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Balance Layout Problems: Mathematical Modeling and Nonlinear Optimization

  • Yuriy Stoyan
  • Tatiana Romanova
  • Alexander Pankratov
  • Anna Kovalenko
  • Peter Stetsyuk
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 114)

Abstract

The paper studies the optimal layout problem of 3D-objects (solid spheres, straight circular cylinders, spherocylinders, straight regular prisms, cuboids and tori) in a container (a cylindrical, a parabolic, or a truncated conical shape) with circular racks. The problem takes into account a given minimal and maximal allowable distances between objects, as well as, behaviour constraints of the mechanical system (equilibrium, moments of inertia and stability constraints). We call the problem the Balance Layout Problem (BLP) and develop a continuous nonlinear programming model (NLP-model) of the problem, using the phi-function technique. We also consider several BLP subproblems; provide appropriate mathematical models and solution algorithms, using nonlinear programming and nonsmooth optimization methods, illustrated with computational experiments.

Keywords

Layout problems Behaviour constraints Distance constraints Phi-functions Quasi-phi-functions NLP-models Optimization algorithms 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yuriy Stoyan
    • 1
  • Tatiana Romanova
    • 1
  • Alexander Pankratov
    • 1
  • Anna Kovalenko
    • 1
  • Peter Stetsyuk
    • 2
  1. 1.Department of Mathematical Modeling and Optimal DesignInstitute for Mechanical Engineering Problems of the National Academy of Sciences of UkraineKharkovUkraine
  2. 2.Department of Methods of Nonsmooth OptimizationGlushkov Institute of Cybernetic of the National Academy of Sciences of UkraineKyivUkraine

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