Preprocessing and Cutting Planes with Conflict Graphs
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This paper addresses the implementation of conflict graph-based routines into the COIN-OR Branch-and-Cut (CBC) solver, including: (i) a conflict graph infrastructure with an improved version of a state-of-the-art conflict detection algorithm to quickly build conflict graphs; this version detects additional conflicts and has the same worst-case complexity of the original algorithm; (ii) a preprocessing routine based on a clique-strengthening scheme that can both reduce the number of nonzeros in the constraint matrix and also produce stronger formulations; (iii) a clique cut separator capable of obtaining dual bounds at the root node that are 26% stronger than the ones provided by the equivalent cut generator of a state-of-the-art commercial solver, 467% stronger than those attained by the clique cut separator of the GLPK solver and 500% stronger than the dual bounds obtained by the clique separation routine of the COIN-OR Cut Generation Library; (iv) an odd-cycle cut separator with a lifting module to produce valid odd-wheel inequalities. This new version of CBC obtained an average gap closed that is 26% better than the previous one and solved 27% more instances.
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