Planar Maximum Coverage Location Problem with Partial Coverage, Continuous Spatial Demand, and Adjustable Quality of Service

  • Manish Bansal
  • Parshin Shojaee
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization

    We consider a generalization of the classical planar maximum coverage location problem (PMCLP) in which partial coverage is allowed, facilities have adjustable quality of service (QoS) or service range, and demand zones and service zone of each facility are represented by two-dimensional spatial objects such as rectangles, circles, polygons, etc. We denote this generalization by … Read more

    Stochastic RWA and Lightpath Rerouting in WDM Networks

  • Maryam Daryalal
  • Merve Bodur
    • Categories Stochastic Programming, Telecommunications Tags , , ,

    In a telecommunication network, Routing and Wavelength Assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity due to stranded bandwidth. At this … Read more

    A converging Benders’ decomposition algorithm for two-stage mixed-integer recourse models

  • Ward Romeijnders
  • Niels van der Laan
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

    We propose a new solution method for two-stage mixed-integer recourse models. In contrast to existing approaches, we can handle general mixed-integer variables in both stages, and thus, e.g., do not require that the first-stage variables are binary. Our solution method is a Benders’ decomposition, in which we iteratively construct tighter approximations of the expected second-stage … Read more

    Twenty years of continuous multiobjective optimization in the twenty-first century

  • Gabriele Eichfelder
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some … Read more

    Polyhedral Separation via Difference of Convex (DC) Programming

  • Annabella Astorino
  • Massimo Di Francesco
  • Manlio Gaudioso
  • Enrico Gorgone
  • Benedetto Manca
    • Categories Nonsmooth Optimization

    We consider polyhedral separation of sets as a possible tool in supervised classification. In particular we focus on the optimization model introduced by Astorino and Gaudioso and adopt its reformulation in Difference of Convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of … Read more

    On Hölder Calmness of Minimizing Sets

  • Diethard Klatte
  • Bernd Kummer
    • Categories Convex and Nonsmooth Optimization Tags , ,

    We present conditions for Hölder calmness and upper Hölder continuity of optimal solution sets to perturbed optimization problems in finite dimensions. Studies on Hölder type stability were a popular subject in variational analysis already in the 1980ies and 1990ies, and have become a revived interest in the last decade. In this paper, we focus on … Read more

    ADMM and inexact ALM: the QP case

  • Stefano Cipolla
  • Jacek Gondzio
    • Categories Quadratic Programming Tags , ,

    Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent ($n \geq 3$). Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the … 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 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

    The Arc-Item-Load and Related Formulations for the Cumulative Vehicle Routing Problem

  • Mauro Henrique Mulati
  • Ricardo Fukasawa
  • Flávio Keidi Miyazawa
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization Tags , , , ,

    The Capacitated Vehicle Routing Problem (CVRP) consists of finding the cheapest way to serve a set of customers with a fleet of vehicles of a given capacity. While serving a particular customer, each vehicle picks up its demand and carries its weight throughout the rest of its route. While costs in the classical CVRP are … Read more

    Branch-and-bound and objective branching with three objectives

  • Nicolas Forget
  • Sune Lauth Gadegaard
  • Kathrin Klamroth
  • Lars Relund Nielsen
  • Anthony Przybylski
    • Categories Multi-Criteria Optimization

    The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the efficient computation of upper and lower bound sets. Besides the classical dominance test, bound sets are used to improve the computational time by imposing inequalities derived from (partial) dominance in the objective space. This process is called objective branching since it is mostly … Read more