A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms
Igor Litvinchev, Andreas Fischer, Tetyana Romanova, Petro Stetsyuk
Source 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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.