Using pattern matching for tiling and packing problems

Amintoosi, Mahmood; Yazdi, Hadi Sadoghi; Fathy, Mahmood; Monsefi, Reza

doi:10.1016/j.ejor.2006.02.029

Cited by 7 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The tests were conducted via three data sets, provide final patterns with only few gaps. As to the polyominoes tiling problems, the published approaches are mainly either neuro-based (Manabe and Asai, 2001;Takefuji and Lee, 1990) or sequence-based approaches (Amintoosi et al, 2007;Gwee and Lim, 1996). Comparisons performed by Babu and Babu (2001) on a single data set reveal the effectiveness of their proposed algorithm over that of Jain and Gea (1998).…”

Section: Literature Reviewmentioning

confidence: 99%

“…Takefuji and Lee (1990) tested their algorithm on a 7 × 7 sheet involving 10 polyominoes and while adjusting the algorithm parameters, optimal solutions were reached in all cases. In Amintoosi et al (2007), six data sets were tested; the larger one consists of a 15 × 21 sheet and 10 polyominoes. On the average, an optimal solution is obtained in 57% of the algorithm runs.…”

Section: Literature Reviewmentioning

confidence: 99%

“…However, the six benchmark data sets addressed in Amintoosi et al (2007) would be adequate, since they are the most recent known to us. However, the six benchmark data sets addressed in Amintoosi et al (2007) would be adequate, since they are the most recent known to us.…”

Section: Polyominoes Tilingmentioning

confidence: 99%

See 2 more Smart Citations

A mixed-integer model for two-dimensional polyominoes strip packing and tiling problems

Kashkoush

Shalaby

Abdelhafiez

2012

IJOR

View full text Add to dashboard Cite

Two-dimensional irregular strip packing problem is one of the common cutting and packing problems, where it is required to assign (cut or pack) a set of 2D irregular-shaped items to a rectangular sheet. The sheet width is fixed, while its length is extendable and has to be minimised. In this paper, a new mixed-integer programming (MIP) model is introduced to optimally solve a special case of the problem, where item shapes are polygons with orthogonal edges, named polyominoes. Polyominoes strip packing may be classified as polyominoes tiling; a problem that can also be handled by the proposed model. Reasonable problem sizes (e.g. 45 polyominoes inside a 10 × 25 sheet) are solvable using an ordinary PC. Larger problem sizes are expected to be solvable when using state-of-the-art computational facilities. The model is also verified via a set of benchmark problems that are collected from the literature and provided optimal solution for all cases.Reference to this paper should be made as follows: Kashkoush, M.N., Shalaby, M.A. and Abdelhafiez, E.A. (2012) 'A mixed-integer model for two-dimensional polyominoes strip packing and tiling problems', Int. . He has over ten years of academic and consultation experience in design and improvements of production systems and has special interest in textile industry. His main research interests are quality improvement, modelling and optimisation, and performance measurement and analysis.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

A mixed-integer model for two-dimensional polyominoes strip packing and tiling problems

Kashkoush

Shalaby

Abdelhafiez

2012

IJOR

View full text Add to dashboard Cite

show abstract

“…represented by a regular language. Amintoosi et al (2007) used pattern matching to deal with the problem based on the frontiers (edges) of the items.…”

Section: Quasi-polyomino Tiling and Strip Packing Problemsmentioning

confidence: 99%

“…Chapter 4. Integer programming models for the quasi-polyomino strip packing problem Asai, Nakayama and Ninomiya (1996) 11 11 10 Asai2 Asai, Nakayama and Ninomiya (1996) 12 12 10 Asai3 Asai, Nakayama and Ninomiya (1996) 12 12 11 Asai4 Asai, Nakayama and Ninomiya (1996) 14 14 13 Amintoosi Amintoosi et al (2007) 10 10 21 Manabe1…”

mentioning

confidence: 99%

Irregular and quasi-polyomino strip packing problems

Rodrigues¹

View full text Add to dashboard Cite

The irregular strip packing problem consists in the cutting of a set of two-dimensional pieces from an object of fixed width using the minimum possible length. Despite its economic importance for many industries, because of its resolution difficulty few exact methods have addressed this problem. Recently, a mixed integer programming model in which pieces are placed on a grid has been proposed. Although the model has proved the optimality for some large instances, it has a large number of non-overlap constraints, which grows quickly according to the discretization resolution and number of distinct pieces. This thesis proposes a clique covering model to reduce the number of constraints and improve the linear relaxation. The coverings were obtained by a heuristic developed by the author. The model has outperformed the previous model in most evaluated instances and obtained an optimal solution for instances with up to 25 pieces (22 distinct pieces) subject to grid discretization. Recently, another mixed integer programming model was proposed for the problem, but it may allow a large number of symmetric solutions. In this thesis, new symmetry breaking constraints are proposed to improve the model. Computational experiments were performed for instances with convex pieces. The results show the proposed formulation is better than the previous one for most instances, since it improves lower bounds and reduces run-time and number of nodes explored to prove optimality. A particular case of an irregular item is a polyomino. A polyomino is a set of unit squares connected by joining one of their edges. A quasi-polyomino is a polyomino generalization, since it is a subset of not necessarily connected squares obtained from an equidistant raster grid. Quasi-polyomino cutting and packing problems have many real applications, e.g., leather cutting, sheet metal stamping, design of printed circuit boards and layout of magazines and newspapers. In this thesis, we study the quasi-polyomino strip packing problem. We propose two integer programming models for the problem and evaluate them using state-of-the-art solvers. We evaluate the models using instances taken from the literature and both models obtained good results, solving to optimality an instance with 320 items (20 distinct items) on a strip of dimensions 44x50. As expected, we found more optimal solutions when there are no rotation and flips and when the dimensions of the items are small.

show abstract