A dynamic adaptive local search algorithm for the circular packing problem

Hifi, Mhand; M’Hallah, Rym

doi:10.1016/j.ejor.2005.11.069

Cited by 41 publications

(26 citation statements)

References 14 publications

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“…For each instance, the number n of circles to be packed, the radius r i of each of the n circles, and the best known solution r are reported in Table 4. For instances 1-13, 16, 17, 19, and 20, the best known solution was obtained in [12]. For the first 23 instances, DS, AS, and RS obtained the best known solution r; thus, improving the solution obtained in [12] for instances 14, 15, and 18.…”

Section: Computational Resultsmentioning

confidence: 98%

“…For instances 1-13, 16, 17, 19, and 20, the best known solution was obtained in [12]. For the first 23 instances, DS, AS, and RS obtained the best known solution r; thus, improving the solution obtained in [12] for instances 14, 15, and 18. For each of these 23 instances, the obtained solution is suspected to be optimal.…”

Section: Computational Resultsmentioning

confidence: 98%

“…It successively considers the n − 2 remaining circles. It identifies, for each C i , its set S i of feasible positions, and chooses, among S i , the position that yields the smallest containing circle C. As it packs a given circle, DS 1 dynamically updates both the radius r and the center (x, y) of C, as in [12].…”

Section: Dynamic Searchmentioning

confidence: 99%

“…Mladenovic et al [20] proposed an approximate algorithm that solves iteratively, till converging to a local optimum, two reformulations of the unit circular packing problem: one using the Cartesian coordinates and one using Polar coordinates. Hifi and M'Hallah [12] proposed an algorithm based upon a dynamic adaptive local search procedure. The algorithm iterates through two complementary steps which are dynamically coupled in search for the smallest circle.…”

Section: Related Literaturementioning

confidence: 99%

“…However, as in [8,11,12], initially sorting the circles in a non-increasing order of their radii offers a good initial order. Furthermore, exploring the immediate neighborhood of the non-ascending order of the radii solution yields in most cases a good near optimal solution.…”

Section: The Restarting Searchmentioning

confidence: 99%

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Adaptive and restarting techniques-based algorithms for circular packing problems

Hifi

M’Hallah

2007

Comput Optim Appl

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International audienceIn this paper, we study the circular packing problem (CPP) which consists of packing a set of non-identical circles of known radii into the smallest circle with no overlap of any pair of circles. To solve CPP, we propose a three-phase approximate algorithm. During its first phase, the algorithm successively packs the ordered set of circles. It searches for each circle's "best" position given the positions of the already packed circles where the best position minimizes the radius of the current containing circle. During its second phase, the algorithm tries to reduce the radius of the containing circle by applying (i) an intensified search, based on a reduction search interval, and (ii) a diversified search, based on the application of a number of layout techniques. Finally, during its third phase, the algorithm introduces a restarting procedure that explores the neighborhood of the current solution in search for a better ordering of the circles. The performance of the proposed algorithm is evaluated on several problem instances taken from the literature

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Section: Computational Resultsmentioning

confidence: 98%

Section: Computational Resultsmentioning

confidence: 98%

Section: Dynamic Searchmentioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

Section: The Restarting Searchmentioning

confidence: 99%

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Adaptive and restarting techniques-based algorithms for circular packing problems

Hifi

M’Hallah

2007

Comput Optim Appl

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A Heuristic Based Algorithm for the 2D Circular Strip Packing Problem

Akeb¹,

Hifi

Lazure

2013

Recent Advances in Computational Optimization

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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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A dynamic adaptive local search algorithm for the circular packing problem

Cited by 41 publications

References 14 publications

Adaptive and restarting techniques-based algorithms for circular packing problems

Adaptive and restarting techniques-based algorithms for circular packing problems

A Heuristic Based Algorithm for the 2D Circular Strip Packing Problem

Near optimal minimal convex hulls of disks

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