The study of Social Network Influence has attracted the interest of scientists. The wide variety of real-world applications of this area, such as viral marketing and disease analysis, highlights the relevance of designing an algorithm capable of solving the problem efficiently. This paper studies the Multiple Round Influence Maximization (MRIM) problem, in which influence is propagated in multiple rounds independently from possibly different seed sets. This problem has two variants: the non-adaptive MRIM, in which the advertiser needs to determine the seed sets for all rounds at the beginning, and the adaptive MRIM, in which the advertiser can select the seed sets adaptively based on the propagation results in the previous rounds. The main difficulty of this optimization problem lies in the computational effort required to evaluate a solution. Since each node is infected with a certain probability, the value of the objective function must be calculated through an influence diffusion model, which results in a computationally complex process. For this purpose, a metaheuristic algorithm based on Variable Neighborhood Search is proposed with the aim of providing high-quality solutions, being competitive with the state of the art.