Applications – Science and Engineering

Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy

  • Didier Henrion
  • Martin Kružík
  • Marek Tyburec
  • Jan Zeman
    • Categories Civil and Environmental Engineering, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , , , ,

    The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all guaranteed globally optimal solutions for frame and shell structures under multiple load cases and self-weight. To this purpose, we exploit the fact that the stiffness matrix is … Read more

    The Bipartite Boolean Quadric Polytope with Multiple-Choice Constraints

  • Andreas Bärmann
  • Alexander Martin
  • Oskar Schneider
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Polyhedra Tags , , , ,

    We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph. In this work, we study the case where there is a partition on one of the two bipartite node sets such … Read more

    Adaptable Energy Management System for Smart Buildings

  • Miguel F. Anjos
  • Juan A. Gomez-Herrera
  • Kenneth McKinnon
  • Ilaria Salerno
    • Categories Applications - OR and Management Sciences, Civil and Environmental Engineering, Optimization of Simulated Systems Tags , , , ,

    This paper presents a novel adaptable energy management system for smart buildings. In this framework we model the energy consumption of a living unit, and its energy exchange with the surroundings. We explicitly consider the impact of the outside environment and design features such as building orientation, automatic shading, and double facade. We formulate this … Read more

    Mixed-integer Linear Programming Models and Algorithms for Generation and Transmission Expansion Planning of Power Systems

  • Antonio Conejo
  • Ignacio E. Grossmann
  • Can Li
  • Peng Liu
  • Benjamin Omell
  • John D. Siirola
    • Categories Applications - Science and Engineering, Energy Tags , , , ,

    With the increasing penetration of renewable generating units, especially in remote areas not well connected with load demand, there are growing interests to co-optimize generation and transmission expansion planning (GTEP) in power systems. Due to the volatility in renewable generation, a planner needs to include the operating decisions into the planning model to guarantee feasibility. … Read more

    Distributionally Robust Facility Location with Bimodal Random Demand

  • Karmel S. Shehadeh
  • Ece Sanci
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Stochastic Programming Tags , , , ,

    In this paper, we consider a decision-maker who wants to determine a subset of locations from a given set of candidate sites to open facilities and accordingly assign customer demand to these open facilities. Unlike classical facility location settings, we focus on a new setting where customer demand is bimodal, i.e., display, or belong to, … Read more

    Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality

  • Rui Gao
    • Categories Robust Optimization, Statistics, Stochastic Programming Tags , , , ,

    Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine learning, existing performance guarantees for generic loss functions are either overly conservative due to the curse of dimensionality, or plausible only in large sample asymptotics. … Read more

    Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Rates

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
  • Anthony Nguyen
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , ,

    In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients, through a stochastic first-order oracle. For solving this class of problems, we propose two algorithms using moving-average stochastic estimates, and analyze … Read more

    Dual optimal design and the Christoffel-Darboux polynomial

  • Yohann De Castro
  • Didier Henrion
  • Jean-Bernard Lasserre
  • Fabrice Gamboa
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , ,

    The purpose of this short note is to show that the Christoffel-Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. ArticleDownload View PDF

    Optimal Residential Users Coordination Via Demand Response: An Exact Distributed Framework

  • Natalia Alguacil Conde
  • Michael David de Souza Dutra
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , ,

    This paper proposes a two-phase optimization framework for users that are involved in demand response programs. In a first phase, responsive users optimize their own household consumption, characterizing not only their appliances and equipment but also their comfort preferences. Subsequently, the aggregator exploits in a second phase this preliminary noncoordinated solution by implementing a coordination … Read more

    The Strip Method for Shape Derivatives

  • Harbir Antil
  • Drew P. Kouri
  • Sean Hardesty
  • Denis Ridzal
    • Categories Infinite Dimensional Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , ,

    A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches … Read more