Developments in mathematical algorithms and computational tools for proton CT and particle therapy treatment planning

  • Yair Censor
  • Keith E. Schubert
  • Reinhard W. Schulte
    • Categories Basic Sciences Applications, Biomedical Applications, Constrained Nonlinear Optimization Tags , , , , , , , ,

    We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensitymodulated particle therapy (IMPT) treatment planning. Proton therapy necessitates a high level of delivery accuracy to exploit the selective targeting imparted by the Bragg peak. For this purpose, pCT utilizes the proton beam itself … Read more

    Appointment Scheduling for Medical Diagnostic Centers considering Time-sensitive Pharmaceuticals: A Dynamic Robust Optimization Approach

  • Aleida Braaksma
  • Mohammad Mahdavi Mazdeh
  • Mahdi Heydari
  • Mohammad Namakshenas
    • Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization, Robust Optimization Tags , , , , ,

    This paper studies optimal criteria for the appointment scheduling of outpatients in a medical imaging center. The main goal of this study is to coordinate the assignments of radiopharmaceuticals and the scheduling of outpatients on imaging scanners. We study a special case of a molecular imaging center that offers services for various diagnostic procedures for … Read more

    Mathematical models for the minimization of open stacks problem

  • Maria José Pinto
  • Horacio Hideki Yanasse
  • Mateus Martin
    • Categories Applications - OR and Management Sciences Tags , , , ,

    In this paper, we address the Minimization of Open Stacks Problem (MOSP). This problem often appears during production planning of manufacturing industries, such as in the cutting of objects to comply with space constraints around the cutting machine in the glass, furniture, and metallurgical industries. The MOSP is also pertinent to the field of VLSI … Read more

    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

    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

    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