Packing unequal rectangles and squares in a fixed size circular container using formulation space search

López, Claudia O.; Beasley, John E.

doi:10.1016/j.cor.2018.02.012

Cited by 16 publications

(17 citation statements)

References 49 publications

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“…In the last two decades, many intensive studies were proposed and presented for both one-dimensional and two-dimensional BPP by [26][27][28][29]30]. Traditional evolutionary algorithms have been applied for the BPP such as ant colony optimization with a local search routine of [31][32], and a genetic algorithm by [33].…”

Section: Bppmentioning

confidence: 99%

Applying the big bang-big crunch metaheuristic to large-sized operational problems

Qawqzeh

Jaradat

Al-Yousef

et al. 2020

IJECE

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In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.

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Section: Bppmentioning

confidence: 99%

Applying the big bang-big crunch metaheuristic to large-sized operational problems

Qawqzeh

Jaradat

Al-Yousef

et al. 2020

IJECE

View full text Add to dashboard Cite

show abstract

“…Cassioli et al [21] proposed a heuristic method based on an iterative local search for the problem of packing the maximum number of identical rectangles within a convex region. An FSS algorithm was proposed by Beasley et al [22] to solve the packing problem of rectangle in circular container. Scheithauer et al [23] solved the problem of guillotine cutting rectangle from rectangular and defective boards with dynamic programming.…”

Section: Rectangle Packing Of Irregular Platesmentioning

confidence: 99%

“…SPGAL [19] is based on genetic algorithm; HRBB [10] algorithm is a heuristic recursive algorithm; Jin et al [24] proposed a heuristic algorithm to solve the packing problem of rectangular plates with defects. In addition, the FSS [22] algorithm and the method proposed by Birgin et al [20] are exact algorithms. As can be seen from the above table, SPGAL and HRBB are two algorithms for solving the packing problem of non-defective rectangular plates with different constraints (OF, RG).…”

Section: Comparative Analysismentioning

confidence: 99%

Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

et al. 2020

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Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL) heuristic proposed in this paper to obtain feasible solutions, and then applies the genetic algorithm to optimize the quality of solutions further. The HL heuristic is constructed on the basis of computational geometry and level packing. This heuristic aims to divide the irregular plate into multiple subplates horizontally, calculates the movable positions of the rectangle in the subplates, determines whether or not the rectangle can be packed in the movable positions through computational geometry, and fills the scraps appropriately. Theoretical analysis confirms that the rectangles obtained through the HL heuristic are inside the plate and do not overlap with the defects. In addition, the packed rectangles do not overlap each other and satisfy the guillotine constraint. Accordingly, the packing problem can be solved. Experiments on irregular slates with defects show that the slate utilization through our method is between 89% and 95%. This result is better than manual packing and can satisfy actual production requirements.

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“…Toledo et al [15] showed that using a square grid in the packing problem can simplify even the non-trivial handling of the geometry required in case of irregular objects. However, we are interested only in regular packing, which involves standard shapes of objects and containers, unlike the ones where the distance of objects to the container centroid is not Euclidean [16,17]. In the work of Torres-Escobar et al [3], the grid is discretized with a set of points in which circular objects can be assigned such that there are no overlaps and to maximize the space occupied.…”

Section: Introductionmentioning

confidence: 99%

A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container

et al. 2020

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This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, we concentrate on mathematical modeling in such an application, where using the “bee” tetrahex is chosen for the new Compact Muon Solenoid (CMS) design upgrade, which is one of four detectors used in Large Hadron Collider (LHC) experiment at European Laboratory for Particle Physics (CERN). We start from the existing hexagonal containers with hexagonal cells packed inside, and uniform clustering applied. We compare the center-aligned (CA) and vertex-aligned (VA) models, analyzing cluster rotations providing the increased packing efficiency. We formally describe the geometrical properties of clustering approaches and show that cluster sharing is inevitable at the container border with uniform clustering. In addition, we propose a new vertex-aligned model decreasing the number of shared clusters in the uniform scenario, but with a smaller number of clusters contained inside the container. Also, we describe a non-uniform tetrahex cluster packing scheme in the proposed container model. With the proposed cluster packing solution, it is accomplished that all clusters are contained inside the container region. Since cluster-sharing is completely avoided at the container border, the maximal packing efficiency is obtained compared to the existing models.

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Packing unequal rectangles and squares in a fixed size circular container using formulation space search

Cited by 16 publications

References 49 publications

Applying the big bang-big crunch metaheuristic to large-sized operational problems

Applying the big bang-big crunch metaheuristic to large-sized operational problems

Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container

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