Integer Programming

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

    On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming

  • Maxime Gasse
  • Ambros Gleixner
  • Andrea Lodi
  • Felipe Serrano
  • Benjamin Müller
  • Gonzalo Muñoz
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Nonlinear Optimization Tags ,

    The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens … Read more

    On the complexity of binary polynomial optimization over acyclic hypergraphs

  • Alberto Del Pia
  • Silvia Di Gregorio
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

    In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we provide a novel class of BPO that can be solved efficiently both from a theoretical and computational perspective. … Read more

    Outlier detection in time series via mixed-integer conic quadratic optimization

  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , , , ,

    We consider the problem of estimating the true values of a Wiener process given noisy observations corrupted by outliers. The problem considered is closely related to the Trimmed Least Squares estimation problem, a robust estimation procedure well-studied from a statistical standpoint but poorly understood from an optimization perspective. In this paper we show how to … Read more

    Integrality of Linearizations of Polynomials over Binary Variables using Additional Monomials

  • Christopher Hojny
  • Marc E. Pfetsch
  • Matthias Walter
    • Categories (Mixed) Integer Nonlinear Programming, Polyhedra Tags , ,

    Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an integral relaxation polytope, generalizing work by Del Pia and Khajavirad (SIAM Journal on Optimization, 2018) and Buchheim, Crama and Rodríguez-Heck … Read more

    Multi-objective Optimization Based Algorithms for Solving Mixed Integer Linear Minimum Multiplicative Programs

  • Hadi Charkhgard
  • Vahid Mahmoodian
  • Yu Zhang
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Global Optimization

    We present two new algorithms for a class of single-objective non-linear optimization problems, the so-called Mixed Integer Linear minimum Multiplicative Programs (MIL-mMPs). This class of optimization problems has a desirable characteristic: a MIL-mMP can be viewed as a special case of the problem of optimization over the efficient set in multi-objective optimization. The proposed algorithms … Read more