A New Search Procedure for the Two-dimensional Orthogonal Packing Problem

Grandcolas, Stéphane; Pinto, Cedric

doi:10.1007/s10852-015-9278-z

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…Each time a satisfying placement P x is dicovered, another branch-and-bound procedure determines if P x can be extended to a complete solution. More recently Grandcolas et al [15] proposed improvements to the method that result in search space reductions. However, the instances that can be solved in an acceptable time are of limited size.…”

Section: Searching Horizontal and Vertical Placementsmentioning

confidence: 99%

“…5, the profile is delimited by a green line), and S is the set of items which have still to be packed. If S is not empty, the function explores recursively all the possibilities for the (leftmost) lowest horizontal segment s of the profile π, either putting an item on s (lines 8-11), or removing the area delimited by s (lines [13][14][15]. The items of S which are candidates are those whose interval in P x is contained in [l s , r s ], where l s and r s are the positions of the extremities of s on the x-axis, and which have a support at s height (line 6, function getCandidates).…”

Section: Searching For P Ymentioning

confidence: 99%

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A hybrid metaheuristic for the two-dimensional strip packing problem

Grandcolas

Pain-Barre

2021

Ann Oper Res

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In this paper we present a hybrid metaheuristic approach called PVS for the two-dimensional strip packing problem (2SPP). PVS (progress and verify strategy) relies on two procedures: a local search algorithm that delivers satisfying placements of the items on the horizontal axis, and an exact procedure that searches for the positions of the items on the vertical axis. This last one explores all the possibilities, starting with the most promising ones, and can be stopped at any moment. PVS follows a specific anytime strategy which continuously improves the current solution until it is provably optimal or a given time limit is reached. Experimental results show that the method is competitive on moderate-sized instances compared to the best known approaches.

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Section: Searching Horizontal and Vertical Placementsmentioning

confidence: 99%

Section: Searching For P Ymentioning

confidence: 99%

A hybrid metaheuristic for the two-dimensional strip packing problem

Grandcolas

Pain-Barre

2021

Ann Oper Res

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“…Due to the type of representation used by Genetic Algorithms, the operators are forced to repair infeasible solutions that emerge during evolutionary process, altering Darwinian evolution principles [23]. Finally, different algorithms have been proposed for different SPP variants by several authors [24]- [30].…”

Section: Introductionmentioning

confidence: 99%

Un algoritmo genético eficiente para el strip-packing problem

Gatica¹,

Villagrán²,

Contreras‐Bolton³

et al. 2015

I&U

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<p>Given a set of rectangular pieces and a fixed width with infinite length, the strip-packing problem (SPP) of two dimensions (2D), with a rotation of pieces in 90° consists of orthogonally placing all the pieces on the strip, without overlapping them, minimizing the height of the strip used. Several algorithms have been proposed to solve this problem, being Genetic Algorithms one of the most popular approach due to it effectiveness solving NP-Hard problems. In this paper, three binary representations, and classic crossover and mutation operators are introduced. A comparison of the three binary representations on a subset of benchmarking instances is performed. The representation R2 outperforms the results obtained by representation R1 and R3. Indeed, some of the best-known results found by previous published approaches are improved. </p>

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