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.

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

“…The best two algorithms using the one-step approach are given by the following combinations: 1S-0.94-5, with θ = 0.94 and K = 5 and 1S-0.97-3, with θ = 0.97 and K = 3. The two-step algorithm (2S) also proposed by Han et al (2012) is in general inferior to the one-step algorithms, with the exception of one instance (see J70 in Table 5) where the two-step algorithm found a better solution with fewer bins than all the one-step algorithms. Table 5 shows the computational results obtained by the two-step algorithm 2S and the one-step algorithms 1S-0.94-5 and 1S-0.97-3.…”

“…Algorithm CA1−2Ph−imp produces the best known results for five of the eight instances (the best known solution of instance J70, H80 and h149 is given by CA1 − 2Ph in Table 4). The behavior of algorithm CA1 is also interesting because on average it works better than the algorithms proposed by Han et al (2012), and it is faster than CA1-2Ph-imp requiring a similar computational time than 1S-0.97-3 on average. In fact, we can see that CA1 reduces the number of bins used in 1S-0.94-5 and 1S-0.97-3 in 4 instances.…”

“…Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that may or may not be orthogonal to the edges of the stock sheet, and allocating pieces to bins or stock sheets. To our knowledge, Han et al (2012) is the only other paper that tackles this problem. They propose two different construction heuristics.…”

“…We test the performance of the alternative variants using the test data presented by Han et al (2012). They consider eight instances, four provided by a company in glass cutting for conservatories and another four generated using properties of the industrial data.…”

A Universal CAD System for Cutting Stock Problem

“…Most of these problems are geometry-dependent (e.g., facility layout, vehicle routing, packing, or cutting stock problems) [4][5][6][7][8][9]. Solving them calls for a colourful variability of geometry representation, search methods (i.e., algorithms), and objectives selection.…”