Certified Constraint Propagation and Dual Proof Analysis in a Numerically Exact MIP Solver

TL;DR

This paper introduces a certified, numerically exact MIP solver that combines constraint propagation and dual proof analysis, ensuring correctness with minimal performance loss, and demonstrates a 23% efficiency gain on benchmark tests.

Contribution

The paper develops a novel integration of constraint propagation and dual proof analysis in an exact MIP solver using safe rounding methods for provable correctness.

Findings

Achieved 23% performance improvement on MIPLIB 2017 benchmarks.

Ensured provable correctness with roundoff-error-free computations.

Demonstrated effectiveness of certification techniques in practical MIP solving.

Abstract

This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while sacrificing as little computational performance as possible in comparison to a pure floating-point implementation. The study also addresses the adaptation of certification techniques for correctness verification. Computational studies demonstrate the effectiveness of these techniques, showcasing a 23% performance improvement on the MIPLIB 2017 benchmark test set.