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Improvements over recent years in the performance of Integer Linear Programming (ILP) and Boolean Satisfiability (SAT) solvers have encouraged the modeling of complex engineering problems as ILP. An example is the Clustering Problem in Mobile Ad-Hoc Networks (MANETs). The Clustering Problem in MANETs consists of selecting the most suitable nodes of a given MANET topology as clusterheads, and ensuring that regular nodes are connected to clusterheads such that the lifetime of the network is maximized. This paper proposes enhanced ILP formulations for the Clustering Problem, through the enablement of multi-hop connections and intra-cluster communication, and assesses the performance of state-of-the art generic ILP and SAT solvers in solving the enhanced formulations.