Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices

Fast domain propagation of linear constraints has become a crucial component of today’s best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, … Read more

The SCIP Optimization Suite 7.0

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 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies … Read more

Linear Programming using Limited-Precision Oracles

Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations … Read more

On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens … Read more

Two-row and two-column mixed-integer presolve using hash-based pairing methods

In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolving techniques successfully is … Read more

A massively parallel interior-point solver for linear energy system models with block structure

Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers—already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an … Read more

First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method

In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving … Read more

MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library

We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of 5,721 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, these sets were compiled using … Read more

On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley’s Cutting Plane Algorithm

Recently, Kronqvist et al.rediscovered the supporting hyperplane algorithm of Veinott and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm applied to a particular … Read more

Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms

One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over … Read more