Handling Symmetries in Mixed-Integer Semidefinite Programs

Symmetry handling is a key technique for reducing the running time of branch-and-bound methods for solving mixed-integer linear programs. In this paper, we generalize the notion of (permutation) symmetries to mixed-integer semidefinite programs (MISDPs). We first discuss how symmetries of MISDPs can be automatically detected by finding automorphisms of a suitably colored auxiliary graph. Then … Read more

Handling Sub-symmetry in Integer Programming using Activation Handlers

Symmetry in integer programs (IPs) can be exploited in order to reduce solving times. Usually only symmetries of the original IP are handled, but new symmetries may arise at some nodes of the branch-and-bound tree. While symmetry-handling inequalities (SHIs) can easily be used to handle original symmetries, handling sub-symmetries arising later on is more intricate. … Read more

A Unified Framework for Symmetry Handling

Handling symmetries in optimization problems is essential for devising efficient solution methods. In this article, we present a general framework that captures many of the already existing symmetry handling methods (SHMs). While these SHMs are mostly discussed independently from each other, our framework allows to apply different SHMs simultaneously and thus outperforming their individual effect. … Read more

Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs

The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on propagation techniques for cyclic groups. Our algorithms come with the guarantee to find all possible variable fixings that can be derived from … Read more

Schreier-Sims Cuts meet Stable Set: Preserving Problem Structure when Handling Symmetries

Symmetry handling inequalities (SHIs) are a popular tool to handle symmetries in integer programming. Despite their successful application in practice, only little is known about the interaction of SHIs with optimization problems. In this article, we focus on SST cuts, an attractive class of SHIs, and investigate their computational and polyhedral consequences for optimization problems. … Read more