Integer Programming

On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley’s Cutting Plane Algorithm

  • Ambros Gleixner
  • Felipe Serrano
  • Robert Schwarz
    • Categories (Mixed) Integer Nonlinear Programming, Convex Optimization Tags , ,

    Recently, Kronqvist et al.rediscovered the supporting hyperplane algorithm of Veinott and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm applied to a particular … Read more

    Oracle-Based Algorithms for Binary Two-Stage Robust Optimization

  • Nicolas Kämmerling
  • Jannis Kurtz
    • Categories 0-1 Programming, Robust Optimization, Transportation

    In this work we study binary two-stage robust optimization problems with objective uncertainty. The concept of two-stage robustness is tailored for problems under uncertainty which have two different kinds of decision variables, first-stage decisions which have to be made here-and-now and second-stage decisions which can be determined each time after an uncertain scenario occured. We … Read more

    A Python package for multi-stage stochastic programming

  • Shabbir Ahmed
  • Lingquan Ding
  • Alexander Shapiro
    • Categories Integer Programming, Optimization Software and Modeling Systems, Stochastic Programming

    This paper presents a Python package to solve multi-stage stochastic linear programs (MSLP) and multi-stage stochastic integer programs (MSIP). Algorithms based on an extensive formulation and Stochastic Dual Dynamic (Integer) Programming (SDDP/SDDiP) method are implemented. The package is synthetically friendly and has a number of features which are not available in the competing software packages. … Read more

    Stochastic Lipschitz Dynamic Programming

  • Shabbir Ahmed
  • Filipe G. Cabral
  • Bernardo Freitas Paulo da Costa
    • Categories Dynamic Programming, Integer Programming, Stochastic Programming Tags , , ,

    We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more

    A mixed-integer optimization approach to an exhaustive cross-validated model selection for regression

  • Dennis Kreber
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , , ,

    We consider a linear regression model for which we assume that many of the observed regressors are irrelevant for the prediction. To avoid overfitting, we conduct a variable selection and only include the true predictors for the least square fitting. The best subset selection gained much interest in recent years for addressing this objective. For … Read more

    There’s No Free Lunch: On the Hardness of Choosing a Correct Big-M in Bilevel Optimization

  • Thomas Kleinert
  • Martine Labbé
  • Martin Schmidt
  • Fränk Plein
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , , ,

    One of the most frequently used approaches to solve linear bilevel optimization problems consists in replacing the lower-level problem with its Karush-Kuhn-Tucker (KKT) conditions and by reformulating the KKT complementarity conditions using techniques from mixed-integer linear optimization. The latter step requires to determine some big-M constant in order to bound the lower level’s dual feasible … Read more

    Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

  • Simge Küçükyavuz
  • Hasan Manzour
  • Ali Shojaie
  • Hao-Hsiang Wu
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , , ,

    Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a … Read more

    Knapsack Polytopes – A Survey

  • Tristan Gally
  • Oliver Habeck
  • Christopher Hojny
  • Frederic Matter
  • Marc E. Pfetsch
  • Andreas Schmitt
  • Hendrik Lüthen
    • Categories 0-1 Programming, Polyhedra Tags , , , , ,

    The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy a given single linear inequality with non-negative coefficients. This paper provides a comprehensive overview of knapsack polytopes. We discuss basic polyhedral properties, (lifted) cover and other valid inequalities, cases for which complete linear descriptions are known, geometric properties for small dimensions, … Read more

    Discrete Optimization Methods for Group Model Selection in Compressed Sensing

  • Bubacarr Bah
  • Jannis Kurtz
  • Oliver Schaudt
    • Categories Applications - Science and Engineering, Combinatorial Optimization, Integer Programming Tags , , ,

    In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be group-sparse in the sense that its support is contained in the union … Read more

    Planning Out-of-Hours Services for Pharmacies

  • Christina Büsing
  • Arie M.C.A. Koster
  • Timo Gersing
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Scheduling Tags , , , , ,

    The supply of pharmaceuticals is one important factor in a functioning health care system. In the German health care system, the chambers of pharmacists are legally obliged to ensure that every resident can find an open pharmacy at any day and night time within an appropriate distance. To that end, the chambers of pharmacists create … Read more