branch-and-bound methods

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

    The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint

  • Koichi Fujii
  • Sunyoung Kim
  • Masakazu Kojima
  • Hans D Mittelmann
  • Yuji Shinano
    • Categories 0-1 Programming, Branch and Cut Algorithms, Semi-definite Programming Tags , , , , ,

    Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48\% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which … Read more

    MatQapNB User Guide: A branch-and-bound program for QAPs in Matlab with the Newton-Bracketing method

  • Koichi Fujii
  • Naoki Ito
  • Sunyoung Kim
  • Masakazu Kojima
  • Hans D Mittelmann
  • Kim-Chuan Toh
  • Yuji Shinano
    • Categories Global Optimization Applications, Optimization Software Design Principles, Quadratic Programming Tags , , ,

    MatQapNB is a MATLAB toolbox that implements a parallel branch-and-bound method using NewtBracket (the Newton bracketing method [4]) for its lower bounding procedure. It can solve small to medium scale Quadratic Assignment Problem (QAP) instances with dimension up to 30. MatQapNB was used in the numerical experiments on QAPs in the recent article “Solving challenging … Read more

    Parallel Interval Continuous Global Optimization Algorithms

  • Abdeljalil Benyoub
    • Categories Branch and Cut Algorithms, Global Optimization, Parallel Algorithms Tags , , , , ,

    We theorically study, on a distributed memory architecture, the parallelization of Hansen’s algorithm for the continuous global optimization with inequality constraints, using interval arithmetic. We propose a parallel algorithm based on a dynamic redistribution of the working list among the processors. On the other hand, we exploit the reduction technique, developped by Hansen, for computing … Read more