Integer Programming

Outer Approximation for Global Optimization of Mixed-Integer Quadratic Bilevel Problems

  • Veronika Grimm
  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , ,

    Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel problems and the most recent algorithms use branch-and-cut techniques from mixed-integer programming that are especially tailored for the bilevel context. In this paper, we consider MIQP-QP … Read more

    Inversion of Convection-Diffusion Equation with Discrete Sources

  • Mirko Hahn
  • Sven Leyffer
  • Bart van Bloemen Waanders
  • Lars Ruthotto
  • Meenarli Sharma
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization

    We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem … Read more

    Convex Hulls for Non-Convex Mixed-Integer Quadratic Programs with Bounded Variables

  • Laura Galli
  • Adam N. Letchford
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Polyhedra

    We consider non-convex mixed-integer quadratic programs in which all variables are explicitly bounded. Many exact methods for such problems use additional variables, representing products of pairs of original variables. We study the convex hull of feasible solutions in this extended space. Some other approaches use bit representation to convert bounded integer variables into binary variables. … Read more

    Exact and Heuristic Approaches for a New Circular Layout Problem

  • Truden Christian
  • Philipp Hungerländer
  • Kerstin Maier
  • Veronika Pachatz
    • Categories (Mixed) Integer Linear Programming, Meta Heuristics, Production and Logistics Tags , , , ,

    We discuss a new facility layout problem, the so-called Directed Circular Facility Layout Problem (DCFLP). The DCFLP aims to find an optimal arrangement of machines on a circular material handling system such that the total weighted sum of the center-to-center distances between all pairs of machines measured in clockwise direction is minimized. Several real-world applications, … Read more

    Sample Average Approximation for Stochastic Nonconvex Mixed Integer Nonlinear Programming via Outer Approximation

  • David E. Bernal Neira
  • Kevin C Furman
  • Ignacio E. Grossmann
  • Can Li
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming Tags , , ,

    Stochastic mixed-integer nonlinear programming (MINLP) is a very challenging type of problem. Although there have been recent advances in developing decomposition algorithms to solve stochastic MINLPs, none of the existing algorithms can address stochastic MINLPs with continuous distributions. We propose a sample average approximation-based outer approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs … Read more

    The Impact of Neighboring Markets on Renewable Locations, Transmission Expansion, and Generation Investment

  • Jonas Egerer
  • Veronika Grimm
  • Thomas Kleinert
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    Many long-term investment planning models for liberalized electricity markets either optimize for the entire electricity system or focus on confined jurisdictions, abstracting from adjacent markets. In this paper, we provide models for analyzing the impact of the interdependencies between a core electricity market and its neighboring markets on key long-run decisions. This we do both … Read more

    Computational Aspects of Infeasibility Analysis in Mixed Integer Programming

  • Timo Berthold
  • Stefan Heinz
  • Jakob Witzig
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The … Read more

    Conflict-Free Learning for Mixed Integer Programming

  • Timo Berthold
  • Jakob Witzig
    • Categories (Mixed) Integer Linear Programming

    Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, … Read more

    Implementing Automatic Benders Decomposition in a Modern MIP Solver

  • Pierre Bonami
  • Domenico Salvagnin
  • Andrea Tramontani
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags ,

    We describe the automatic Benders decomposition implemented in the commercial solver IBM CPLEX. We propose several improvements to the state-of-the-art along two lines: making a numerically robust method able to deal with the general case and improving the efficiency of the method on models amenable to decomposition. For the former, we deal with: unboundedness, failures … Read more

    Rational Polyhedral Outer-Approximations of the Second-Order Cone

  • Burak Kocuk
    • Categories Integer Programming, Linear, Cone and Semidefinite Programming Tags , ,

    It is well-known that the second-order cone can be outer-approximated to an arbitrary accuracy by a polyhedral cone of compact size defined by irrational data. In this paper, we propose two rational polyhedral outer-approximations of compact size retaining the same guaranteed accuracy. The first outer-approximation has the same size as the optimal but irrational outer-approximation … Read more