results are then used to initialize the population of a multi-objective evolutionary algorithm. The proposed approach is tested on three publicly available real-world networks, where we show that the evolutionary algorithm is able to improve upon the solutions found by the heuristics, while also converging faster than an evolutionary algorithm started from scratch.

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