The 3D-Packing by Meta Data Structure and Packing Heuristics

The three dimensional (3D) packing problem is to arrange given rectangular boxes in a rectangular box of the minimum volume without overlapping each other. As an approach, this paper introduces the system of three sequences of the box labels, the sequence-triple, to encode the topology of the 3Dpacking. The topology is the system of relative relations in pairs of boxes such as right-of, above, front-of, etc. It will be proved that the sequence-triple represents the topology of the tractable 3D-packings which is a 3D-packing such that there is an order of the boxes along which all the boxes are extracted one by one in a certain fixed direction without disturbing other remaining boxes. The idea is extended to the system of five ordered sequences, the sequence-quintuple. A decoding rule is given by which any 3D-packing is represented. These coding systems are applied to design heuristic algorithms by simulated annealing which search the codes for better 3D-packings. Experimental results were very convincing its usefulness as automated packing algorithms. key words: 3D-packing, placement, sequence-pair, sequence-