Packing, partitioning, and covering symresacks

Hojny, Christopher

doi:10.1016/j.dam.2020.03.002

Cited by 7 publications

(6 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These subgroups are required to act on binary matrices and to be able to reorder their columns arbitrarily. Moreover, if the variables affected by the corresponding permutations or groups interact with set packing or partitioning constraints in a certain way, all constraint handlers provide specialized separation and propagation mechanisms to find stronger cutting planes and reductions [46,51,52]. The common ground of these constraint handlers is that they enforce solutions that are lexicographically maximal in their orbit of symmetric solutions.…”

Section: Previously Existing Symmetrymentioning

confidence: 99%

The SCIP Optimization Suite 8.0

Bestuzheva¹,

Besançon²,

Chen³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack. Keywords Constraint integer programming • linear programming • mixed-integer linear programming • mixed-integer nonlinear programming • optimization solver • branch-andcut • branch-and-price • column generation • parallelization • mixed-integer semidefinite programming Mathematics Subject Classification 90C05 • 90C10 • 90C11 • 90C30 • 90C90 • 65Y05 * Extended author information is available at the end of the paper.

show abstract

Section: Previously Existing Symmetrymentioning

confidence: 99%

The SCIP Optimization Suite 8.0

Bestuzheva¹,

Besançon²,

Chen³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the static setting, a fundamental domain F ⊆ R n is defined before the solving process starts. In the case of mixed-integer programming, such a fundamental domain is usually a polyhedron, and to enforce that only solutions within F ∩ are computed, symmetry handling constraints (SHCs) [4,[6][7][8][9][10][11][12][13][14] are added to the initial formulation. Opposed to the static setting, a dynamic fundamental domain is not determined a priori.…”

Section: Introductionmentioning

confidence: 99%

A unified framework for symmetry handling

van Doornmalen,

Hojny

2024

Math. Program.

Self Cite

View full text Add to dashboard Cite

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. While these methods are mostly discussed independently from each other, our framework allows to apply different methods simultaneously and thus outperforming their individual effect. Moreover, most existing symmetry handling methods 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 symmetry handling methods as implemented in the solver on a broad set of instances.

show abstract

“…Besides propagation, further methods for handling symmetries in binary programs exist such as cutting planes [7,9,10,14,19,20,21,22,35], branching rules [30,31], or model reformulations [6].…”

Section: Introductionmentioning

confidence: 99%

Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs

Doornmalen¹,

Hojny²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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 symmetry arguments, i.e., one cannot find more variable fixings than those found by our algorithms. Since every permutation symmetry group of a binary program has cyclic subgroups, the derived algorithms can be used to handle symmetries in any symmetric binary program. In experiments we also provide numerical evidence that our algorithms handle symmetries more efficiently than other variable fixing algorithms for cyclic symmetries.

show abstract

Packing, partitioning, and covering symresacks

Cited by 7 publications

References 24 publications

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite 8.0

A unified framework for symmetry handling

Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs

Contact Info

Product

Resources

About