Robustification of the k-Means Clustering Problem and Tailored Decomposition Methods: When More Conservative Means More Accurate

  • Jan Pablo Burgard
  • Carina Moreira Costa
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , , , ,

    k-means clustering is a classic method of unsupervised learning with the aim of partitioning a given number of measurements into k clusters. In many modern applications, however, this approach suffers from unstructured measurement errors because the k-means clustering result then represents a clustering of the erroneous measurements instead of retrieving the true underlying clustering structure. … Read more

    Riemannian conjugate gradient methods with inverse retraction

  • Hiroyuki Sato
  • Xiaojing Zhu
    • Categories Nonlinear Optimization Tags , , , , ,

    We propose a new class of Riemannian conjugate gradient (CG) methods, in which inverse retraction is used instead of vector transport for search direction construction. In existing methods, differentiated retraction is often used for vector transport to move the previous search direction to the current tangent space. However, a different perspective is adopted here, motivated … Read more

    Two novel gradient methods with optimal step sizes

  • Oscar S. Dalmau
  • Rafael Herrera
  • Harry Oviedo
    • Categories Convex Optimization, Nonlinear Optimization Tags , , ,

    In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems. The proposed step sizes employ second-order information in order to obtain faster gradient-type methods. Both step sizes are derived from two unconstrained optimization models that involve approximate information of the Hessian of … Read more

    Gradient Sampling Methods with Inexact Subproblem Solves and Gradient Aggregation

  • Frank E. Curtis
  • Minhan Li
    • Categories Nonsmooth Optimization Tags , , , ,

    Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to solve a convex quadratic subproblem in each iteration. In this paper, a strategy is proposed that allows the use … Read more

    Two-Stage Sort Planning for Express Parcel Delivery

  • Alan L. Erera
  • Alejandro Toriello
  • Reem Khir
    • Categories Production and Logistics Tags , ,

    Recent years have brought significant changes in the operations of parcel transportation services, most notably due to the growing demand for e-commerce worldwide. Parcel sortation systems are used within sorting facilities in these transportation networks to enable the execution of effective consolidation plans with low per-unit handling and shipping costs. Designing and implementing effective parcel … Read more

    Personnel scheduling during Covid-19 pandemic

  • Manuel Iori
  • Anand Subramanian
  • Giorgio Zucchi
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , , ,

    This paper addresses a real-life personnel scheduling problem in the context of Covid-19 pandemic, arising in a large Italian pharmaceutical distribution warehouse. In this case study, the challenge is to determine a schedule that attempts to meet the contractual working time of the employees, considering the fact that they must be divided into mutually exclusive … Read more

    Linearization and Parallelization Schemes for Convex Mixed-Integer Nonlinear Optimization

  • Meenarli Sharma
  • Prashant Palkar
  • Ashutosh Mahajan
    • Categories (Mixed) Integer Nonlinear Programming, Parallel Algorithms Tags , , , ,

    We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and some at the other branch-and-bound nodes. Two of the techniques are specifically applicable to commonly found univariate … Read more

    The Equivalence of Fourier-based and Wasserstein Metrics on Imaging Problems

  • Gennaro Auricchio
  • Stefano Gualandi
  • Giuseppe Toscani
  • Andrea Codegoni
  • Marco Veneroni
    • Categories Convex and Nonsmooth Optimization, Linear Programming, Network Optimization

    We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the original one, the new Fourier-based metrics are well-defined also for probability distributions with different centers of mass, and for discrete probability measures … Read more

    Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

  • Enrico Meli
  • Benedetta Morini
  • Margherita Porcelli
  • Cristina Sgattoni
    • Categories Mechanical Engineering, Nonlinear Systems and Least-Squares

    Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a … Read more

    A Bin Packing Problem with Mixing Constraints for Containerizing Items for Logistics Service Providers

  • Sajini Anand P S
  • Stefan Guericke
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Telecommunications

    Large logistics service providers often need to containerize and route thousands or millions of items per year. In practice, companies specify business rules of how to pack and transport items from their origin to destination. Handling and respecting those business rules manually is a complex and time-consuming task. We propose a variant of the variable … Read more