Applications – Science and Engineering

Combinatorial Integral Approximation for Mixed-Integer PDE-Constrained Optimization Problems

  • Mirko Hahn
  • Sebastian Sager
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , ,

    We apply the basic principles underlying combinatorial integral approximation methods for mixed-integer optimal control with ordinary differential equations in general, and the sum-up rounding algorithm specifically, to optimization problems with partial differential equation (PDE) constraints. By doing so, we identify two possible generalizations that are applicable to problems involving PDE constraints with mesh-dependent integer variables, … Read more

    FINITE ELEMENT MODEL UPDATING FOR STRUCTURAL APPLICATIONS

  • Maria Girardi
  • Margherita Porcelli
  • Cristina Padovani
  • Daniele Pellegrini
  • Leonardo Robol
    • Categories Civil and Environmental Engineering, Nonlinear Optimization Tags , , , ,

    A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown … Read more

    A Decision Tool based on a Multi-Objective Methodology for designing High-Pressure Thermal Treatments in Food Industry

  • Miriam R. Ferrández
  • Benjamin Ivorra
  • Pilar M. Ortigosa
  • Ángel M. Ramos
  • Juana L. Redondo
    • Categories Meta Heuristics, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    In this work, we propose a methodology for designing High-Pressure Thermal processes for food treatment. This approach is based on a multi-objective preference-based evolutionary optimization algorithm, called WASF-GA, combined with a decision strategy which provides the food engineer with the best treatment in accordance with some quality requirements. The resulting method is compared to a … Read more

    Optimal Black Start Allocation for Power System Restoration

  • Shmuel Oren
  • Deepak Rajan
  • Georgios Patsakis
  • Jennifer Rios
    • Categories (Mixed) Integer Linear Programming, Energy Tags , ,

    Equipment failures, operator errors, natural disasters and cyber-attacks can and have caused extended blackouts of the electric grid. Even though such events are rare, preparedness for them is critical because extended power outages endanger human lives, compromise national security, or result in economic losses of billions of dollars. Since most of the generating units cannot … Read more

    Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks

  • Martin Robinius
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Detlef Stolten
  • Lara Welder
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to … Read more

    Combining Multi-Level Real-time Iterations of Nonlinear Model Predictive Control to Realize Squatting Motions on Leo

  • Christian Kirches
  • Ivan Koryakovskiy
  • Manuel Kudruss
  • Katja Mombaur
  • Heike Vallery
    • Categories Constrained Nonlinear Optimization, Control Applications, Nonlinear Systems and Least-Squares Tags , , , , ,

    Today’s humanoid robots are complex mechanical systems with many degrees of freedom that are built to achieve locomotion skills comparable to humans. In order to synthesize whole-body motions, real-tme capable direct methods of optimal control are a subject of contemporary research. To this end, Nonlinear Model Predictive Control is the method of choice to realize … Read more

    Tight-and-cheap conic relaxation for the AC optimal power flow problem

  • Miguel F. Anjos
  • Christian Bingane
  • Sébastien Le Digabel
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Semi-definite Programming Tags , , ,

    The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite … Read more

    Bounding and Counting Linear Regions of Deep Neural Networks

  • Srikumar Ramalingam
  • Thiago Serra
  • Christian Tjandraatmadja
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , , , ,

    We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the maximum number of linear regions … Read more

    Smart “Predict, then Optimize”

  • Adam N. Elmachtoub
  • Paul Grigas
    • Categories Applications - OR and Management Sciences, Data-Mining, Statistics

    Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is to predict, then optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in a downstream optimization … Read more

    A Random Block-Coordinate Douglas-Rachford Splitting Method with Low Computational Complexity for Binary Logistic Regression

  • Luis M. Briceno-Arias
  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Giovanni Chierchia
    • Categories Convex Optimization, Statistics Tags , , ,

    In this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas Rachford splitting method. Our algorithm sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach … Read more