Ambros Gleixner

Analyzing the numerical correctness of branch-and-bound decisions for mixed-integer programming

  • Alexander Hoen
  • Ambros Gleixner
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags , ,

    Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While the practical success of floating-point MIP solvers bears witness to their overall numerical robustness, it is well-known that numerically challenging input can lead them to produce incorrect results. … Read more

    MIP-DD: Delta Debugging for Mixed Integer Programming Solvers

  • Alexander Hoen
  • Dominik Kamp
  • Ambros Gleixner
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags ,

    The recent performance improvements in mixed-integer programming (MIP) have been accompanied by a significantly increased complexity of the codes of MIP solvers, which poses challenges in fixing implementation errors. In this paper, we introduce MIP-DD, a solver-independent tool, which to the best of our knowledge is the first open-source delta debugger for MIP. Delta debugging … Read more

    Cut-based Conflict Analysis in Mixed Integer Programming

  • Gioni Mexi
  • Felipe Serrano
  • Timo Berthold
  • Ambros Gleixner
  • jakobnordstrom
    • Categories (Mixed) Integer Linear Programming, 0-1 Programming, Integer Programming Tags , , , , ,

    For almost two decades, mixed integer programming (MIP) solvers have used graph- based conflict analysis to learn from local infeasibilities during branch-and-bound search. In this paper, we improve MIP conflict analysis by instead using reasoning based on cuts, inspired by the development of conflict-driven solvers for pseudo- Boolean optimization. Phrased in MIP terminology, this type … Read more

    A diving heuristic for mixed-integer problems with unbounded semi-continuous variables

  • Katrin Halbig
  • Alexander Hoen
  • Ambros Gleixner
  • Jakob Witzig
  • Dieter Weninger
    • Categories Integer Programming Tags , , , ,

    Semi-continuous decision variables arise naturally in many real-world applications. They are defined to take either value zero or any value within a specified range, and occur mainly to prevent small nonzero values in the solution. One particular challenge that can come with semi-continuous variables in practical models is that their upper bound may be large … Read more

    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

    The MIP Workshop 2023 Computational Competition on Reoptimization

  • Suresh Bolusani
  • Mathieu Besançon
  • Ambros Gleixner
  • Timo Berthold
  • Claudia D'Ambrosio
  • Gonzalo Muñoz
  • Joseph Paat
  • Dimitri Thomopulos
    • Categories Combinatorial Optimization, Integer Programming, Optimization Software and Modeling Systems Tags , , , ,

    This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge … Read more

    The SCIP Optimization Suite 9.0

  • Suresh Bolusani
  • Mathieu Besançon
  • Ksenia Bestuzheva
  • Antonia Chmiela
  • Joao Dionisio
  • Tim Donkiewicz
  • Jasper van Doornmalen
  • Leon Eifler
  • Mohammed Ghannam
  • Ambros Gleixner
  • Christoph Graczyk
  • Katrin Halbig
  • Ivo Hedtke
  • Alexander Hoen
  • Christopher Hojny
  • Rolf van der Hulst
  • Dominik Kamp
  • Thorsten Koch
  • Kevin Kofler
  • Jurgen Lentz
  • Julian Manns
  • Gioni Mexi
  • Erik Mühmer
  • Marc E. Pfetsch
  • Franziska Schlösser
  • Felipe Serrano
  • Yuji Shinano
  • Mark Turner
  • Stefan Vigerske
  • Dieter Weninger
  • Liding Xu
    • Categories Integer Programming, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , , , , , , ,

    The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a … Read more

    Branch and Price for the Length-Constrained Cycle Partition Problem

  • Mohammed Ghannam
  • Ambros Gleixner
  • Gioni Mexi
  • Edward Lam
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Transportation Tags , , , ,

    The length-constrained cycle partition problem (LCCP) is a graph optimization problem in which a set of nodes must be partitioned into a minimum number of cycles. Every node is associated with a critical time and the length of every cycle must not exceed the critical time of any node in the cycle. We formulate LCCP … Read more

    Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization

  • Leon Eifler
  • Ambros Gleixner
    • Categories (Mixed) Integer Linear Programming, Linear Programming, Other Topics Tags , , ,

    This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: … Read more

    A proof system for certifying symmetry and optimality reasoning in integer programming

  • Jasper van Doornmalen
  • Leon Eifler
  • Ambros Gleixner
  • Christopher Hojny
    • Categories (Mixed) Integer Linear Programming Tags , , , ,

    We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and Nordström (2022) for binary programs to handle any additional difficulties arising from unbounded and continuous variables, and covers a broad range of … Read more