Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Sander Borst, Leon Eifler, Ambros Gleixner

TL;DR

This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver, and addresses the adaptation of certification techniques for correctness verification.

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.

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

TL;DR

This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver, and addresses the adaptation of certification techniques for correctness verification.

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.
Paper Structure (12 sections, 15 equations, 1 figure, 2 tables)

This paper contains 12 sections, 15 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Constraint Propagation and Conflict Analysis
  3. Constraint Propagation
  4. Dual Proof Analysis
  5. Application in Numerically Exact MIP Solving
  6. Numerically Safe Constraint Propagation
  7. Numerically Safe Dual Proof Analysis
  8. Producing Certificates of Correctness
  9. Computational Study
  10. Experimental Setup and Test Set
  11. Experimental Results
  12. Conclusion and Outlook

Figures (1)

  • Figure 1: Performance profile for different configurations. For each configuration it is shown how many instances achieved a running time within a given factor of the shortest running time for that instances. Only the instances that could be solved by at least one of the given configurations are included in these statistics.