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2D/3D Packing based on LFF (Less Flexibility First) principle

2D/3D Packing based on LFF (Less Flexibility First) principle. Problem. packing a list of (2D) rectangles or (3D) boxes of various sizes which can be rotated and placed by any orientation into one container to maximize the volume utilization of the container

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2D/3D Packing based on LFF (Less Flexibility First) principle

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  1. 2D/3D Packing based on LFF (Less Flexibility First) principle

  2. Problem • packing a list of (2D) rectangles or (3D) boxes of various sizes which can be rotated and placed by any orientation into one container to maximize the volume utilization of the container • (Our 2D LFF packing produces today’s highest density results)

  3. 2D Packing

  4. side hollow corner 3D Packing Flexibility • Flexibility of empty space Pf • Flexibility of a box to be packed Rf corner：x； side：y； hollow：z Rif = ….

  5. Structure k-d tree • 2D 4-d tree • 3D 6-d tree (x1, y1, z1)(x2, y2, z2) B(x2,y2,z2) A(x1,y1,z1)

  6. --> • CCPS (Candidate Corner Packing Step) • Greedy • An simple Example

  7. Test result • LFF is better than LL in most cases especially when the boxes are complex (more kinds, great contrast), but not very effective when large number and few kinds of boxes

  8. improvement • Heuristic 1 • Considering the weight of boxes • Bottom First strategy Flexibility of box: Rif = {r1 * (1 –Bi/ Pa ) + r2 * ( 1– max( li, wi , hi )/ min( L,W, H )) + r3 * ( 1 – Qi/Qt )} Qi - weight of box i，Qt– weight of all boxes; r1 + r2 + r3 = 1 Heuristic 1 Original

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