Packing non - convex polytopes into a parallelepiped
نویسندگان
چکیده
The paper considers the problem of packing non-convex polytopes of arbitrary spatial shapes into a parallelepiped of minimal height. The polytopes are oriented, rotation is not permitted. A mathematical model of the problem is developed and some of its peculiarities are analyzed. Due to these peculiarities a solution method is proposed which is based on a meta-heuristic to find some approximation of a global minimum solution. Within the solution process a sequence of local minima is computed. Some examples and computational results are also given.
منابع مشابه
Packing of convex polytopes into a parallelepiped
This paper deals with the problem of packing convex polytopes into a parallelepiped of minimal height. It is assumed that the polytopes are oriented, i. e. rotations are not permitted. A mathematical model of the problem is developed and peculiarities of them are addressed. Based on these peculiarities a method to compute local optimal solutions is constructed. Both an approximate and an exact ...
متن کاملInstitute for Mathematical Physics Densest Lattice Packings of 3{polytopes Densest Lattice Packings of 3{polytopes
Based on Minkowski's work on critical lattices of 3-dimensional convex bodies we present an eecient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As an application we calculate densest lattice packings of all regular and Archimedean polytopes.
متن کاملConvex and Combinatorial Geometry Fest
Karoly Bezdek and Egon Schulte are two geometers who have made important and numerous contributions to Discrete Geometry. Both have trained many young mathematicians and have actively encouraged the development of the area by professors of various countries. Karoly Bezdek studied the illumination problem among many other problems about packing and covering of convex bodies. More recently he has...
متن کاملDensest lattice packings of 3-polytopes
Based on Minkowski’s work on critical lattices of 3-dimensional convex bodies we present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As an application we calculate densest lattice packings of all regular and Archimedean polytopes.
متن کاملMultidimensional parallelepiped model—a new type of non-probabilistic convex model for structural uncertainty analysis
Non-probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is lacking. The interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non-probabilistic convex mod...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007