Branch-and-Bound

Automatic Reformulations for Convex Mixed-Integer Nonlinear Optimization: Perspective and Separability

  • Meenarli Sharma
  • Ashutosh Mahajan
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems Tags , , , ,

    Tight reformulations of combinatorial optimization problems like Convex Mixed-Integer Nonlinear Programs (MINLPs) enable one to solve these problems faster by obtaining tight bounds on the optimal value. We consider two techniques for reformulation: perspective reformulation and separability detection. We develop routines for the automatic detection of problem structures suitable for these reformulations and implement new … Read more

    A branch-and-prune algorithm for discrete Nash equilibrium problems

  • Stefan Schwarze
  • Oliver Stein
    • Categories (Mixed) Integer Nonlinear Programming, Game Theory Tags , , ,

    We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. … Read more

    Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs

  • Jasper van Doornmalen
  • Christopher Hojny
    • Categories 0-1 Programming Tags , , ,

    The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on propagation techniques for cyclic groups. Our algorithms come with the guarantee to find all possible variable fixings that can be derived from … Read more

    A solver for multiobjective mixed-integer convex and nonconvex optimization

  • Gabriele Eichfelder
  • Oliver Stein
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , , ,

    This paper proposes a general framework for solving multiobjective nonconvex optimization problems, i.e., optimization problems in which multiple objective functions have to be optimized simultaneously. Thereby, the nonconvexity might come from the objective or constraint functions, or from integrality conditions for some of the variables. In particular, multiobjective mixed-integer convex and nonconvex optimization problems are … Read more

    New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

  • Loay Alkhalifa
  • Hans D Mittelmann
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform … Read more

    Lower bound on size of branch-and-bound trees for solving lot-sizing problem

  • Santanu S. Dey
  • Prachi Shah
    • Categories 0-1 Programming, Integer Programming Tags , ,

    We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split disjunctions. Article Download View Lower bound on size of branch-and-bound trees for solving lot-sizing problem

    A Branch & Bound Algorithm for Robust Binary Optimization with Budget Uncertainty

  • Christina Büsing
  • Timo Gersing
  • Arie M.C.A. Koster
    • Categories 0-1 Programming, Branch and Cut Algorithms, Robust Optimization Tags , , , ,

    Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due … Read more

    A Theoretical and Computational Analysis of Full Strong-Branching

  • Santanu S. Dey
  • Yatharth Dubey
  • Marco Molinaro
  • Prachi Shah
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , ,

    Full strong-branching (henceforth referred to as strong-branching) is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an analysis of the performance of the strong-branching rule both from a theoretical and a computational perspective. On … Read more

    Adjustable robust optimization with objective uncertainty

  • Boris Detienne
  • Henri Lefebvre
  • Enrico Malaguti
  • Michele Monaci
    • Categories Applications - OR and Management Sciences, Convex Optimization, Robust Optimization Tags , , , , ,

    In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and … Read more

    Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Nicholas A. G. Johnson
    • Categories Applications - OR and Management Sciences, Data-Mining, Statistics Tags , , , ,

    We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental problem in Operations Research and Machine Learning which arises in various applications, including data compression, latent semantic indexing, … Read more