Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints

Abstract

The paper examines a new problem in the irregular packing
literature that has existed in industry for decades;
two-dimensional irregular (convex) bin packing with guillotine
constraints. Due to the cutting process of certain materials, cuts
are restricted to extend from one edge of the stock-sheet to
another, called guillotine cutting. This constraint is common
place in glass cutting and is an important constraints in
two-dimensional cutting and packing problems. In the literature,
various exact and approximate algorithms exist for finding the two
dimensional cutting patterns that satisfy the guillotine cutting
constraint. However, to the best of our knowledge, all of the
algorithms are designed for solving rectangular cutting where cuts
are orthogonal with the edges of the stock-sheet. In order to
satisfy the guillotine cutting constraint using these approaches,
when the pieces are non-rectangular, practitioners implement a two
stage approach. First, pieces are enclosed within rectangle shapes
and then the rectangles are packed. Clearly, imposing this
condition is likely to lead to additional waste. This
paper aims to generate guillotine-cutting layouts of irregular
shapes using a number of strategies. The investigation compares
two two-stage approaches; one approximates pieces by rectangles,
the other approximates pairs of pieces by rectangles using
phi-functions for optimal clustering. Both these approaches use
state of the art rectangle bin packing with guillotine
constraints. Further, we design and implement a one-stage approach
using a self-adapted forest search algorithm. Experimental results
show the one-stage strategy to produce good solutions in less time
over the two-stage approach.

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