mixed-integer nonlinear programming

Experimental operation of a solar-driven climate system with thermal energy storages using mixed-integer nonlinear MPC

  • Adrian Bürger
  • Daniel Bull
  • Parantapa Sawant
  • Markus Bohlayer
  • Angelika Altmann-Dieses
  • Marco Braun
  • Moritz Diehl
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear Model Predictive Control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as … Read more

    Solving Heated Oil Pipeline Problems Via Mixed Integer Nonlinear Programming Approach

  • Yu-Hong Dai
  • Yakui Huang
  • Bo Li
  • Muming Yang
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , , , , ,

    It is a crucial problem how to heat oil and save running cost for crude oil transport. This paper strictly formulates such a heated oil pipeline problem as a mixed integer nonlinear programming model. Nonconvex and convex continuous relaxations of the model are proposed, which are proved to be equivalent under some suitable conditions. Meanwhile, … Read more

    Visible points, the separation problem, and applications to MINLP

  • Felipe Serrano
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization Tags , , , ,

    In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point to restrict the feasible region in order to obtain a tighter domain. To ensure validity, we require … Read more

    A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming

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

    Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and … Read more

    Intersection disjunctions for reverse convex sets

  • James R. Luedtke
  • Eli Towle
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Global Optimization Theory Tags , , , ,

    We present a framework to obtain valid inequalities for optimization problems constrained by a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are particularly interested in cases where the closure of the convex set is either non-polyhedral, or is defined … Read more

    Intersection cuts for factorable MINLP

  • Felipe Serrano
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , ,

    Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection … Read more

    Convergence of Finite-Dimensional Approximations for Mixed-Integer Optimization with Differential Equations

  • Falk M. Hante
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We consider a direct approach to solve mixed-integer nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach … Read more

    Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks

  • Radu Baltean-Lugojan
  • Pierre Bonami
  • Ruth Misener
  • Andrea Tramontani
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming Tags , , , , ,

    Semidefinite programming relaxations complement polyhedral relaxations for quadratic optimization, but global optimization solvers built on polyhedral relaxations cannot fully exploit this advantage. This paper develops linear outer-approximations of semidefinite constraints that can be effectively integrated into global solvers. The difference from previous work is that our proposed cuts are (i) sparser with respect to the … Read more

    Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP

  • Lena C. Altherr
  • Marc E. Pfetsch
  • Andreas Schmitt
  • Philipp Leise
    • Categories (Mixed) Integer Nonlinear Programming, Mechanical Engineering, Robust Optimization Tags , , , , , , ,

    Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goal of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in … Read more

    Design, Implementation and Simulation of an MPC algorithm for Switched Nonlinear Systems under Combinatorial Constraints

  • Angelika Altmann-Dieses
  • Moritz Diehl
  • Sebastian Sager
  • Adrian Bürger
  • Clemens Zeile
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , , ,

    Within this work, we present a warm-started algorithm for Model Predictive Control (MPC) of switched nonlinear systems under combinatorial constraints based on Combinatorial Integral Approximation (CIA). To facilitate high-speed solutions, we introduce a preprocessing step for complexity reduction of CIA problems, and include this approach within a new toolbox for solution of CIA problems with … Read more