A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

Igor Litvinchev (), Andreas Fischer, Tetyana Romanova and Petro Stetsyuk
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Igor Litvinchev: Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, San Nicolas de los Garza CP 66455, Mexico
Andreas Fischer: Faculty of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany
Tetyana Romanova: A. Pidhornyi Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 61046 Kharkiv, Ukraine
Petro Stetsyuk: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, 03187 Kyiv, Ukraine

Mathematics, 2024, vol. 12, issue 7, 1-17

Abstract: Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems.

Keywords: packing; generalized spheres; composed objects; arbitrary norms; mathematical modeling; nonlinear optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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