An efficient heuristic algorithm for arbitrary shaped rectilinear block packing problem

Chen, Duanbing; Liu, Jingfa; Fu, Yan; Shang, Mingsheng

doi:10.1016/j.cor.2009.09.011

Cited by 15 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For each instance, the width W of the container was set to W = ⌈ √ ∑ n j=1 A(R j ) ⌉ , where A(R j ) denotes the area of item R j . For more details of this width setting, readers could refer to Chen et al (2010). We tested our exact algorithms SSSR in Section 3.4 and EAPSR in Section 4.7 on these six instances and compared their results.…”

Section: Computational Resultsmentioning

confidence: 99%

Exact algorithms for the rectilinear block packing problem

Matsushita

Hu²,

Hashimoto

et al. 2018

JAMDSM

View full text Add to dashboard Cite

The rectilinear block packing problem is a problem of packing a set of rectilinear blocks into a larger rectangular container with fixed width and unrestricted height. A rectilinear block is a polygonal block whose interior angles are either 90 • or 270 •. The objective is to pack all the blocks into the container so as to minimize the height of the container. This problem is among classical combinatorial optimization problems and is known to be NP-hard. In this paper, we propose two exact algorithms for the rectilinear block packing problem: one is based on two IP problems and the other is based on a new solution representation. The basic idea of our algorithms is that we iteratively compute lower and upper bounds on the optimal value until the lower bound on the value of an optimal solution for the current search space becomes larger than or equal to the best upper bound found during the search by then, or the search space becomes empty, which means that an optimal solution of this problem has been found. The computational results show that both algorithms obtain five exact and one heuristic solutions for six instances. The algorithm based on a new solution representation improves the running time of the algorithm based on two IP problems.

show abstract

Section: Computational Resultsmentioning

confidence: 99%

Exact algorithms for the rectilinear block packing problem

Matsushita

Hu²,

Hashimoto

et al. 2018

JAMDSM

View full text Add to dashboard Cite

show abstract

“…12,9,11,8,10,6,8,13,6,7,8,11,10,13,12,12,7,6,14,11,7,8,10,10,11,12,11,11,8,12,8,10,8,11,12,13,7,7,9} …”

Section: Step5 Produce the New Solutions VI For The Onlookers From Tmentioning

confidence: 99%

“…But most published research [8][9] mainly focused on the packing problem without additional behavioral constraints (for instance, equilibrium, inertia, stability, etc.). In this paper, we study the circular packing problem with equilibrium constraints, which requires the packing system satisfying with constraints of the static non-equilibrium, in addition to the requirement of non-overlapping and high space utility as the general circular packing problem [10].…”

Section: Introductionmentioning

confidence: 99%

Swarm Intelligence Algorithms for Circles Packing Problem with Equilibrium Constraints

Wang

Huang

Zhu

2013

2013 12th International Symposium on Distributed Computing and Applications to Business, Engineering &Amp; Science

View full text Add to dashboard Cite

Circles packing problem with equilibrium constraints is difficult to solve due to its NP-hard nature. Aiming at this NP-hard problem, three swarm intelligence algorithms are employed to solve this problem. Particle Swarm Optimization and Ant Colony Optimization has been used for the circular packing problem with equilibrium constraints. In this paper, Artificial Bee Colony Algorithm (ABC) for equilibrium constraints circular packing problem is presented. Then we compare the performances of well-known swarm intelligence algorithms (PSO, ACO, ABC) for this problem. The results of experiment show that ABC is comparatively satisfying because of its stability and applicability.

show abstract

“…Common applications are found in sheet metal, leather, furniture, shipbuilding and textile industries. Furthermore, the problem can be classified according to its dimensionality as either 1D (Poldi and Arenales, 2009), 2D (Chen et al, 2010) or 3D (Egeblad et al, 2007). Based on items' geometry, the problem may also be classified as regular or irregular.…”

Section: Literature Reviewmentioning

confidence: 99%

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

An efficient heuristic algorithm for arbitrary shaped rectilinear block packing problem

Cited by 15 publications

References 23 publications

Exact algorithms for the rectilinear block packing problem

Exact algorithms for the rectilinear block packing problem

Swarm Intelligence Algorithms for Circles Packing Problem with Equilibrium Constraints

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

Contact Info

Product

Resources

About