Integer Programming

A Feasible Active Set Method with Reoptimization for Convex Quadratic Mixed-Integer Programming

  • Christoph Buchheim
  • Marianna De Santis
  • Stefano Lucidi
  • Francesco Rinaldi
  • Long Trieu
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , ,

    We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence … Read more

    Constraint Qualification Failure in Action

  • Hassan L. Hijazi
  • Leo Liberti
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming Tags , , , ,

    This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers’ failure. CitationH. L. Hijazi and L.Liberti “Constraint … Read more

    Solving Bilevel Mixed Integer Program by Reformulations and Decomposition

  • Yu An
  • Bo Zeng
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , ,

    In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-constraint … Read more

    Mixed-integer Quadratic Programming is in NP

  • Alberto Del Pia
  • Santanu S. Dey
  • Marco Molinaro
    • Categories Integer Programming Tags , ,

    Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing … Read more

    A scalable bounding method for multi-stage stochastic integer programs

  • Osman Y. Ozaltin
  • Burhaneddin Sandikçi
    • Categories Integer Programming, Parallel Algorithms, Stochastic Programming Tags , , , ,

    Many dynamic decision problems involving uncertainty can be appropriately modeled as multi-stage stochastic programs. However, most practical instances are so large and/or complex that it is impossible to solve them on a single computer, especially due to memory limitations. Extending the work of Sandikci et al. (2013) on two-stage stochastic mixed-integer-programs (SMIPs), this paper develops … Read more

    Branch-and-bound for bi-objective integer programming

  • Sophie N. Parragh
  • Fabien Tricoire
    • Categories Combinatorial Optimization, Integer Programming, Multi-Criteria Optimization Tags , , , ,

    In Pareto bi-objective integer optimization the optimal result corresponds to a set of non- dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team orienteering problem with … Read more

    Tight MIP Formulations of the Power-Based Unit Commitment Problem

  • Claudio Gentile
  • Germán Morales-España
  • Andres Ramos
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , , , , ,

    This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startup and shutdown processes are also … Read more

    A Tight MIP Formulation of the Unit Commitment Problem with Start-up and Shut-down Constraints

  • Claudio Gentile
  • Germán Morales-España
  • Andres Ramos
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , ,

    This paper provides the convex hull description for the following basic operating constraints of a single power generation unit in Unit Commitment (UC) problems: 1) generation limits, 2) startup and shutdown capabilities, and 3) minimum up and down times. Although the model does not consider some crucial constraints, such as ramping, the proposed constraints can … Read more

    On Global Optimization

  • Isaac Siwale
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more

    Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems

  • Kerem Akartunali
  • Ioannis Fragkos
  • Andrew J. Miller
  • Tao Wu
    • Categories Applications - OR and Management Sciences, Integer Programming

    Despite the significant attention they have drawn, big bucket lot-sizing problems remain notoriously difficult to solve. Previous work of Akartunali and Miller (2012) presented results (computational and theoretical) indicating that what makes these problems difficult are the embedded single-machine, single-level, multi-period submodels. We therefore consider the simplest such submodel, a multi-item, two-period capacitated relaxation that … Read more