Biomedical Applications

Approaches to iterative algorithms for solving nonlinear equations with an application in tomographic absorption spectroscopy

  • Francisco J. Aragón Artacho
  • Weiwei Cai
  • Yair Censor
  • Aviv Gibali
  • Chongyuan Shui
  • David Torregrosa-Belén
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupling, we consider a situation where straightforward translation to a fixed point problem is not possible because the operators that represent the … Read more

    Bi-level multi-criteria optimization to include linear energy transfer into proton treatment planning

  • Katrin Teichert
  • Mara Schubert
    • Categories Biomedical Applications, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    In proton therapy treatment planning, the aim is to ensure tumor control while sparing the various surrounding risk structures. The biological effect of the irradiation depends on both physical dose and linear energy transfer (LET). In order to include LET alongside physical dose in plan creation, we propose to formulate the proton treatment planning problem … Read more

    Multi-model Partially Observable Markov Decision Processes

  • Weiyu Li
  • Brian T. Denton
    • Categories Applications - OR and Management Sciences, Biomedical Applications, Stochastic Programming Tags , , ,

    We propose a new multi-model partially observable Markov decision process (MPOMDP) model to address the issue of model ambiguity in partially observable Markov decision process. Here, model ambiguity is defined as the case where there are multiple credible optimization models with the same structure but different model parameters. The proposed MPOMDP model aims to learn … Read more

    Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

  • Yair Censor
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , , ,

    The superiorization methodology can be thought of as lying conceptually between feasibility-seeking and constrained minimization. It is not trying to solve the full-fledged constrained minimization problem composed from the modeling constraints and the chosen objective function. Rather, the task is to find a feasible point which is “superior” (in a well-defined manner) with respect to … Read more

    Superiorization as a novel strategy for linearly constrained inverse radiotherapy treatment planning

  • Florian Barkmann
  • Yair Censor
  • Niklas Wahl
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

    Objective: We apply the superiorization methodology to the intensity-modulated radiation therapy (IMRT) treatment planning problem. In superiorization, linear voxel dose inequality constraints are the fundamental modeling tool within which a feasibility-seeking projection algorithm will seek a feasible point. This algorithm is then perturbed with gradient descent steps to reduce a nonlinear objective function. Approach: Within … Read more

    The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

  • Francisco J. Aragón Artacho
  • Yair Censor
  • Aviv Gibali
  • David Torregrosa-Belén
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

    In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced … Read more

    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

    Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19

  • Laurent Alfandari
  • Debajyoti Biswas
    • Categories Biomedical Applications

    The COVID-19 pandemic has had an unprecedented impact on global health and the economy since its inception in December, 2019 in Wuhan, China. Non-pharmaceutical interventions (NPI) like lockdowns and curfews have been deployed by affected countries for controlling the spread of infections. In this paper, we develop a Mixed Integer Non-Linear Programming (MINLP) epidemic model … Read more

    Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19

  • Laurent Alfandari
  • Debajyoti Biswas
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Biomedical Applications

    The COVID-19 pandemic has had an unprecedented impact on global health and the economy since its inception in December, 2019 in Wuhan, China. Non-pharmaceutical interventions (NPI) like lockdowns and curfews have been deployed by affected countries for controlling the spread of infections. In this paper, we develop a Mixed Integer Non-Linear Programming (MINLP) epidemic model … Read more

    A new matheuristic and improved instance generation for kidney exchange programmes

  • Maxence Delorme
  • Jacek Gondzio
  • William Pettersson
  • Sergio García
  • Joerg Kalcsics
  • David Manlove
  • James Trimble
    • Categories Biomedical Applications, Combinatorial Optimization Tags , ,

    Kidney exchange programmes increase the rate of living donor kidney transplants, and operations research techniques are vital to such programmes. These techniques, as well as changes to policy regarding kidney exchange programmes, are often tested using random instances created by a Saidman generator. We devise a new matheuristic that can optimally solve a benchmark set … Read more