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

Yuri Stoyan and Tatiana Romanova ()
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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

Chapter Chapter 15 in Modeling and Optimization in Space Engineering, 2012, pp 363-388 from Springer

Abstract: 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.

Keywords: Mathematical modelling; Packing and cutting; Phi-functions; Optimisation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-4469-5_15

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DOI: 10.1007/978-1-4614-4469-5_15

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