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Polygon Packing

Asanka Herath Buddhika Kottahachchi. Polygon Packing. What?. Given a set of polygons, determine a layout such that the rectangle enclosing them is minimal, allowing translation and rotation. Why?. It has important applications in the apparel industry

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Polygon Packing

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  1. Asanka HerathBuddhika Kottahachchi Polygon Packing

  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?

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