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

被引:3
|
作者
Litvinchev, Igor [1 ]
Fischer, Andreas [2 ]
Romanova, Tetyana [3 ,4 ]
Stetsyuk, Petro [5 ]
机构
[1] Autonomous Univ Nuevo Leon, Fac Mech & Elect Engn, San Nicolas De Los Garza, Mexico
[2] Tech Univ Dresden, Fac Math, D-01062 Dresden, Germany
[3] A Pidhornyi Inst Mech Engn Problems, Natl Acad Sci Ukraine, UA-61046 Kharkiv, Ukraine
[4] Univ Leeds, Business Sch, Leeds Univ, Leeds LS2 9JT, England
[5] VM Glushkov Inst Cybernet, Natl Acad Sci Ukraine, UA-03187 Kiev, Ukraine
关键词
packing; generalized spheres; composed objects; arbitrary norms; mathematical modeling; nonlinear optimization; GLOBAL OPTIMIZATION; SHAPE;
D O I
10.3390/math12070935
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
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页数:17
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