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The majority-inverter graph (MIG) is a homogeneous logic network widely used in logic synthesis for majority-based emerging technologies. Many logic optimization algorithms have been proposed for MIGs, including rewriting, resubstitution, and graph mapping. However, unlike AIGs, research on optimization flows for MIGs is limited. In this paper, we explore combinations of well-developed MIG optimization algorithms using an on-the-fly design space exploration strategy and present the latest best results on MIG size minimization of EPFL benchmarks. Significant reductions (of 88% and 79%) are observed for two specific benchmarks and an average of 14% improvement is achieved compared to the state-of-the-art flow.