From Linear Relaxations to Global Constraint Propagation

Abstract

Recently, many algorithms have been designed to propagate global constraints. Unfortunately, some global constraints, such the At-Most-1 constraint and the Extended-GCC are NP-Hard to propagate. Often, these constraints can easily be written as integer linear programs. Using linear relaxations and other techniques developed by the operation research community, we want to efficiently propagate such constraints.

We model constraints as integer programs that we relax into linear programs. For each value v in a variable domain dom(x), we create a binary variable x _v . The assignment x _v = 1 indicates that x = v while x _v = 0 indicates that x ≠ v.

This is joint work with Emmanuel Hebrard and Toby Walsh.