Finding groups from a set of interconnected nodes is a recurrent paradigm in a variety of practical problems that can be modeled as a graph, as those emerging from Social Networks. However, finding an optimal partition of a graph is a computationally complex task, calling for the development of approximative heuristics. In this regard, the work presented in this paper tackles the optimal partitioning of graph instances whose connections among nodes are directed and weighted, a scenario significantly less addressed in the literature than their unweighted, undirected counterparts. To efficiently solve this problem, we design several heuristic solvers inspired by different processes and phenomena observed in Nature (namely, Water Cycle Algorithm, Firefly Algorithm, an Evolutionary Simulated Annealing and a Population based Variable Neighborhood Search), all resorting to a reformulated expression for the well-known modularity function to account for the direction and weight of edges within the graph. Extensive simulations are run over a set of synthetically generated graph instances, aimed at elucidating the comparative performance of the aforementioned solvers under different graph sizes and levels of intra- and inter-connectivity among node groups. We statistically verify that the approach relying on the Water Cycle Algorithm outperforms the rest of heuristic methods in terms of Normalized Mutual Information with respect to the true partition of the graph.