arXiv subjects

Rolf van der Hulst

Publications and source records attributed to Rolf van der Hulst.

8 recordsLinked to original sources

arXiv2026

A Row-wise Algorithm for Graph Realization

Given a $\{0, 1\}$-matrix $M$, the graph realization problem for $M$ asks if there exists a spanning forest such that the columns of $M$ are incidence vectors of paths in the forest. The problem is closely related to the recognition of network matrices, which are a large subclass of totally unimodular matrices and have many applications in mixed-integer programming. Existing efficient algorithms for graph realization grow a submatrix in a column-wise fashion whilst maintaining a graphic realization. In the context of mixed-integer linear programming, this limits the set of submatrices of the constraint matrix that can efficiently be determined to be network matrices to network submatrices that span all rows and a subset of the columns. This paper complements the existing work by providing an algorithm that works in a row-wise fashion and uses similar data structures, and enables the detection of arbitrary graphic submatrices. The main challenge in designing efficient algorithms for the graph realization problem is ambiguity as there may exist many graphs realizing $M$. The key insight for designing an efficient row-wise algorithm is that a graphic matrix is uniquely represented by an SPQR-tree, a graph decomposition that stores all graphs with the same set of cycles. The developed row-wise algorithm uses data structures that are compatible with the column-wise algorithm and can be combined with the latter to detect maximal graphic submatrices.

cs.DM↗

arXiv2026

A hybrid solution approach for the Integrated Healthcare Timetabling Competition 2024

In this work, we present the solution approach for the Integrated Healthcare Timetabling Competition 2024 submitted by Team Twente, which ultimately ranked third among the finalists. Our approach combines mixed-integer programming, constraint programming, and simulated annealing in a 3-phase solution approach based on decomposition into subproblems. In addition to describing our approach and design decisions, we share our insights and, for the first time, lower bounds on the optimal solution values for the benchmark instances. We analyze the results based on solution quality for the competition and an extended runtime Additionally, we investigate the different soft constraints and specific parts of the algorithm. Finally, we highlight open problems and future research directions for further improving the approach.

cs.AI↗

arXiv2026

Folding Mixed-Integer Linear Programs and Reflection Symmetries

For mixed-integer linear programming and linear programming it is well known that symmetries can have a negative impact on the performance of branch-and-bound and linear optimization algorithms. A common strategy to handle symmetries in linear programs is to reduce the dimension of the linear program by aggregating symmetric variables and solving a linear program of reduced dimension. In their work ``Dimension Reduction via Color Refinement'' (DRCR), Grohe, Kersting, Mladenov and Selman show that it is sufficient to run a fast color refinement algorithm to detect permutation symmetries and reduce the dimension of the linear program. We extend DRCR in two directions. First, we show that DRCR can be extended to reflection symmetries, which generalize permutation symmetries. Second, we show the folklore result that DRCR can be applied to the continuous columns of mixed-integer linear programs. In order to derive additional reductions on the integer variables we use affine totally unimodular decompositions to reformulate mixed-integer linear programs into mixed-integer linear programs with fewer integer variables. Computational experiments on MIPLIB 2017 collection set using SCIP 10 show that DRCR is an effective tool for handling symmetries. For the linear programming relaxations, DRCR with reflection symmetries yields a modest reduction in running time compared to the original DRCR procedure. For mixed-integer linear programming models, DRCR is very effective at reducing the solution time compared to the default configuration of SCIP. Moreover, the developed DRCR detection algorithms are fast and scale well to large problem instances.

math.OC↗

arXiv2025

The SCIP Optimization Suite 10.0

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 SCIP Optimization Suite 10.0. The updates in SCIP 10.0 include a new solving mode for exactly solving rational mixed-integer linear programs, a new presolver for detecting implied integral variables, a novel cut-based conflict analysis and separator for flower inequalities, two new heuristics, a novel tool for explaining infeasibility, a new interface for nonlinear solvers as well as improvements in symmetry handling, branching strategies, and SCIP's Benders' decomposition framework. SCIP Optimization Suite 10.0 also includes new and improved features in the the presolving library PaPILO, the parallel framework UG, and the decomposition framework GCG. Moreover, the SCIP Optimization Suite 10.0 contains MIP-DD, the first open-source delta debugger for mixed-integer programming solvers. 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.

math.OC↗

arXiv2025

Implied Integrality in Mixed-Integer Optimization

Implied-integer detection is a well-known presolving technique that is used by many Mixed-Integer Linear Programming solvers. Informally, a variable is said to be implied integer if its integrality is enforced implicitly by integrality of other variables and the constraints of a problem. In this work we formalize the definition of implied integrality by taking a polyhedral perspective. Our main result characterizes implied integrality as occurring when a subset of integer variables is fixed to integer values and the polyhedron on the remaining variables is integral. While integral polyhedra are well-understood theoretically, existing detection methods infer implied integrality only for one variable at a time. We introduce new detection methods based on the detection of integral polyhedra, extending existing techniques to multiple variables. Additionally, we discuss the computational complexity of recognizing implied integers. We conduct experiments using a new detection method that uses totally unimodular submatrices to identify implied integrality. For the MIPLIB 2017 collection dataset our results indicate that, on average, 18.8% of the variables are classified as implied integer after presolving, compared to just 3.3% identified by state-of-the-art techniques. Moreover, we are able to reduce the average percentage of variables whose integrality needs to be enforced after presolving from 70.2% to 59.0%.

cs.DM↗

arXiv2024

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.

math.OC↗

arXiv2023

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 paper 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. Further, the paper 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.

math.OC↗

arXiv2021

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. 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.

math.OC↗