Consistency for 0-1 Programming

Danial Davarnia; J. N. Hooker

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arXiv · 1812.02215

Consistency for 0-1 Programming

Danial Davarnia·J. N. Hooker

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Abstract

Concepts of consistency have long played a key role in constraint programming but never developed in integer programming (IP). Consistency nonetheless plays a role in IP as well. For example, cutting planes can reduce backtracking by achieving various forms of consistency as well as by tightening the linear programming (LP) relaxation. We introduce a type of consistency that is particularly suited for 0-1 programming and develop the associated theory. We define a 0-1 constraint set as LP-consistent when any partial assignment that is consistent with its linear programming relaxation is consistent with the original 0-1 constraint set. We prove basic properties of LP-consistency, including its relationship with Chvatal-Gomory cuts and the integer hull. We show that a weak form of LP-consistency can reduce or eliminate backtracking in a way analogous to k-consistency but is easier to achieve. In so doing, we identify a class of valid inequalities that can be more effective than traditional cutting planes at cutting off infeasible 0-1 partial assignments.

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Danial Davarnia, J. N. Hooker. 2018-12-05. Consistency for 0-1 Programming. https://arxiv.org/abs/1812.02215

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