Designing reliable future energy systems by iteratively including extreme periods in time-series aggregation

  • Adam R. Brandt
  • Lucas Elias Kuepper
  • Holger Teichgraeber
    • Categories Energy, Facility Planning and Design

    Generation Capacity Expansion Planning (GCEP) requires high temporal resolution to account for the volatility of renewable energy supply. Because the GCEP optimization problem is often computationally intractable, time-series input data are often aggregated to representative periods using clustering. However, clustering removes extreme events, which are important to achieve reliable system designs. We present a method … Read more

    MILP models for the continuous Berth Allocation and Quay Crane Assignment Problem considering crane movement and setup times

  • Ramon Alvarez-Valdes
  • Juan F. Correcher
  • Federico Perea
    • Categories (Mixed) Integer Linear Programming, Scheduling, Transportation Tags , , ,

    In this technical report we present several Mixed Integer Linear Programming (MILP) models for the Berth Allocation and Quay Crane Assignment Problem (BACASP) considering crane movement and setup time (from now on: BACASP-S). First, we propose a MILP for the continuous-quay time-invariant BACASP in which both berthing time and position variables are continuous. Then, we … Read more

    On Properties of Univariate Max Functions at Local Maximizers

  • Tim Mitchell
  • Michael L. Overton
    • Categories Nonsmooth Optimization Tags , , , ,

    More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum eigenvalue of a univariate real analytic Hermitian matrix family is twice continuously differentiable, with Lipschitz second derivative, at all local maximizers, a property that … Read more

    On fault-tolerant low-diameter clusters in graphs

  • Yajun Lu
  • Hosseinali Salemi
  • Balabhaskar Balasundaram
  • Austin Buchanan
    • Categories 0-1 Programming, Branch and Cut Algorithms, Network Optimization Tags , , , ,

    Cliques and their generalizations are frequently used to model “tightly knit” clusters in graphs and identifying such clusters is a popular technique used in graph-based data mining. One such model is the $s$-club, which is a vertex subset that induces a subgraph of diameter at most $s$. This model has found use in a variety … Read more

    Accelerated Stochastic Peaceman-Rachford Method for Empirical Risk Minimization

  • Jianchao Bai
  • Fengmiao Bian
  • Xiaokai Chang
  • Lin Du
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    This work is devoted to studying an Accelerated Stochastic Peaceman-Rachford Splitting Method (AS-PRSM) for solving a family of structural empirical risk minimization problems. The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite-sum of smooth convex component functions. The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction … Read more

    Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

  • Falk M. Hante
  • Richard Krug
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the … Read more

    Interdicting Low-Diameter Cohesive Subgroups in Large-Scale Social Networks

  • Niloufar Daemi
  • Juan Borrero
  • Balabhaskar Balasundaram
    • Categories (Mixed) Integer Linear Programming, Graphs and Matroids, Network Optimization Tags , ,

    The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly-knit communities whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this … Read more

    Energy-efficient Automated Vertical Farms

  • Maxence Delorme
  • Alberto Santini
    • Categories Combinatorial Optimization, Production and Logistics Tags , , , ,

    Autonomous vertical farms (VFs) are becoming increasingly more popular, because they allow to grow food minimising water consumption and the use of pesticides, while greatly increasing the yield per square metre, compared with traditional agriculture. To meet sustainability goals, however, VFs must operate at maximum efficiency; it would be otherwise impossible to compete with the … Read more

    Solving a Class of Cut-Generating Linear Programs via Machine Learning

  • Danial Davarnia
  • Atefeh Rajabalizadeh
    • Categories Branch and Cut Algorithms, Data-Mining, Linear Programming Tags , , , ,

    Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome … Read more

    Worst-case evaluation complexity of derivative-free nonmonotone line search methods for solving nonlinear systems of equations

  • Flávia Chorobura
  • Geovani Nunes Grapiglia
    • Categories Nonlinear Optimization

    In this paper we study a class of derivative-free nonmonotone line search methods for solving nonlinear systems of equations, which includes the method N-DF-SANE proposed in (IMA J. Numer. Anal. 29: 814–825, 2009). These methods correspond to derivative-free optimization methods applied to the minimization of a suitable merit function. Assuming that the mapping defining the … Read more