Optimal Fillings - A new spatial subdivision problem related to packing and covering

A new metaheuristic genetic-based placement algorithm for 2D strip packing

Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic algorithm is proposed to solve it. I...

In the Local Theory of Packing

In this paper we are concerned with three lattice problems: the lattice packing problem, the lattice covering problem and the lattice packing-covering problem. One way to find optimal lattices for these problems is to enumerate all finitely many, locally optimal lattices. For the lattice packing problem there are two classical algorithms going back to Minkowski and Voronoi. For the covering and...

Optimal filling of shapes.

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuri...

Computational Approaches to Lattice Packing and Covering Problems

We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the sense that they approximate optimal covering lattices and optimal packing-covering lattices within any desired accuracy. Both algorithms involve semidefinit...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...