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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Vydané v:	Computers & operations research Ročník 50; s. 97 - 114
Hlavní autori:	Russo, Mauro, Sforza, Antonio, Sterle, Claudio
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier Ltd 01.10.2014 Elsevier Pergamon Press Inc
Predmet:	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
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Abstract	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.
AbstractList	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. 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.
Author	Russo, Mauro Sforza, Antonio Sterle, Claudio
Author_xml	– sequence: 1 givenname: Mauro surname: Russo fullname: Russo, Mauro email: m.russo@uniplan.it organization: Uniplan Software S.r.l., Via Manzoni 21, 84018 Scafati, Salerno, Italy – sequence: 2 givenname: Antonio surname: Sforza fullname: Sforza, Antonio email: sforza@unina.it organization: Department of Electrical Engineering and Information Technology, University “Federico II” of Naples, Via Claudio 21, 80125 Naples, Italy – sequence: 3 givenname: Claudio surname: Sterle fullname: Sterle, Claudio email: claudio.sterle@unina.it organization: Department of Electrical Engineering and Information Technology, University “Federico II” of Naples, Via Claudio 21, 80125 Naples, Italy
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Keywords	Knapsack function Guillotine cutting Dynamic programming Refinement method Cutting stock problem Redundancy Large scale Combinatorial optimization Knapsack problem
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SubjectTerms	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
Title	An exact dynamic programming algorithm for large-scale unconstrained two-dimensional guillotine cutting problems
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