Applications – Science and Engineering

Electric Power Infrastructure Planning: Mixed-Integer Programming Model and Nested Decomposition Algorithm

  • Ignacio E. Grossmann
  • Dimitri J. Papageorgiou
  • Cristiana L. Lara
  • D. Mallapragada
  • A. Venkatesh
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering Tags , , , , ,

    This paper addresses the long-term planning of electric power infrastructures considering high renewable penetration. To capture the intermittency of these sources, we propose a deterministic multi-scale Mixed-Integer Linear Programming (MILP) formulation that simultaneously considers annual generation investment decisions and hourly operational decisions. We adopt judicious approximations and aggregations to improve its tractability. Moreover, to overcome … Read more

    A Hierarchical Alternating Direction Method of Multipliers for Fully Distributed Unit Commitment

  • Zhang Chen
    • Categories Applications - Science and Engineering Tags , ,

    Abstract—This paper discusses a hierarchical alternating direction method of multipliers (ADMM) approach for the unit commitment (UC) problem in a fully distributed manner. Decentralized unit commitment operation schemes have several advantages when compared with the traditional centralized management system for smart grid. Specifically, decentralized management is more flexible, less computationally intensive, and easier to implement … Read more

    Algorithmic Results for Potential-Based Flows: Easy and Hard Cases

  • Martin Gross
  • Marc E. Pfetsch
  • Lars Schewe
  • Martin Schmidt
  • Martin Skutella
    • Categories Applications - Science and Engineering, Integer Programming, Network Optimization Tags , , , , ,

    Potential-based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize … Read more

    A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities

  • Martin Schmidt
  • Mathias Sirvent
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test … Read more

    The Multiple Checkpoint Ordering Problem

  • Philipp Hungerländer
  • Kerstin Maier
    • Categories 0-1 Programming, Combinatorial Optimization, Facility Planning and Design Tags , , ,

    The multiple Checkpoint Ordering Problem (mCOP) aims to find an optimal arrangement of n one-dimensional departments with given lengths such that the total weighted sum of their distances to m given checkpoints is minimized. In this paper we suggest an integer linear programming (ILP) approach and a dynamic programming (DP) algorithm, which is only exact … Read more

    Invex Optimization Revisited

  • Ksenia Bestuzheva
  • Hassan L. Hijazi
    • Categories Applications - Science and Engineering, Global Optimization Theory, Nonlinear Optimization Tags , , ,

    Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point method always converges to a global optimizer. In this work, we provide necessary conditions for KT-invexity in n-dimensions and … Read more

    Optimizing power generation in the presence of micro-grids

  • Boris Detienne
  • Michael Poss
  • De Boeck Jérome
  • Pan Stefania
  • Wim van Ackooij
    • Categories 0-1 Programming, Applications - Science and Engineering, Stochastic Programming Tags , , ,

    In this paper we consider energy management optimization problems in a future wherein an interaction with micro-grids has to be accounted for. We will model this interaction through a set of contracts between the generation companies owning centralized assets and the micro-grids. We will formulate a general stylized model that can, in principle, account for … Read more

    Estimating L1-Norm Best-Fit Lines for Data

  • J. Paul Brooks
  • JH Dulá
    • Categories Applications - OR and Management Sciences, Data-Mining, Statistics Tags , , ,

    The general formulation for finding the L1-norm best-fit subspace for a point set in $m$-dimensions is a nonlinear, nonconvex, nonsmooth optimization problem. In this paper we present a procedure to estimate the L1-norm best-fit one-dimensional subspace (a line through the origin) to data in $\Re^m$ based on an optimization criterion involving linear programming but which … Read more

    Data-Driven Robust Optimization Based on Kernel Learning

  • Xiaolin Huang
  • Chao Shang
  • Fengqi You
    • Categories Chemical Engineering, Robust Optimization Tags , , , ,

    We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart problem retains the … Read more

    A New Voltage Stability-Constrained Optimal Power Flow Model: Sufficient Condition, SOCP Representation, and Relaxation

  • Bai Cui
  • Xu Andy Sun
    • Categories Applications - Science and Engineering Tags , , ,

    A simple characterization of the solvability of power flow equations is of great importance in the monitoring, control, and protection of power systems. In this paper, we introduce a sufficient condition for power flow Jacobian nonsingularity. We show that this condition is second-order conic representable when load powers are fixed. Through the incorporation of the … Read more