DTS: A Tree Based Representation for 3D-Block Packing

3D packing problem is to arrange rectangular boxes (blocks) of given sizes in a rectangular box of the minimum volume without overlapping each other. As a representation for 3D packings, this paper proposes a novel encoding method, called DTS (double tree and sequence). The feature of the DTS is: (1) It can represent any minimal packings. (2) The size of the solution space (the number of codes) of DTS is much smaller than any conventional representation which can represent any packings. Experimental comparisons with conventional representations indicate the superiority of the proposed representation DTS