Month: September 2020

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

    A Column Generation Based Heuristic for the Split Delivery Vehicle Routing Problem with Time Windows

  • Pedro Munari
  • Martin Savelsbergh
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming

    The vehicle routing problem with time windows (VRPTW) is one of the most studied variants of routing problems. We consider the Split Delivery VRPTW (SDVRPTW), an extension in which customers can be visited multiple times, if advantageous. While this additional flexibility can result in significant cost reductions, it also results in additional modeling and computational … Read more

    On complexity and convergence of high-order coordinate descent algorithms

  • V. S. Amaral
  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • Diaulas S. Marcondes
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , ,

    Coordinate descent methods with high-order regularized models for box-constrained minimization are introduced. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with … Read more

    A Modified Simplex Partition Algorithm to Test Copositivity

  • Mohammadreza Safi
  • Seyed Saeed Nabavi
  • Richard J. Caron
    • Categories Global Optimization Theory Tags , , , ,

    A real symmetric matrix $A$ is copositive if $x^\top Ax\geq 0$ for all $x\geq 0$. As $A$ is copositive if and only if it is copositive on the standard simplex, algorithms to determine copositivity, such as those in Sponsel et al. (J Glob Optim 52:537–551, 2012) and Tanaka and Yoshise (Pac J Optim 11:101–120, 2015) … Read more

    Randomized Assortment Optimization

  • Zhengchao Wang
  • Heikki Peura
  • Wolfram Wiesemann
    • Categories Robust Optimization, Yield Management

    When a firm selects an assortment of products to offer to customers, it uses a choice model to anticipate their probability of purchasing each product. In practice, the estimation of these models is subject to statistical errors, which may lead to significantly suboptimal assortment decisions. Recent work has addressed this issue using robust optimization, where … Read more

    Solving the Time Dependent Minimum Tour Duration and Delivery Man Problems with Dynamic Discretization Discovery

  • Mike Hewitt
  • Duc Minh Vu
  • Duc D. Vu
    • Categories (Mixed) Integer Linear Programming, Scheduling, Transportation Tags , , , ,

    In this paper, we present exact methods for solving the Time Dependent Minimum Duration Problem (TDMTDP) and the Time Dependent Delivery Man Problem (TD-DMP). Both methods are based on a Dynamic Discretization Discovery (DDD) approach for solving the Time Dependent Traveling Salesman Problem with Time Windows (TD-TSPTW). Unlike the TD-TSPTW, the problems we consider in … Read more

    Limited-memory Common-directions Method for Large-scale Optimization: Convergence, Parallelization, and Distributed Optimization

  • Ching-pei Lee
  • Po-Wei Wang
  • Chih-Jen Lin
    • Categories Parallel Algorithms, Unconstrained Optimization Tags , , ,

    In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second- order methods. At each iteration, a subspace of a limited dimension size is constructed using first-order information from previous iterations, and an ef- ficient Newton method is deployed to find an approximate minimizer within this subspace. With … Read more

    Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling

  • Andreas Bärmann
  • Alexander Martin
  • Oskar Schneider
    • Categories Cutting Plane Approaches, Polyhedra, Scheduling Tags , , , ,

    Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to … Read more

    Connecting optimization with spectral analysis of tri-diagonal matrices

  • Jean-Bernard Lasserre
    • Categories Global Optimization, Global Optimization Theory, Nonlinear Optimization Tags

    We show that the global minimum (resp. maximum) of a continuous func- tion on a compact set can be approximated from above (resp. from below) by computing the smallest (rest. largest) eigenvalue of a hierarchy of (r × r) tri-diagonal matrices of increasing size. Equivalently it reduces to computing the smallest (resp. largest) root of … Read more