(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

    Mixed-Integer Optimal Control under Minimum Dwell Time Constraints

  • Nicolò Robuschi
  • Sebastian Sager
  • Clemens Zeile
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , , , ,

    Tailored mixed-integer optimal control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems by solving one continuous nonlinear program and one mixed-integer linear program. … Read more

    Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints

  • Sven de Vries
  • Bernd Perscheid
    • Categories (Mixed) Integer Nonlinear Programming, Graphs and Matroids, Quadratic Programming Tags ,

    Cutting planes from the Boolean Quadric Polytope (BQP) can be used to reduce the optimality gap of the NP-hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal-Gomory closure of the BQP are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which … Read more

    Near-optimal Robust Bilevel Optimization

  • Miguel F. Anjos
  • Mathieu Besançon
  • Luce Brotcorne
    • Categories (Mixed) Integer Nonlinear Programming, Complementarity and Variational Inequalities, Robust Optimization Tags , , , , , ,

    Bilevel optimization studies problems where the optimal response to a second mathematical optimization problem is integrated in the constraints. Such structure arises in a variety of decision-making problems in areas such as market equilibria, policy design or product pricing. We introduce near-optimal robustness for bilevel problems, protecting the upper-level decision-maker from bounded rationality at the … 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

    A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

  • Brian Dandurand
  • Kibaek Kim
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Robust Optimization Tags , , ,

    We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists in choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to … 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

    Optimal Design of Retailer-Prosumer Electricity Tariffs Using Bilevel Optimization

  • Veronika Grimm
  • Lars Schewe
  • Martin Schmidt
  • Galina Orlinskaya
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , , ,

    We compare various flexible tariffs that have been proposed to cost-effectively govern a prosumer’s electricity management – in particular time-of-use (TOU), critical-peak-pricing (CPP), and a real-time-pricing tariff (RTP). As the outside option, we consider a fixed-price tariff (FP) that restricts the specific characteristics of TOU, CPP, and RTP, so that the flexible tariffs are at … Read more

    Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

  • Dominik Garmatter
  • Margherita Porcelli
  • Francesco Rinaldi
  • Martin Stoll
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Optimization of Systems modeled by PDEs Tags , , ,

    Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the Branch-and-Bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially … Read more

    A Unified Approach to Mixed-Integer Optimization Problems With Logical Constraints

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal component analysis and sparse learning problems. These problems exhibit logical relationships between continuous and discrete variables, which are usually reformulated linearly … Read more