Polygon Packing Asanka Herath Buddhika Kottahachchi

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

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 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.

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.

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

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

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

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

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.

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.

Commercial Implementations

Questions?