A constructive bin-oriented heuristic for the two-dimensional bin packing problem with guillotine cuts

Charalambous, Christoforos; Fleszar, Krzysztof

doi:10.1016/j.cor.2010.12.013

Cited by 29 publications

(26 citation statements)

References 11 publications

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“…We consider two rotations for the insertion of each piece (0 o and 90 o ) and therefore we are solving the 2DBP|R|G problem in the typology presented in Dyckhoff (1990). Table 6 compares the total number of bins used by the constructive algorithm CA1 with fast heuristic algorithms: the Knapsack-Problem-based heuristics of Lodi et al (1999) (KP), the Guillotine Bottom-Left heuristic of Polyakovsky and MHallah (2009) (GBL) and the Constructive Heuristic of Charalambous and Fleszar (2011) …”

Section: Comparison With the State Of The Art Algorithms In Rectangulmentioning

confidence: 99%

“…Algorithm CA1 − 2Ph produces better results than any other constructive algorithm. However, the state of the art procedure on rectangular bin packing problems with guillotine cuts is the CHBP algorithm proposed by Charalambous and Fleszar (2011), in which their constructive algorithm (CH) is followed by a post-optimization phase. CHBP requires only 7064 bins.…”

Section: (Ch)mentioning

confidence: 99%

“…The approach uses threshold parameters to control the number of blocks generated and as a result the computational time. The second constructive heuristic, a two-stage algorithm, combines pairs of pieces into rectangles by using the phi-functions presented by Bennell et al (2011), and then uses the guillotine bin packing algorithm developed by Charalambous and Fleszar (2011) to pack the rectangles. The combination of the pieces into rectangles using phi-functions requires significant computational effort, up to eighteen hours in the largest instance (149 pieces), although the packing algorithm by Charalambous and Fleszar (2011) takes less than one second.…”

Section: Introductionmentioning

confidence: 99%

“…The second constructive heuristic, a two-stage algorithm, combines pairs of pieces into rectangles by using the phi-functions presented by Bennell et al (2011), and then uses the guillotine bin packing algorithm developed by Charalambous and Fleszar (2011) to pack the rectangles. The combination of the pieces into rectangles using phi-functions requires significant computational effort, up to eighteen hours in the largest instance (149 pieces), although the packing algorithm by Charalambous and Fleszar (2011) takes less than one second. Most recently, Fleszar (2013) developed an heuristic algorithm based on the insertions of the pieces one at a time obtaining slightly worse results but the computational time is much shorter.…”

Section: Introductionmentioning

confidence: 99%

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

Martínez-Sykora

Álvarez-Valdés

Bennell

et al. 2015

Omega

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This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focused on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraints.

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Section: Comparison With the State Of The Art Algorithms In Rectangulmentioning

confidence: 99%

Section: (Ch)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Martínez-Sykora

Álvarez-Valdés

Bennell

et al. 2015

Omega

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“…The forest constructs multiple layouts in parallel according to dynamic measures of the quality of the partial layout. In order to benchmark our approach we implement a state of the art rectangle guillotine cutting algorithm of Charalambous and Fleszar (2011) and generate solutions by approximating each piece by its minimum enclosing rectangle. Further, we attempt to improve on practice in the two stage approach by using phi-functions to cluster all pairs of pieces in their minimum rectangle enclosure and use a greedy heuristic to select a subset to pack, again using the approach of Charalambous and Fleszar (2011).…”

Section: Introductionmentioning

confidence: 99%

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

Han

Bennell

Zhao

et al. 2013

European Journal of Operational Research

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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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A Scalable Approach for the K-Staged Two-Dimensional Cutting Stock Problem

Dusberger

Raidl

2017

Operations Research Proceedings

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A constructive bin-oriented heuristic for the two-dimensional bin packing problem with guillotine cuts

Cited by 29 publications

References 11 publications

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

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

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

A Scalable Approach for the K-Staged Two-Dimensional Cutting Stock Problem

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