6 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
Uniform determinantal representations
The problem of expressing a specific polynomial as the determinant of a
square matrix of affine-linear forms arises from algebraic geometry,
optimisation, complexity theory, and scientific computing. Motivated by recent
developments in this last area, we introduce the notion of a uniform
determinantal representation, not of a single polynomial but rather of all
polynomials in a given number of variables and of a given maximal degree. We
derive a lower bound on the size of the matrix, and present a construction
achieving that lower bound up to a constant factor as the number of variables
is fixed and the degree grows. This construction marks an improvement upon a
recent construction due to Plestenjak-Hochstenbach, and we investigate the
performance of new representations in their root-finding technique for
bivariate systems. Furthermore, we relate uniform determinantal representations
to vector spaces of singular matrices, and we conclude with a number of future
research directions.Comment: 23 pages, 3 figures, 4 table
JasperNL/scip-symretope: Code Repository for "Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs"
Online supplementary material for the paper "Efficient propagation techniques for handling cyclic symmetries in binary programs
Enabling Research Through The SCIP Optimization Suite 8.0
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.</p
The SCIP Optimization Suite 8.0.0
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP