A new constraint programming approach for the orthogonal packing problem

Clautiaux, François; Jouglet, Antoine; Carlier, Jacques; Moukrim, Aziz

doi:10.1016/j.cor.2006.05.012

Cited by 76 publications

(92 citation statements)

References 14 publications

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“…In the logic based Benders' decomposition, the classical master problem is frequently solved as a MILP and the slave through constraint programming (although other solution techniques can be used). Constraint programming techniques were used by Clautiaux et al [68] to solve the recognition version of the SPP.…”

Section: Chapter 5 Logic Based Benders' Decomposition For Orthogonalmentioning

confidence: 99%

Mathematical models and decomposition algorithms for cutting and packing problems

Delorme¹

2017

4OR-Q J Oper Res

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Section: Chapter 5 Logic Based Benders' Decomposition For Orthogonalmentioning

confidence: 99%

Mathematical models and decomposition algorithms for cutting and packing problems

Delorme¹

2017

4OR-Q J Oper Res

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“…The first column contains instance names; in each name, the first number is the percentage of waste and the second is the number of items n. Further columns report the results of various algorithms. At first we report two exact algorithms for OPP: the schedule-or-postpone exact algorithm for 2D OPP [CJCM08] 5 and the graph-theoretical exact algorithm from [FSvdV07] (data taken from [CJCM08]), executed on a Pentium M 1.8 GHz. For the schedule-or-postpone algorithm, 'fails' is the number of backtracks and 'chpts' is the number of choice points (position fixings).…”

Section: D Opp Instances Of Clautiaux Et Almentioning

confidence: 99%

“…At first we considered the 27 infeasible OPP instances from [CJCM08]. (In their paper, only 26 infeasible instances are cited, but the complete set has 15 feasible and 27 infeasible instances).…”

Section: D Opp Instances Of Clautiaux Et Almentioning

confidence: 99%

“…While in [CJCM08] this was done exactly using integer factorization (which has the interesting effect that the items are more often larger in width than in height), we computed the sizes as real numbers and always rounded them down. Due to the relatively large integer container sizes (the containers are cubes with sizes W 1 = W 2 = W 3 = 1000), the deviation from the nominal waste percentage e was small (below 0.5%).…”

Section: Generation Of Instancesmentioning

confidence: 99%

“…To generate test instances, we applied an idea from [BKRS09] which is similar to that used for the 2D OPP instances from [CJCM08]: given the percentage e of container volume which should be waste, distribute the remaining volume among the items. While in [CJCM08] this was done exactly using integer factorization (which has the interesting effect that the items are more often larger in width than in height), we computed the sizes as real numbers and always rounded them down.…”

Section: Generation Of Instancesmentioning

confidence: 99%

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Conservative scales in packing problems

et al. 2011

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Packing problems (sometimes also called cutting problems) are combinatorial optimization problems concerned with placement of objects (items) in one or several containers. Some packing problems are special cases of several other problems such as resource-constrained scheduling, capacitated vehicle routing, etc. In this paper we consider a bounding technique for one-and higher-dimensional orthogonal packing problems, called conservative scales (CS) (in the scheduling terminology, redundant resources). CS are related to the possible structure of resource consumption: filling of a bin, distribution of the resource to the jobs, etc. In terms of packing, CS are modified item sizes such that the set of feasible packings is not reduced. In fact, every CS represents a valid inequality for a certain binary knapsack polyhedron.CS correspond to dual variables of the set-partitioning model of a special 1D cutting-stock problem. Some CS can be constructed by (data-dependent) dualfeasible functions ((D)DFFs). We discuss the relation of CS to DFFs: CS assume that at most 1 copy of each object can appear in a combination, whereas DFFs allow several copies. The literature has investigated so-called extremal maximal DFFs (EMDFFs) which should provide very strong CS. Analogously, we introduce the notions of maximal CS (MCS) and extremal maximal CS (EMCS) and show that EMDFFs do not necessarily produce (E)MCS. We propose fast greedy methods to "maximize" a given CS. Using the fact that EMCS define facets of the binary knapsack polyhedron, we use lifted cover inequalities as EMCS. For higherdimensional orthogonal packing, we propose a Sequential LP (SLP) method over the set of CS and investigate its convergence. Numerical results are presented.

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Packing by Scheduling: Using Constraint Programming to Solve a Complex 2D Cutting Stock Problem

Luo

Beck

2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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A new constraint programming approach for the orthogonal packing problem

Cited by 76 publications

References 14 publications

Mathematical models and decomposition algorithms for cutting and packing problems

Mathematical models and decomposition algorithms for cutting and packing problems

Conservative scales in packing problems

Packing by Scheduling: Using Constraint Programming to Solve a Complex 2D Cutting Stock Problem

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