Polygon%20Packing

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Polygon Packing

• Asanka HerathBuddhika Kottahachchi

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What?

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

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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.

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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

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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

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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.

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Commercial Implementations
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Questions?