MPQ-trees for the Orthogonal Packing Problem

Joncour, Cédric; Pêcher, Arnaud; Valicov, Petru

doi:10.1007/s10852-011-9159-z

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…Table 2 summarizes the results. We reported the characteristics of the problems, and the computation times of different approaches, that can be found in the literature: Fekete et al in [9] (FS), Clautiaux et al in [4] (Cl07), Clautiaux et al in [5] (Cl08 er for the version with energetic reasoning and Cl08 ss for the version using the solutions of subset-sum problems, and no preprocessing methods or lower bounds evaluation at the root node in both versions), Grandcolas and Pinto in [10] (GP) (a SAT encoding of Fekete and Schepers characterization that uses an external SAT solver), Joncour et al in [14] (JP) (an approach based on the characterization of Fekete et al using MPQ-trees), and the results of the approach that we described in this paper (SMP 1 ). Times are in seconds.…”

Section: Resultsmentioning

confidence: 99%

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

Grandcolas¹,

Pinto²

2015

J Math Model Algor

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Section: Resultsmentioning

confidence: 99%

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

Grandcolas¹,

Pinto²

2015

J Math Model Algor

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“…The link between guillotine cuts and interval graphs was analyzed by Perboli (2002). Recently, Joncour et al (2010) introduced an efficient algorithm to manage the interval-graph structure by means of MPQ-trees, combinatorial structures introduced in Korte & Möhring (1989).…”

Section: Fig 1 Shelf Packings In 2d and 3dmentioning

confidence: 99%

Recent Advances in Multi-dimensional Packing Problems

Crainic¹,

Perboli²,

Tadei³

2012

New Technologies - Trends, Innovations and Research

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The chapter is organized as follows. We address packing issues in Section 2, introducing the main mathematical models and the rules to define where to place an item into a bin (usually already holding some items), and discussing efficiency, effectiveness, and implementation aspects. Section 3 is dedicated to Multi-Dimensional Packing problems. We describe bounds, exact methods, and meta-heuristics, discussing their effectiveness compared to their computational effort. A more general discussion of the flexibility, simplicity of implementation, and public availability of the codes of these methods is the topic of Section 4. 2. Multi-Dimensional Packing: models and packing rules One of the main issues in addressing Multi-Dimensional Packing problems is defining the position where to place items inside the bin (

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“…Clautiaux et al (2007Clautiaux et al ( , 2008 developed an improved reduction procedure and an exact method based on a new constraintbased scheduling model, respectively. Some other new approaches, such as the improved heuristic recursive strategy by Zhang et al (2007), the quasi-physical strategy by Huang and Kang (2002), a greedy randomized adaptive search procedure by Alvarez-Valdes et al (2005), the general-purpose hill-climbing method by Lewis (2009), a polynomial-time DNA-computing solution by Alonso Sanches and Soma (2009) and MPQ-trees by Joncour et al (2010), have been developed to cope with the packing problem. A branch-cut-and-price algorithm has been exploited for a 2-D two-stage cutting by Belov and Scheithauer (2006).…”

Section: Introductionmentioning

confidence: 99%

Hybrid algorithm for the two-dimensional rectangular layer-packing problem

Chen

Zhai

Zhu

et al. 2014

Journal of the Operational Research Society

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In this paper, a rectangular layer-packing algorithm (RLPA) combined with modified genetic algorithm (GA) or particle swarm optimization (PSO) algorithm is developed to solve the problem with emerging restraints, which is raised from the two-dimensional rectangular packing problem with some small rectangles that need to be packed into a fixed rectangular object. RLPA is designed from the BL algorithm and lowest horizontal line algorithm. GA and PSO are also modified to satisfy the constraint conditions. Best GA or PSO parameters are obtained by conducting experiments on some typical instances. The results are also compared, which validate the quality of the solutions and show the effectiveness of the modified algorithm.

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MPQ-trees for the Orthogonal Packing Problem

Cited by 3 publications

References 14 publications

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

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

Recent Advances in Multi-dimensional Packing Problems

Hybrid algorithm for the two-dimensional rectangular layer-packing problem

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