This paper is concerned with phonetic reconstruction of the consonant system of Middle Chinese. We propose to cast the problem as a Mixed Integer Programming problem, which is able to automatically explore homophonic information from ancient rhyme dictionaries and phonetic information from modern Chinese dialects, the descendants of Middle Chinese. Numerical evaluation on a wide range of synthetic and real data demonstrates the effectiveness and robustness of the new method. We apply the method to information from Gu\v angy\`un (Author's note: The Gu\v angy\`un here is Chinese Pinyin in Latex, for HTML code, it should be Guǎngyùn) and 20 modern Chinese dialects to obtain a new phonetic reconstruction result. A linguistically-motivated discussion of this result is also provided.
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