Integer Programming

Acceleration and Stabilization Techniques for Column Generation Applied to Capacitated Resource Management Problems

  • Alper Uygur
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Scheduling Tags , , ,

    This research presents a very efficient method of solving a broad class of large-scale capacitated resource management problems by introducing a new formulation and decomposition. A heuristic called Likelihood of Assignment is utilized not only to find high quality initial integer feasible solutions, but also to guide the Branch-and-Price (B&P) Algorithm towards stabilization. Although Column … Read more

    REDUCTION OF TWO-STAGE PROBABILISTIC OPTIMIZATION PROBLEMS WITH DISCRETE DISTRIBUTION OF RANDOM DATA TO MIXED INTEGER PROGRAMMING PROBLEMS

  • Andrey Kibzun
  • Vladimir I. Norkin
  • Andrey Naumov
    • Categories (Mixed) Integer Nonlinear Programming, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We consider models of two-stage stochastic programming with a quantile second stage criterion and optimization models with a chance constraint on the second stage objective function values. Such models allow to formalize requirements to reliability and safety of the system under consideration, and to optimize the system in extreme conditions. We suggest a method of … Read more

    Locally Ideal Formulations for Piecewise Linear Functions with Indicator Variables

  • Jeff Linderoth
  • James R. Luedtke
  • Srikrishna Sridhar
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering

    In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. CitationTechnical Report #1788, Computer Sciences Department, University of Wisconsin-Madison.ArticleDownload … Read more

    On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

  • Andrey Kibzun
  • Vladimir I. Norkin
  • Andrey Naumov
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , ,

    We suggest a method for equivalent transformation of a quantile optimization problem with discrete distribution of random parameters to mixed integer programming problems. The number of additional integer (in fact boolean) variables in the equivalent problems equals to the number of possible scenarios for random data. The obtained mixed integer problems are solved by standard … Read more

    On the Transportation Problem with Market Choice

  • Pelin Damci-Kurt
  • Santanu S. Dey
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Linear Programming, Transportation Tags , , ,

    We study a variant of the classical transportation problem in which suppliers with limited capacities have a choice of which demands (markets) to satisfy. We refer to this problem as the transportation problem with market choice (TPMC). While the classical transportation problem is known to be strongly polynomial-time solvable, we show that its market choice … Read more

    Incremental and Encoding Formulations for Mixed Integer Programming

  • Juan Pablo Vielma
  • Sercan Yildiz
    • Categories (Mixed) Integer Linear Programming

    The standard way to represent a choice between n alternatives in Mixed Integer Programming is through n binary variables that add up to one. Unfortunately, this approach commonly leads to unbalanced branch-and-bound trees and diminished solver performance. In this paper, we present an encoding formulation framework that encompasses and expands existing approaches to mitigate this … Read more

    On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs

  • Yogesh Awate
  • Gérard Cornuéjols
  • Bertrand Guenin
  • Levent Tunçel
    • Categories (Mixed) Integer Linear Programming Tags , ,

    We compare the relative strength of valid inequalities for the integer hull of the feasible region of mixed integer linear programs with two equality constraints, two unrestricted integer variables and any number of nonnegative continuous variables. In particular, we prove that the closure of Type~2 triangle (resp. Type~3 triangle; quadrilateral) inequalities, are all within a … Read more

    Intersection Cuts for Mixed Integer Conic Quadratic Sets

  • Kent Andersen
  • Anders Jensen
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Balas introduced intersection cuts for mixed integer linear sets. Intersection cuts are given by closed form formulas and form an important class of cuts for solving mixed integer linear programs. In this paper we introduce an extension of intersection cuts to mixed integer conic quadratic sets. We identify the formula for the conic quadratic intersection … Read more

    Exact algorithms for the Traveling Salesman Problem with Draft Limits

  • Maria Battarra
  • Artur Alves Pessoa
  • Anand Subramanian
  • Eduardo Uchoa
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , , ,

    This paper deals with the Traveling Salesman Problem (TSP) with Draft Limits (TSPDL), which is a variant of the well-known TSP in the context of maritime transportation. In this recently proposed problem, draft limits are imposed due to restrictions on the port infrastructures. Exact algorithms based on three mathematical formulations are proposed and their performance … Read more

    On the Rank of Cutting-Plane Proof Systems

  • Sebastian Pokutta
  • Andreas S. Schulz
    • Categories 0-1 Programming, Cutting Plane Approaches, Polyhedra Tags , , , , , ,

    We introduce a natural abstraction of propositional proof systems that are based on cut- ting planes. This leads to a new class of proof systems that includes many well-known meth- ods, such as Gomory-Chvátal cuts, lift-and-project cuts, Sherali-Adams cuts, or split cuts. The rank of a proof system corresponds to the number of rounds that … Read more