Exploiting Parallel Processing
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Exploiting Parallel Processing

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Exploiting Parallel Processing Presentation Transcript

  • 1. Polygon Packing Asanka Herath Buddhika 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 Maker’s 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?