An exact dynamic programming algorithm for large-scale unconstrained two-dimensional guillotine cutting problems

In the unconstrained two-dimensional cutting problems (U2DCP) small rectangular objects have to be extracted from a large rectangular sheet, with no limits on the number of small objects. The exact U2DCP solving approaches present in literature show some limits in tackling very large size instances,...

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Bibliographic Details
Published in:Computers & operations research Vol. 50; pp. 97 - 114
Main Authors: Russo, Mauro, Sforza, Antonio, Sterle, Claudio
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.10.2014
Elsevier
Pergamon Press Inc
Subjects:
Algorithms
Applied sciences
Computation
Cutting
Dynamic programming
Exact sciences and technology
Flows in networks. Combinatorial problems
Guillotine cutting
Knapsack function
Knapsack problem
Mathematical analysis
Mathematical models
Mathematical problems
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Proof theory
Studies
Two dimensional
Knapsack function
Guillotine cutting
Dynamic programming
Refinement method
Cutting stock problem
Redundancy
Large scale
Combinatorial optimization
Knapsack problem
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:In the unconstrained two-dimensional cutting problems (U2DCP) small rectangular objects have to be extracted from a large rectangular sheet, with no limits on the number of small objects. The exact U2DCP solving approaches present in literature show some limits in tackling very large size instances, due to the high memory requirements. In this work we propose five improvements, three original and two derived from the literature, in order to overcome these limits and to reduce the computational burden of the knapsack function based U2DCP solving approaches. These improvements, based on proofed theoretical results, allow to reduce the search space and to avoid redundant solutions without loss of the feasible ones. The presented improvements, together with several computational refinements, are integrated in a new dynamic programming algorithm, which modifies the one by Russo et al. (2013 [16]). The proposed algorithm has been experienced on test instances present in literature and compared with the best U2DCP solving approaches. The obtained results show that it significantly outperforms them and it determines the optimal solution of unsolved very large size instances.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2014.04.001