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An Algorithm-Independent Measure of Progress for Linear Constraint Propagation

Authors Boro Sofranac, Ambros Gleixner, Sebastian Pokutta

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Author Details

Boro Sofranac
  • Zuse Institute Berlin, Germany
  • TU Berlin, Germany
Ambros Gleixner
  • Zuse Institute Berlin, Germany
  • HTW Berlin, Germany
Sebastian Pokutta
  • Zuse Institute Berlin, Germany
  • TU Berlin, Germany

Funding

This research was partially conducted within the Research Campus MODAL funded by the German Federal Ministry of Education and Research (BMBF grant numbers 05M14ZAM, 05M20ZBM) as well as the DFG Cluster of Excellence MATH+ (EXC-2046/1, project id 390685689) funded by the Deutsche Forschungsgemeinschaft (DFG).

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Boro Sofranac, Ambros Gleixner, and Sebastian Pokutta. An Algorithm-Independent Measure of Progress for Linear Constraint Propagation. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CP.2021.52

Abstract

Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure - independently of the algorithmic design - the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Mixed discrete-continuous optimization
Keywords
  • Bounds Propagation
  • Mixed Integer Programming

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