A Tree Based Novel Representation for 3D-Block Packing

The 3D packing problem consists of arranging nonoverlapping rectangular boxes (blocks) of given sizes in a rectangular box of minimum volume. As a representation of 3D packings, this paper proposes a novel encoding method called Double Tree and Sequence (DTS). The following are features of DTS: 1) It can represent any minimal packing. 2) It can be decoded into the corresponding 3D packing in O(n ²) time, where n is the number of rectangular boxes. 3) The size of the solution space (the number of codes) of DTS is significantly smaller than any conventional representation that can represent any packing. Experimental comparisons with conventional representations indicate the superiority of the proposed representation DTS.