In this paper, we propose a system combination method for grammatical error correction (GEC), based on nonlinear integer programming (IP). Our method optimizes a novel F score objective based on error types, and combines multiple end-to-end GEC systems. The proposed IP approach optimizes the selection of a single best system for each grammatical error type present in the data. Experiments of the IP approach on combining state-of-the-art standalone GEC systems show that the combined system outperforms all standalone systems. It improves F0.5 score by 3.61% when combining the two best participating systems in the BEA 2019 shared task, and achieves F0.5 score of 73.08%. We also perform experiments to compare our IP approach with another state-of-the-art system combination method for GEC, demonstrating IP's competitive combination capability.
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