Optimization of Systems modeled by PDEs

A Mixed-Integer PDE-Constrained Optimization Formulation for Electromagnetic Cloaking

  • Sven Leyffer
  • Todd S. Munson
  • Ryan Vogt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , ,

    We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more

    Randomized Sketching Algorithms for Low Memory Dynamic Optimization

  • Drew P. Kouri
  • Ramchandran Muthukumar
  • Madeleine Udell
    • Categories Dynamic Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization

    This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a … Read more

    Spectral Gap Optimization of Divergence Type Diffusion Operators

  • Spring Berman
  • Hans D Mittelmann
  • Shiba Biswal
  • Karthik Elamvazhuthi
    • Categories Applications - Science and Engineering, Control Applications, Optimization of Systems modeled by PDEs Tags , ,

    In this paper, we address the problem of maximizing the spectral gap of a divergence type diffusion operator. Our main application of interest is characterizing the distribution of a swarm of agents that evolve on a bounded domain in Rn according to a Markov process. A subclass of the divergence type operators that we introduce … 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

    Maximizing the storage capacity of gas networks: a global MINLP approach

  • Robert Burlacu
  • Martin Gross
  • Marc E. Pfetsch
  • Lars Schewe
  • Mathias Sirvent
  • Herbert Egger
  • Alexander Martin
  • Martin Skutella
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs Tags , , , ,

    In this paper, we study the transient optimization of gas networks, focusing in particular on maximizing the storage capacity of the network. We include nonlinear gas physics and active elements such as valves and compressors, which due to their switching lead to discrete decisions. The former is described by a model derived from the Euler … Read more

    Provably High-Quality Solutions for the Meal Delivery Routing Problem

  • Martin Savelsbergh
  • Barış Yıldız
    • Categories Integer Programming, Optimization of Systems modeled by PDEs, Transportation Tags , , , , ,

    Online restaurant aggregators with integrated meal delivery networks have become more common and more popular in the past few years. Meal delivery is arguably the ultimate challenge in last mile logistics: a typical order is expected to be delivered within an hour (much less if possible), and within minutes of the food becoming ready. We … Read more

    Moments and convex optimization for analysis and control of nonlinear partial differential equations

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Milan Korda
    • Categories Distributed Control, Optimization of Systems modeled by PDEs, Semi-definite Programming Tags , , , ,

    This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a \emph{linear} equation in the space of Borel measures. This equation is then used as a constraint of an infinite-dimensional linear programming problem (LP). This LP is … Read more

    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

    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

    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