Monkey Algorithm for Packing Circles with Binary Variables

Torres-Escobar, Rafael; Marmolejo-Saucedo, José Antonio; Litvinchev, Igor; Vasant, Pandian

doi:10.1007/978-3-030-00979-3_58

Cited by 8 publications

(5 citation statements)

References 14 publications

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“…The two-stage scheme presented in Section 2 can be applied for the general optimized multi-spherical covering. An extension of the covering approach to the case of more complex objects [33][34][35][36] is an interesting direction for the future research. Some results on this topic are on the way.…”

Section: Discussionmentioning

confidence: 99%

An Optimized Covering Spheroids by Spheres

et al. 2020

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Covering spheroids (ellipsoids of revolution) by different spheres is studied. The research is motivated by packing non-spherical particles arising in natural sciences, e.g., in powder technologies. The concept of an ε -cover is introduced as an outer multi-spherical approximation of the spheroid with the proximity ε . A fast heuristic algorithm is proposed to construct an optimized ε -cover giving a reasonable balance between the value of the proximity parameter ε and the number of spheres used. Computational results are provided to demonstrate the efficiency of the approach.

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Section: Discussionmentioning

confidence: 99%

An Optimized Covering Spheroids by Spheres

et al. 2020

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“…For example, a cluster layout can be optimized to increase packing density with maximal distance among clusters [1], or the aim could be to minimize the size of the container still containing the cluster collection [9]. Our work is similar to studies that intend to maximize the packed area by embedding as many clusters as possible in the container area [2,3,10]. Litvinchev et al [2] studied this problem with the aim of packing a certain number of circular-like objects such as circles, ellipses, rhombuses, and polygons of known size into a rectangular shape.…”

Section: Introductionmentioning

confidence: 96%

“…A problem of packing objects in the container of a given shape is common in many applications such as computer science, manufacturing, industrial engineering, and production [1]. Various container types are studied, such as rectangular [2,3], circular [4], or polygonal geometrical shapes [5,6]. Also, problems of embedding many different items are investigated, where the inner components can be regular circular-like [7] or irregular objects [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…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. The optimal packing of discs in regular rings of uniform circles with minimal distance is examined in [18].…”

Section: Introductionmentioning

confidence: 99%

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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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“…Authors simplify the packing problem by using a regular grid to model the inner positions of the packed items. This formulation is further adopted by [42,43] and applied for cutting and packing of circles and ellipses. The goal is to pack as many items as possible to increase the efficiency and to decrease area of the container that needs to be produced.…”

Section: Introductionmentioning

confidence: 99%

On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container

Prvan

Ožegović

Mišura

2019

Mathematical Problems in Engineering

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In this paper, a problem of packing hexagonal and dodecagonal sensors in a circular container is considered. We concentrate on the sensor manufacturing application, where sensors need to be produced from a circular wafer with maximal silicon efficiency (SE) and minimal number of sensor cuts. Also, a specific application is considered when produced sensors need to cover the circular area of interest with the largest packing efficiency (PE). Even though packing problems are common in many fields of research, not many authors concentrate on packing polygons of known dimensions into a circular shape to optimize a certain objective. We revisit this problem by using some well-known formulations concerning regular hexagons. We provide mathematical expressions to formulate the difference in efficiency between regular and semiregular tessellations. It is well-known that semiregular tessellation will cause larger silicon waste, but it is important to formulate the ratio between the two, as it affects the sensor production cost. The reason why we have replaced the “perfect” regular tessellation with semiregular one is the need to provide spacings at the sensor vertices for placing mechanical apertures in the design of the new CMS detector. Archimedean {3,122} semiregular tessellation and its more flexible variants with irregular dodecagons can provide these triangular spacings but with larger number of sensor cuts. Hence, we construct an irregular convex hexagon that is semiregularly tessellating the targeted area. It enables the sensor to remain symmetric and hexagonal in shape, even though irregular, and produced with minimal number of cuts with respect to dodecagons. Efficiency remains satisfactory, as we show that, by producing the proposed irregular hexagon sensors from the same wafer as a regular hexagon, we can obtain almost the same SE.

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Monkey Algorithm for Packing Circles with Binary Variables

Cited by 8 publications

References 14 publications

An Optimized Covering Spheroids by Spheres

An Optimized Covering Spheroids by Spheres

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

On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container

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