Applications – Science and Engineering

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

  • Ksenia Bestuzheva
  • Carleton Coffrin
  • Hassan L. Hijazi
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Convex Optimization Tags , , , ,

    This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent … Read more

    Best subset selection for eliminating multicollinearity

  • Ken Kobayashi
  • Tomomi Matsui
  • Ryuhei Miyashiro
  • Kazuhide Nakata
  • Yuichi Takano
  • Ryuta Tamura
    • Categories Applications - Science and Engineering, Global Optimization, Integer Programming Tags , , , , ,

    This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities … Read more

    Heuristics for Packing Semifluids

  • João Pedro Pedroso
    • Categories Applications - Science and Engineering, Combinatorial Optimization

    Physical properties of materials are seldom studied in the context of packing problems. In this work we study the behavior of semifluids: materials with particular characteristics, that share properties both with solids and with fluids. We describe the importance of some specific semifluids in an industrial context, and propose methods for tackling the problem of … Read more

    Towards Simulation Based Mixed-Integer Optimization with Differential Equations

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that … Read more

    1-Bit Compressive Sensing: Reformulation and RRSP-Based Sign Recovery Theory

  • Chunlei Xu
  • Yun-Bin Zhao
    • Categories Convex Optimization, Data-Mining Tags , , , , ,

    Recently, the 1-bit compressive sensing (1-bit CS) has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. In this paper, we first … Read more

    A Subgradient Method for Free Material Design

  • Michal Kočvara
  • Yurii Nesterov
  • Yu Xia
    • Categories Applications - Science and Engineering, Mechanical Engineering Tags , , , , , , , , ,

    A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due to its large scale, second-order methods cannot solve the free material design problem in reasonable size. We formulate the free material optimization (FMO) problem into … Read more

    Regularized monotonic regression

  • Oleg Burdakov
  • Oleg Sysoev
    • Categories Quadratic Programming, Statistics Tags , , , , ,

    Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the MR formulated … Read more

    Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods

  • Björn Geißler
  • Antonio Morsi
  • Lars Schewe
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Detailed modeling of gas transport problems leads to nonlinear and nonconvex mixed-integer optimization or feasibility models (MINLPs) because both the incorporation of discrete controls of the network as well as accurate physical and technical modeling is required in order to achieve practical solutions. Hence, ignoring certain parts of the physics model is not valid for … Read more

    DESSLib – Benchmark Instances for Optimization of Decentralized Energy Supply Systems

  • Fritz Arnold
  • Björn Bahl
  • André Bardow
  • Arie M.C.A. Koster
  • Marco E. Lübbecke
  • Sebastian Goderbauer
  • Philip Voll
    • Categories Applications - Science and Engineering Tags , , , , , ,

    DESSLib (http://www.math2.rwth-aachen.de/DESSLib) provides benchmark instances obtained by real world data for synthesis problems of decentralized energy supply systems (DESS). In this paper, the considered optimization problem is described in detail. For a description of the functions and parameters used to describe the system and equipment, see the documentation found on DESSLib website http://www.math2.rwth-aachen.de/DESSLib. ArticleDownload View … Read more

    An Adaptive Discretization MINLP Algorithm for Optimal Synthesis of Decentralized Energy Supply Systems

  • Björn Bahl
  • André Bardow
  • Arie M.C.A. Koster
  • Marco E. Lübbecke
  • Sebastian Goderbauer
  • Philip Voll
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , , ,

    Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and … Read more