mixed-integer nonlinear programming

The Cost of Not Knowing Enough: Mixed-Integer Optimization with Implicit Lipschitz Nonlinearities

  • Martin Schmidt
  • Mathias Sirvent
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Global Optimization Tags , , ,

    It is folklore knowledge that nonconvex mixed-integer nonlinear optimization problems can be notoriously hard to solve in practice. In this paper we go one step further and drop analytical properties that are usually taken for granted in mixed-integer nonlinear optimization. First, we only assume Lipschitz continuity of the nonlinear functions and additionally consider multivariate implicit … Read more

    The SCIP Optimization Suite 5.0

  • Leon Eifler
  • Tristan Gally
  • Gerald Gamrath
  • Ambros Gleixner
  • Robert Lion Gottwald
  • Gregor Hendel
  • Christopher Hojny
  • Thorsten Koch
  • Matthias Miltenberger
  • Marc E. Pfetsch
  • Felipe Serrano
  • Dieter Weninger
  • Jakob Witzig
  • Patrick Gemander
  • Benjamin Müller
  • Christian Puchert
  • Daniel Rehfeldt
  • Franziska Schlösser
  • Yuji Shinano
  • Merlin Viernickel
  • Stefan Vigerske
  • Jonas T. Witt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , , , , , , , ,

    This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over … Read more

    Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

  • Mirko Hahn
  • Sven Leyffer
  • Victor M. Zavala
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , ,

    We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more

    Global optimization of mixed-integer ODE constrained network problems using the example of stationary gas transport

  • Oliver Habeck
  • Marc E. Pfetsch
  • Stefan Ulbrich
    • Categories Global Optimization Tags , , ,

    In this paper we propose a new approach for finding global solutions of mixed-integer nonlinear optimization problems with ordinary differential equation constraints on networks. Instead of using a first discretize then optimize approach, we combine spatial and variable branching with appropriate discretizations of the differential equations to derive relaxations of the original problem. To construct … Read more

    Minotaur: A Mixed-Integer Nonlinear Optimization Toolkit

  • Sven Leyffer
  • Jeff Linderoth
  • James R. Luedtke
  • Ashutosh Mahajan
  • Todd S. Munson
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Optimization Software and Modeling Systems Tags , ,

    We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting … Read more

    A multi-period production and distribution optimization model for radiopharmaceuticals

  • Ioannis G. Akrotirianakis
  • Amit Chakraborty
    • Categories (Mixed) Integer Nonlinear Programming, Biomedical Applications, Production and Logistics Tags , , ,

    This paper addresses the manufacturing and distribution of short-lived radio-pharmaceuticals which are mainly used in diagnostic imaging studies. We develop a mixed integer nonlinear optimization model that is flexible enough to capture the complex underlying nuclear physics of the production process of fludeoxyglucose (FDG), which is widely used in oncology and cardiology, as well as … Read more

    Bi-Perspective Functions for Mixed-Integer Fractional Programs with Indicator Variables

  • Adam N. Letchford
  • Qiang Ni
  • Zhaoyu Zhong
    • Categories (Mixed) Integer Nonlinear Programming, Telecommunications Tags , ,

    Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. … Read more

    A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities

  • Martin Schmidt
  • Mathias Sirvent
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test … Read more

    Solving Mixed-Integer Nonlinear Programs using Adaptively Refined Mixed-Integer Linear Programs

  • Robert Burlacu
  • Björn Geißler
  • Lars Schewe
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

    We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope an iterative algorithm … Read more

    Airport Capacity Extension, Fleet Investment, and Optimal Aircraft Scheduling in a Multi-Level Market Model: On the Effects of Market Regulations

  • Mathias Sirvent
  • Martin Weibelzahl
    • Categories (Mixed) Integer Nonlinear Programming, Game Theory, Transportation Tags , , , ,

    In this paper we present a four-level market model that accounts for airport capacity extension, fleet investment, aircraft scheduling, and ticket trade in a liberalized aviation market with independent decision makers. In particular, budget-constrained airports decide on the first level on their optimal runway capacity extension and on a corresponding airport charge. Airports anticipate optimal … Read more