A formulation space search heuristic for packing unequal circles in a fixed size circular container

López, Claudia O.; Beasley, John E.

doi:10.1016/j.ejor.2015.10.062

Cited by 28 publications

(28 citation statements)

References 37 publications

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“…). Similar to [23,24,26] the value of the radius was increased linearly with respect to the number of the circle. The following expression was used: As we can see from these tables, larger values of the mipgap correspond to "roundish" objects (circles and octagons) while for "angular" objects (squares and rhombuses) the mipgap is much smaller.…”

Section: Computational Resultsmentioning

confidence: 99%

Packing a limited number of unequal circular objects in a rectangular container

Litvinchev¹,

Mosquera²

2017

Proceedings of the First EAI International Conference on Computer Science and Engineering

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A problem of packing a limited number of unequal circular objects in a fixed size rectangular container is considered. The circular object is considered in a general sense, as a set of points that are all the same distance (not necessary Euclidean) from a center. The aim is to maximize the (weighted) number of objects placed into the container or minimize the waste. This problem has numerous applications in logistics, including production and packing for the textile, apparel, naval, automobile, aerospace and food industries. Frequently the problem is formulated as a nonconvex continuous optimization problem which is solved by heuristic techniques combined with local search procedures. We study a linear integer programming formulation based on approximating container by a regular grid. The nodes of the grid are considered as potential positions for assigning centers of the objects thus giving rise to a large scale linear 0-1 optimization problem with binary variables representing the assignment of centers to the nodes of the grid. Recursive packing allowing nesting circles inside one another is also considered. Numerical results are presented to demonstrate the efficiency of the proposed approach.

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Section: Computational Resultsmentioning

confidence: 99%

Packing a limited number of unequal circular objects in a rectangular container

Litvinchev¹,

Mosquera²

2017

Proceedings of the First EAI International Conference on Computer Science and Engineering

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“…First, the VOROPACK-D algorithm packs circular disks in a container of circular or rectangular shape [35]. There were many studies on packing and cutting problems with mathematical programming and/or heuristic methods [6,8,11,27,34,37,41]. This study uses VOROPACK-D which can quickly find sufficiently good solutions for big problem instances.…”

Section: Contributionsmentioning

confidence: 99%

Near optimal minimal convex hulls of disks

et al. 2021

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The minimal convex hulls of disks problem is to find such arrangements of circular disks in the plane that minimize the length of the convex hull boundary. The mixed-integer non-linear programming model, named [17], works only for small to moderate-sized problems. Here we propose a polylithic framework of the problem for big problem instances by combining the following algorithms and models: (i) A fast disk-packing algorithm based on Voronoi diagrams, non-linear programming (NLP) models for packing disks, and an NLP model for minimizing the discretized perimeter of convex hull; (ii) A fast convex-hull algorithm to compute the convex hulls of disk arrangements and their perimeter lengths; (iii) A mixed-integer NLP model taking the output of as its input. We present complete analytic solutions for small problems up to four disks and a semi-analytic mixed-integer linear programming model which yields exact solutions for strip packing problems with up to one thousand congruent disks. It turns out that the proposed polylithic approach works fine for large problem instances containing up to 1,000 disks. Monolithic and polylithic solutions using usually outperform other approaches. The polylithic approach yields better solutions than the results in [17] and provides a benchmark suite for further research.

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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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A formulation space search heuristic for packing unequal circles in a fixed size circular container

Cited by 28 publications

References 37 publications

Packing a limited number of unequal circular objects in a rectangular container

Packing a limited number of unequal circular objects in a rectangular container

Near optimal minimal convex hulls of disks

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

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