conflict analysis

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

  • Sander Borst
  • Leon Eifler
  • Ambros Gleixner
    • Categories Integer Programming, Optimization Software and Modeling Systems Tags , ,

    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 … Read more

    Improving Conflict Analysis in MIP Solvers by Pseudo-Boolean Reasoning

  • Gioni Mexi
  • Timo Berthold
  • Ambros Gleixner
    • Categories 0-1 Programming, Integer Programming Tags , , ,

    Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in … Read more

    Dual Conflict Analysis for Mixed-Integer Semidefinite Programs

  • Marc E. Pfetsch
    • Categories (Mixed) Integer Linear Programming, Semi-definite Programming Tags ,

    Conflict analysis originally tried to exploit the knowledge that certain nodes in a relaxation-based branch-and-bound are infeasible. It has been extended to derive valid constraints also from feasible nodes. This paper adapts this approach to mixed-integer semidefinite programs. Using dual solutions, the primal constraints are aggregated and the resulting inequalities can be used at different … Read more

    Computational Aspects of Infeasibility Analysis in Mixed Integer Programming

  • Timo Berthold
  • Stefan Heinz
  • Jakob Witzig
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The … Read more

    Local Rapid Learning for Integer Programs

  • Timo Berthold
  • Peter J. Stuckey
  • Jakob Witzig
    • Categories Integer Programming Tags , , , ,

    Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn … Read more

    A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming

  • Timo Berthold
  • Stefan Heinz
  • Jakob Witzig
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and … Read more

    Conflict Driven Diving for Mixed Integer Programming

  • Jakob Witzig
    • Categories (Mixed) Integer Linear Programming Tags , ,

    The analysis of infeasibility plays an important role in solving satisfiability problems (SAT) and mixed integer programs (MIPs). In mixed integer programming, this procedure is called conflict analysis. So far, modern MIP solvers use conflict analysis only for propagation and improving the dual bound, i.e., fathoming nodes that cannot contain feasible solutions. In this short … Read more