Polygon Packing Asanka Herath Buddhika Kottahachchi
What? <ul><li>Given a set of polygons, determine a layout such that the rectangle enclosing them is minimal, allowing tran...
Why? <ul><li>It has important applications in the apparel industry </li></ul><ul><ul><li>Pieces of material (polygons) nee...
Exploiting Parallel Processing <ul><li>Process multiple candidate layouts simultaneously </li></ul><ul><li>Split resources...
Anyone been here before? <ul><li>Lots of existing literature </li></ul><ul><ul><li>Referred to as </li></ul></ul><ul><ul><...
Related problems <ul><li>Can be categorized as </li></ul><ul><ul><li>Decision Problems </li></ul></ul><ul><ul><ul><li>Deci...
Commercial Implementations
Questions?
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Exploiting Parallel Processing

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Exploiting Parallel Processing

  1. 1. Polygon Packing Asanka Herath Buddhika Kottahachchi
  2. 2. What? <ul><li>Given a set of polygons, determine a layout such that the rectangle enclosing them is minimal, allowing translation and rotation. </li></ul>
  3. 3. Why? <ul><li>It has important applications in the apparel industry </li></ul><ul><ul><li>Pieces of material (polygons) need to be cut out of rolls of material to be assembled together as items of clothing </li></ul></ul><ul><ul><li>Considerable amounts of material is wasted as a result of not having an optimal layout for making the cuts </li></ul></ul><ul><li>NP-hard problem. </li></ul><ul><ul><li>Current approaches use heuristics with varying degrees of efficiency. Room for improvement. </li></ul></ul>
  4. 4. Exploiting Parallel Processing <ul><li>Process multiple candidate layouts simultaneously </li></ul><ul><li>Split resources to work on different approaches (…) </li></ul><ul><ul><li>Fast heuristics to determine initial layouts </li></ul></ul><ul><ul><li>Slower relaxed placement methods to optimize initial layouts </li></ul></ul><ul><li>Share information about current bounds and current optimal solution to reduce search space </li></ul><ul><li>Implementation: C and MPI </li></ul>
  5. 5. Anyone been here before? <ul><li>Lots of existing literature </li></ul><ul><ul><li>Referred to as </li></ul></ul><ul><ul><ul><li>Nesting Problem </li></ul></ul></ul><ul><ul><ul><li>Marker Maker’s Problem </li></ul></ul></ul><ul><ul><li>Many related problems (…) </li></ul></ul><ul><ul><li>Our method would follow work done by Benny Kaejr Nielsen and Allan Odgaard (Copenhagen, Denmark) </li></ul></ul><ul><li>Commercial implementations (…) </li></ul><ul><li>At least one attempt at a parallel library for solving nesting problems </li></ul>
  6. 6. Related problems <ul><li>Can be categorized as </li></ul><ul><ul><li>Decision Problems </li></ul></ul><ul><ul><ul><li>Decide whether a given set of shapes fit within a given shape </li></ul></ul></ul><ul><ul><li>Knapsack Problem </li></ul></ul><ul><ul><ul><li>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. </li></ul></ul></ul><ul><ul><li>Bin packing problem. </li></ul></ul><ul><ul><ul><li>Given a set of shapes and a set of regions, minimize the number of regions needed to place all shapes. </li></ul></ul></ul><ul><ul><li>Strip packing problem. </li></ul></ul><ul><ul><ul><li>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. </li></ul></ul></ul>
  7. 7. Commercial Implementations
  8. 8. Questions?

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