A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

Cui, Yaodong; Yang, Ye; Cheng, Xian Fu; Song, Ping

doi:10.1016/j.cor.2006.08.011

Cited by 48 publications

(19 citation statements)

References 19 publications

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“…SPTRS is compared to the parallel genetic algorithms by Kröger (1993Kröger ( , 1995 and Schnecke (1996), respectively. Further competing methods are the genetic algorithm SPGAL by Bortfeldt (2006) and the B&B method HRBB by Cui et al (2008). SPGAL has been tested on a Pentium PC with 2 GHz while HRBB results were achieved on a PC with 2.8 GHz.…”

Section: Results On 2d Test Instancesmentioning

confidence: 99%

“…Table 7 shows the results for instance set SP-HT, series C. For each test case (of three instances) the number of items per instance is given in brackets (column 1). SPTRS is compared to the recursive procedure HR and the simulated annealing method SA+HR by Zhang et al (2005Zhang et al ( , 2006, respectively, the genetic algorithm SPGAL by Bortfeldt (2006) and to Cui et al (2008). HR has been tested on a Dell GX260 PC with 2.4 GHz while HR+SA was run on a DELL GX270 with 3.0 GHz CPU.…”

Section: Results On 2d Test Instancesmentioning

confidence: 99%

“…Most of the algorithms apply metaheuristic search strategies like genetic algorithms or simulated annealing. At the moment, the solution methods proposed by Alvarez-Valdes et al (2008), Belov et al (2008) and Burke et al (2009) belong to the most powerful approaches for the 2D-SPP without guillotine cutting constraint (OF, RF) while the genetic algorithm by Bortfeldt (2006) and the branch and bound method by Cui et al (2008) achieved the best results so far for the guillotine cutting subtypes OG and RG. It is noticeable that three of these five algorithms are based on widely used metaheuristic strategies (cf.…”

Section: Literature Reviewmentioning

confidence: 96%

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A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint

Bortfeldt

Jungmann

2012

Ann Oper Res

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The article presents a tree search algorithm (TRSA) for the strip packing problem in two and three dimensions with guillotine cutting constraint. In the 3D-SPP a set of rectangular items (boxes) and a container with fixed width and height but variable length are given. An arrangement of all boxes within the container has to be determined so that the required length is minimised. The 2D-SPP is analogously defined. The proposed TRSA is based on a tree search algorithm for the container loading problem by Fanslau and Bortfeldt (INFORMS J. Comput. 22:222-235, 2010). The TRSA generates guillotine packing patterns throughout. In a comparison with all recently proposed 3D-SPP methods the TRSA performs very competitive. Fine results are also achieved for the 2D-SPP.

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Section: Results On 2d Test Instancesmentioning

confidence: 99%

Section: Results On 2d Test Instancesmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 96%

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A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint

Bortfeldt

Jungmann

2012

Ann Oper Res

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“…The exact approaches reported in Cui (2008), Lesh et al (2004) and Martello et al (2003) are based on the branch-and-bound techniques. In Kenmochi et al (2009), a branch and bound based exact algorithm also was proposed, where branching is based on two placement schemes and bounding operations are based on dynamic and linear programming.…”

Section: Introductionmentioning

confidence: 99%

A heuristic algorithm for the strip packing problem

2012

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The two-dimensional strip packing problem is to pack a given set of rectangles into a strip with a given width and infinite height so as to minimize the required height of the packing. From the computational point of view, the strip packing problem is an NP-hard problem. With the B*-tree representation, this paper first presents a heuristic packing strategy which evaluates the positions used by the rectangles. Then an effective local search method is introduced to improve the results and a heuristic algorithm (HA) is further developed to find a desirable solution. Computational results on randomly generated instances and popular test instances show that the proposed method is efficient for the strip packing problem.

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“…Their algorithm is fast and outperforms other known metaheuristics, especially for larger test problems. Cui et al (2008) also used a recursive heuristic algorithm for the guillotineable strip packing problem and combined it with branch and bound. Martello et al (2003) recently considered the nonguillotineable strip packing problem using an exact approach.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Branch-and-Bound Approach to the Rectangular Guillotine Strip Cutting Problem

Bąk

Błażewicz

Pawlak

et al. 2011

INFORMS Journal on Computing

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T his paper presents a parallel branch-and-bound method to address the two-dimensional rectangular guillotine strip cutting problem. Our paper focuses on a parallel branching schema. We present a series of computational experiments to evaluate the strength of the approach. Optimal solutions have been found for some benchmark instances that had unknown solutions until now. For many other instances, we demonstrate that the proposed approach is time effective. The efficiency of the parallel version of the algorithm is compared and the speedup, when increasing the number of processors, is clearly demonstrated with an upper bound calculated by a specialised heuristic procedure.

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A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

Cited by 48 publications

References 19 publications

A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint

A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint

A heuristic algorithm for the strip packing problem

A Parallel Branch-and-Bound Approach to the Rectangular Guillotine Strip Cutting Problem

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