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Over the course of the last decade, there have been several improvements in the performance of Integer Linear Programming (ILP) and Boolean Satisfiability (SAT) solvers. These improvements have encouraged the application of SAT and ILP techniques in modeling complex engineering problems. One such problem 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 the development of an improved ILP formulation of the Clustering Problem. Additionally, various enhancements are implemented in the form of extensions to the improved formulation, including the establishment of intra-cluster communication, multihop connections and the enforcement of coverage constraints. The improved formulation and enhancements are implemented in a tool designed to visually create network topologies and cluster them using state-of-the art Generic ILP and SAT solvers. Through this tool, feasibility of using the proposed formulation and enhancements in a real-life practical environment is assessed. It is observed that the Generic ILP solvers, CPLEX, and SCIP, are able to handle large network topologies, while the 0-1 SAT-based ILP solver, BSOLO, is effective at handling the smaller scale networks. It is also observed that while these enhanced formulations enable the generation of complex network solutions, and are suitable for small scale networks, the time taken to generate the corresponding solution does not meet the strict requirements of a practical environment.