Year: 2021

Scalable Subspace Methods for Derivative-Free Nonlinear Least-Squares Optimization

  • Coralia Cartis
  • Lindon Roberts
    • Categories Nonlinear Optimization Tags , ,

    We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular we prove high-probability bounds on the number of iterations before a given optimality is achieved. This framework is specialized to nonlinear least-squares problems, with a … Read more

    Robust Optimization in Nanoparticle Technology: A Proof of Principle by Quantum Dot Growth in a Residence Time Reactor

  • Kevin-Martin Aigner
  • Frauke Liers
  • Jana Dienstbier
  • Wolfgang Peukert
  • Lukas Pflug
  • Jan Hendrik Rolfes
  • Doris Segets
    • Categories Chemical Engineering, Robust Optimization Tags , , ,

    Knowledge-based determination of the best-possible experimental setups for nanoparticle design is highly challenging. Additionally, such processes are accompanied by noticeable uncertainties. Therefore, protection against these uncertainties is needed. Robust optimization helps determining such best possible processes. The latter guarantees quality requirements regardless of how the uncertainties, e.g. with regard to variations in raw materials, heat … Read more

    Optimal Hospital Care Scheduling During the SARS-CoV-2 Pandemic

  • Josh D'Aeth
  • Shubhechyya Ghosal
  • Fiona Grimm
  • David Haw
  • Esma Koca
  • Krystal Lau
  • Huikang Liu
  • Stefano Moret
  • Dheeya Rizmie
  • Peter Smith
  • Giovanni Forchini
  • Marisa Miraldo
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags , , ,

    The COVID-19 pandemic has seen dramatic demand surges for hospital care that have placed a severe strain on health systems worldwide. As a result, policy makers are faced with the challenge of managing scarce hospital capacity so as to reduce the backlog of non-COVID patients whilst maintaining the ability to respond to any potential future … Read more

    How do exponential size solutions arise in semidefinite programming?

  • Gabor Pataki
  • Aleksandr Touzov
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Semi-definite Programming

    Semidefinite programs (SDPs) are some of the most popular and broadly applicable optimization problems to emerge in the last thirty years. A curious pathology of SDPs, illustrated by a classical example of Khachiyan, is that their solutions may need exponential space to even write down. Exponential size solutions are the main obstacle to solve a … Read more

    An Adaptive and Near Parameter-free BRKGA Using Q-Learning Method

  • Antonio Chaves
  • Luiz Henrique Lorena
    • Categories Meta Heuristics Tags , , ,

    The Biased Random-Key Genetic Algorithm (BRKGA) is an efficient metaheuristic to solve combinatorial optimization problems but requires parameter tuning so the intensification and diversification of the algorithm work in a balanced way. There is, however, not only one optimal parameter configuration, and the best configuration may differ according to the stages of the evolutionary process. … Read more

    Cutting Plane Generation Through Sparse Principal Component Analysis

  • Santanu S. Dey
  • Aleksandr M. Kazachkov
  • Andrea Lodi
  • Gonzalo Muñoz
    • Categories Cutting Plane Approaches, Quadratic Programming Tags , , ,

    Quadratically-constrained quadratic programs (QCQPs) are optimization models whose remarkable expressiveness has made them a cornerstone of methodological research for nonconvex optimization problems. However, modern methods to solve a general QCQP fail to scale, encountering computational challenges even with just a few hundred variables. Specifically, a semidefinite programming (SDP) relaxation is typically employed, which provides strong … Read more

    Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

  • Hatim Djelassi
  • Alexander Mitsos
  • Oliver Stein
    • Categories Global Optimization Applications, Semi-infinite Programming

    The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

    Edge Minimizing the Student Conflict Graph

  • Joshua S. Friedman
    • Categories Scheduling

    In many schools, courses are given in sections. Prior to timetabling students need to be assigned to individual sections. We give a hybrid approximation sectioning algorithm that minimizes the number of edges (potential conflicts) in the student conflict graph (SCG). We start with a greedy algorithm to obtain a starting solution and then continue with … Read more

    Scaling Up Exact Neural Network Compression by ReLU Stability

  • Abhinav Kumar
  • Srikumar Ramalingam
  • Thiago Serra
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Combinatorial Optimization

    We can compress a neural network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons in networks with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. … Read more

    An adaptive robust optimization model for parallel machine scheduling

  • Izack Cohen
  • Krzysztof Postek
  • Shimrit Shtern
    • Categories Robust Optimization, Scheduling Tags , ,

    Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is completed and a machine becomes idle. Robust optimization is the natural methodology to cope with the first characteristic of duration … Read more