| The rapid growth of online social networks has brought much attention on information diffusion,which is important for many practical applications,such as the viral marketing,the adoption of political standpoints and/or technical innovations.Influence Maximization(IM)is one of the key algorithmic problems in information diffusion research,which is aimed to select a set of K users(called seed set)from a social network such that the expected number of influenced users(called influence spread),following a given influence diffusion model,is maximized.However,with the popularization of social networks,various social platforms keep emerging to meet different social needs,which makes social populations not confined to one network,but distributed in different social networks.One of the direct effects of this change is that the application based on virus marketing,such as product promotion on a single network,can not meet the breadth requirements of promotion.It is likely that the number of users on a single network can not reach the target population of promotion,or the advertising companies expect to find K users on multiple network platforms in order to maximize the spread range.As a result,influence diffusion on multiple social media platforms has gradually become the focus of attention in academia and industry.Rich social network not only provides convenience for people in social needs,but also provides new ideas for some enterprises in product marketing.It enables some companies to select some influential users through online marketing methods,and let these users recommend products to other users by providing samples or discounts.Through word-of-mouth effect,the maximum number of users who understand or buy the product on the internet.Compared with traditional product promotion methods,this method has the advantage of less investment and more precise advertising.Despite its immense application potential,there has been relatively little research dedicated to IM for multilayer networks.In essence,multiple social media platforms can be modeled as a multilayer network,where each layer of network can be regarded as connected by a specific user.One such realistic scenario is that a user manages multiple social accounts at the same time,so that information can be transmitted between different social media platforms.Most previous studies have ignored the objective fact that information diffusion is the combined effect of multiple influencing factors in real life,and the space of diffusion is not limited to a single network.Therefore,studying the law of information diffusion in more complex networks will help to reveal key factors affecting the spread of information on social networks.On the other side,most existing IM studies,which rely on the greedy strategy,can only obtain a single solution that provides limited insights on the core organization of the target networks.Moreover,such a solution could be biased towards a particular structure inherent inside the criterion(i.e.,the predefined submodular function)to optimize.To this end,this paper focuses on studying the IM problem in multilayer networks.Specifically,we first define some novel concepts,such as the pairwise reciprocal length and the pairwise influence,with respect to the information diffusion process in multilayer networks.Then,we formulate the IM in multilayer networks as a multi-objective optimization problem;and employ the classic Non-dominated Sorting Genetic Algorithm II(NSGA-II)to find a set of Pareto optimal solutions,which can provide a wide range of options for decision markers.To maintain population diversity,as well as to accelerate the convergence of the algorithm,a heuristic population initialization strategy and an efficient two-point crossover operation are combined used.Extensive experiments have been applied to real-world multilayer networks,and the results show that our approach has competitive performance when compared to off-the-shelf IM algorithms with regards to the influence spread and the running time. |
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