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arXiv · 2204.09122

Continuous cutting plane algorithms in integer programming

Didier Chételat·Andrea Lodi
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Abstract

Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous optimization problem over weights parametrizing families of valid inequalities. This problem can also be interpreted as optimizing a neural network to solve an optimization problem over subadditive functions, which we call the subadditive primal problem of the MILP. To do so, we propose a concrete two-step algorithm, and demonstrate empirical gains when optimizing generalized Gomory mixed-integer inequalities over various classes of MILPs. Code for reproducing the experiments can be found at https://github.com/dchetelat/subadditive.

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Didier Chételat, Andrea Lodi. 2022-04-19. Continuous cutting plane algorithms in integer programming. https://arxiv.org/abs/2204.09122

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