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

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Modeling and Optimization in Space Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 73))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematical Modeling, Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine

    Yuri Stoyan & Tatiana Romanova

Authors
  1. Yuri Stoyan
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  2. Tatiana Romanova
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Editor information

Editors and Affiliations

  1. Thales Alenia Space SpA, Str. Antica di Collegno 253, Turin, 10146, Italy

    Giorgio Fasano

  2. Stoneybrook Court 114, Halifax, B3M 3J7, Nova Scotia, Canada

    János D. Pintér

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Stoyan, Y., Romanova, T. (2012). Mathematical Models of Placement Optimisation: Two- and Three-Dimensional Problems and Applications. In: Fasano, G., Pintér, J. (eds) Modeling and Optimization in Space Engineering. Springer Optimization and Its Applications, vol 73. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4469-5_15

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