Branch-and-cut for linear programs with overlapping SOS1 constraints

Tobias Fischer, Marc E. Pfetsch
2017 Mathematical Programming Computation  
SOS1 constraints require that at most one of a given set of variables is nonzero. In this article, we investigate a branch-and-cut algorithm to solve linear programs with SOS1 constraints. We focus on the case in which the SOS1 constraints overlap. The corresponding conflict graph can algorithmically be exploited, for instance, for improved branching rules, preprocessing, primal heuristics, and cutting planes. In an extensive computational study, we evaluate the components of our implementation
more » ... on instances for three different applications. We also demonstrate the effectiveness of this approach by comparing it to the solution of a mixed-integer programming formulation, if the variables appearing in SOS1 constraints are bounded.
doi:10.1007/s12532-017-0122-5 fatcat:3rxna375dfgi3o5l53u5b3zira