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Construct, Merge, Solve & Adapt (CMSA) is a recently developed algorithm for solving combinatorial optimization problems. It combines heuristic elements, such as the probabilistic generation of solutions, with an exact solver that is iteratively applied to sub-instances of the tackled problem instance. In this paper, we present the application of CMSA to an NP-hard problem from the family of dominating set problems in undirected graphs. More specifically, the application in this paper concerns the minimum positive influence dominating set problem, which has applications in social networks. The obtained results show that CMSA outperforms the current state-of-the-art metaheuristics from the literature. Moreover, when instances of small and medium size are concerned CMSA finds many of the optimal solutions provided by CPLEX, while it clearly outperforms CPLEX in the context of the four largest, respectively more complicated, problem instances.