Polygon%20Packing - PowerPoint PPT Presentation

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Polygon%20Packing

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Title: Polygon%20Packing


1
Polygon Packing
  • Asanka HerathBuddhika Kottahachchi

2
What?
  • Given a set of polygons, determine a layout such
    that the rectangle enclosing them is minimal,
    allowing translation and rotation.

3
Why?
  • It has important applications in the apparel
    industry
  • Pieces of material (polygons) need to be cut out
    of rolls of material to be assembled together as
    items of clothing
  • Considerable amounts of material is wasted as a
    result of not having an optimal layout for making
    the cuts
  • NP-hard problem.
  • Current approaches use heuristics with varying
    degrees of efficiency. Room for improvement.

4
Exploiting Parallel Processing
  • Process multiple candidate layouts simultaneously
  • Split resources to work on different approaches
    ()
  • Fast heuristics to determine initial layouts
  • Slower relaxed placement methods to optimize
    initial layouts
  • Share information about current bounds and
    current optimal solution to reduce search space
  • Implementation C and MPI

5
Anyone been here before?
  • Lots of existing literature
  • Referred to as
  • Nesting Problem
  • Marker Makers Problem
  • Many related problems ()
  • Our method would follow work done by Benny Kaejr
    Nielsen and Allan Odgaard (Copenhagen, Denmark)
  • Commercial implementations ()
  • At least one attempt at a parallel library for
    solving nesting problems

6
Related problems
  • Can be categorized as
  • Decision Problems
  • Decide whether a given set of shapes fit within a
    given shape
  • Knapsack Problem
  • Given a set of shapes and a region, find a
    placement of a subset of shapes that maximizes
    the utilization (area covered) of the region.
  • Bin packing problem.
  • Given a set of shapes and a set of regions,
    minimize the number of regions needed to place
    all shapes.
  • Strip packing problem.
  • Given a set of shapes and a width W, minimize the
    length of a rectangular region with width W such
    that all shapes are contained in the region.

7
Commercial Implementations
8
Questions?
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