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Mathematical Models of Placement Optimisation: Two- and Three-Dimensional Problems and Applications

In: Modeling and Optimization in Space Engineering

Author

Listed:
  • Yuri Stoyan

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine)

  • Tatiana Romanova

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine)

Abstract

We study NP-hard placement optimisation problems, which cover a wide spectrum of industrial applications, including space engineering. This chapter considers tools of mathematical modelling and a solution strategy of placement problems illustrated with examples and pictures. A class of 2D and 3D geometric objects, called phi-objects, is introduced and considered as mathematical models of real objects. We review the main concept of our studies, i.e. phi-functions. One may also find a clear definition of phi-function as an analytical tool for describing placement constraints, including containment, non-overlapping, allowable distances, prohibited areas, object translations and rotations. A mathematical model of a basic placement problem is constructed as constrained optimisation problem. We propose a solution strategy for placement problems. The reader will get acquainted with an application problem of the basic placement problem encountered in space engineering and find a number of computational results for 2D and 3D applications.

Suggested Citation

  • Yuri Stoyan & Tatiana Romanova, 2012. "Mathematical Models of Placement Optimisation: Two- and Three-Dimensional Problems and Applications," Springer Optimization and Its Applications, in: Giorgio Fasano & János D. Pintér (ed.), Modeling and Optimization in Space Engineering, edition 127, chapter 0, pages 363-388, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-4469-5_15
    DOI: 10.1007/978-1-4614-4469-5_15
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    Cited by:

    1. Romanova, Tatiana & Stoyan, Yurij & Pankratov, Alexander & Litvinchev, Igor & Plankovskyy, Sergiy & Tsegelnyk, Yevgen & Shypul, Olga, 2021. "Sparsest balanced packing of irregular 3D objects in a cylindrical container," European Journal of Operational Research, Elsevier, vol. 291(1), pages 84-100.

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