4 research outputs found
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. Moreover, most existing SHMs only apply to binary
variables. Our framework allows to easily generalize these methods to general
variable types. Numerical experiments confirm that our novel framework is
superior to the state-of-the-art SHMs implemented in the solver SCIP
The SCIP Optimization Suite 9.0
The SCIP Optimization Suite provides a collection of software packages for
mathematical optimization, centered around the constraint integer programming
(CIP) framework SCIP. This report discusses the enhancements and extensions
included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include
improved symmetry handling, additions and improvements of nonlinear handlers
and primal heuristics, a new cut generator and two new cut selection schemes, a
new branching rule, a new LP interface, and several bug fixes. The SCIP
Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new
Python interface for SoPlex, along with enhancements to existing interfaces.
The SCIP Optimization Suite 9.0 also includes new and improved features in the
LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the
decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions
and enhancements have resulted in an overall performance improvement of SCIP in
terms of solving time, number of nodes in the branch-and-bound tree, as well as
the reliability of the solver.Comment: The release report of the SCIP Optimization Suite version 9.
The Impact of Symmetry Handling for the Stable Set Problem via Schreier-Sims Cuts
Symmetry handling inequalities (SHIs) are an appealing and popular tool for
handling symmetries in integer programming. Despite their practical
application, little is known about their interaction with optimization
problems. This article focuses on Schreier-Sims (SST) cuts, a recently
introduced family of SHIs, and investigate their impact on the computational
and polyhedral complexity of optimization problems. Given that SST cuts are not
unique, a crucial question is to understand how different constructions of SST
cuts influence the solving process.
First, we observe that SST cuts do not increase the computational complexity
of solving a linear optimization problem over any polytope . However,
separating the integer hull of enriched by SST cuts can be NP-hard, even if
is integral and has a compact formulation. We study this phenomenon more
in-depth for the stable set problem, particularly for subclasses of perfect
graphs. For bipartite graphs, we give a complete characterization of the
integer hull after adding SST cuts based on odd-cycle inequalities. For
trivially perfect graphs, we observe that the separation problem is still
NP-hard after adding a generic set of SST cuts. Our main contribution is to
identify a specific class of SST cuts, called stringent SST cuts, that keeps
the separation problem polynomial and a complete set of inequalities, namely
SST clique cuts, that yield a complete linear description.
We complement these results by giving SST cuts based presolving techniques
and provide a computational study to compare the different approaches. In
particular, our newly identified stringent SST cuts dominate other approaches