Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization

Miltenberger, Matthias; Ralphs, Ted K.; Steffy, Daniel E.

doi:10.1007/978-3-319-89920-6_21

Cited by 5 publications

(3 citation statements)

References 7 publications

(7 reference statements)

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“…Recently, the branch and cut (BA C) algorith m co mb ines the advantages from these two methods and improves the defects, i.e. ; we can solve the MILP problems by taking some cutting planes into the branch and bound process [52], [53]. It has proven to be a very successful approach to solving a wide variety of real-world problems.…”

Section: Wo-based Greedy Approachmentioning

confidence: 99%

Security and Energy-aware Collaborative Task Offloading in D2D communication

et al. 2021

Future Generation Computer Systems

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Section: Wo-based Greedy Approachmentioning

confidence: 99%

Security and Energy-aware Collaborative Task Offloading in D2D communication

et al. 2021

Future Generation Computer Systems

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“…Finally, we re-scale the observed rewards in D t−1 before training models, to aid both in training and optimization. Poorly-scaled data may result in slower performance or small inaccuracies in MILP solvers (Miltenberger et al, 2018).…”

Section: Surrogate Model and Acquisition Functionmentioning

confidence: 99%

Constrained Discrete Black-Box Optimization using Mixed-Integer Programming

Papalexopoulos¹,

Tjandraatmadja²,

Anderson³

et al. 2021

Preprint

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Discrete black-box optimization problems are challenging for model-based optimization (MBO) algorithms, such as Bayesian optimization, due to the size of the search space and the need to satisfy combinatorial constraints. In particular, these methods require repeatedly solving a complex discrete global optimization problem in the inner loop, where popular heuristic inner-loop solvers introduce approximations and are difficult to adapt to combinatorial constraints. In response, we propose NN+MILP, a general discrete MBO framework using piecewise-linear neural networks as surrogate models and mixed-integer linear programming (MILP) to optimize the acquisition function. MILP provides optimality guarantees and a versatile declarative language for domain-specific constraints. We test our approach on a range of unconstrained and constrained problems, including DNA binding and the NAS-Bench-101 neural architecture search benchmark. NN+MILP surpasses or matches the performance of algorithms tailored to the domain at hand, with global optimization of the acquisition problem running in a few minutes using only standard software packages and hardware.

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“…Numerics play an important role in solving linear and mixed integer programs (LPs and MIPs) (Miltenberger, Ralphs, and Steffy 2018). All major solvers for LPs and MIPs rely on floating-point arithmetic, hence numerical round-off errors and cancellation effects might occur and therefrom, numerical errors might propagate.…”

Section: Introductionmentioning

confidence: 99%

Learning To Scale Mixed-Integer Programs

Berthold

Hendel

2021

AAAI

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Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes the difference whether these problems can be solved correctly or not. In this paper, we investigate the use of machine learning to choose at the beginning of the solution process between two common scaling methods: Standard scaling and Curtis-Reid scaling. The latter often, but not always, leads to a more robust solution process, but may suffer from longer solution times. Rather than training for overall solution time, we propose to use the attention level of a MIP solution process as a learning label. We evaluate the predictive power of a random forest approach and a linear regressor that learns the (square-root of the) difference in attention level. It turns out that the resulting classification not only reduces various types of numerical errors by large margins, but it also improves the performance of the dual simplex algorithm. The learned model has been implemented within the FICO Xpress MIP solver and it is used by default since release 8.9, May 2020, to determine the scaling algorithm Xpress applies before solving an LP or a MIP.

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Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization

Cited by 5 publications

References 7 publications

Security and Energy-aware Collaborative Task Offloading in D2D communication

Security and Energy-aware Collaborative Task Offloading in D2D communication

Constrained Discrete Black-Box Optimization using Mixed-Integer Programming

Learning To Scale Mixed-Integer Programs

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