Developing a simulated annealing algorithm for the cutting stock problem

Lai, Kin Keung; Chan, Jimmy W. M.

doi:10.1016/s0360-8352(96)00205-7

Cited by 131 publications

(59 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Once again, the initial solution supplied is that of the input rectangles sorted by decreasing height and the best solution seen during the search is returned at the end. Simulated annealing techniques have also been applied to the orthogonal stock-cutting problem in Lai and Chan (1996).…”

Section: The Simulated Annealing Bottom-left-fillmentioning

confidence: 99%

A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem

Burke

Kendall

Whitwell

2009

INFORMS Journal on Computing

105

View full text Add to dashboard Cite

T he best-fit heuristic is a simple yet powerful one-pass approach for the two-dimensional rectangular stockcutting problem. It had achieved the best published results on a wide range of benchmark problems until the development of the approaches described in this paper. Here, we illustrate how improvements in solution quality can be achieved by the hybridisation of the best-fit heuristic together with simulated annealing and the bottom-left-fill algorithm. We compare and contrast the new hybrid approach with other approaches from the literature in terms of execution times and the quality of the solutions achieved. Using a range of standard benchmark problems from the literature, we demonstrate how the new approach achieves significantly better results than previously published methods on almost all of the problem instances. In addition, we provide results on 10 new benchmark problems to encourage further research and greater comparison between current and future methods.

show abstract

Section: The Simulated Annealing Bottom-left-fillmentioning

confidence: 99%

A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem

Burke

Kendall

Whitwell

2009

INFORMS Journal on Computing

105

View full text Add to dashboard Cite

show abstract

“…Finally, we have included the test problems used by Leung et al [17], consisting of 3 instances from Lai and Chan [14], 5 from Jakobs [13], and 2 from Leung et al [17]. There are unweighted problems in which the value of each piece corresponds to its area, and the objective is to minimize the waste of the stock rectangle.…”

Section: Test Problemsmentioning

confidence: 99%

“…Wu et al [24] develop a constructive algorithm for the special case where P i = Q i ∀i, in which at each step a piece is cut in a corner of the current cutting pattern, and the piece to be cut is decided according to a fitness evaluation function which estimates the quality of the solution that would be obtained if the piece were to be cut. Lai and Chan [14], [15], and Leung el al. [16], [17] propose simulated annealing and genetic algorithms in which each solution is given by an ordered list of pieces, and the list is translated into a cutting pattern by a placement algorithm, either the bottom-left algorithm or the difference algorithm [14].…”

Section: Introductionmentioning

confidence: 99%

“…Lai and Chan [14], [15], and Leung el al. [16], [17] propose simulated annealing and genetic algorithms in which each solution is given by an ordered list of pieces, and the list is translated into a cutting pattern by a placement algorithm, either the bottom-left algorithm or the difference algorithm [14]. Combinations and changes of solutions are made on the ordered lists.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems

Álvarez-Valdés

Parreño

Tamarit

2005

Journal of the Operational Research Society

View full text Add to dashboard Cite

This paper presents a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional non-guillotine cutting problem, the problem of cutting the rectangular pieces from a large rectangle so as to maximize the value of the pieces cut. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well known instances previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures.

show abstract

“…For instance the following may be mentioned: genetic and evolutionary algorithms (Jakobs 1996;Hadjiconstantinou and Iori 2007;Lai and Chan 1997a;Leung et al 2001;Beasley 2004;Burke et al 2004;Gonçalves 2007;Gonçalves and Resende 2011), a simulated annealing algorithm (Dowsland 1993;Lai and Chan 1997b;Leung et al 2001Leung et al , 2003Leung et al , 2012Burke et al 2004), and a Tabu search algorithm (AlvarezValdes et al 2007;Wei et al 2011). A comparison of the efficiency of heuristic and metaheuristic algorithms can be found in Hopper and Turton (2001).…”

Section: Introductionmentioning

confidence: 99%

A hybrid evolutionary algorithm for the two-dimensional packing problem

Kierkosz

Łuczak

2013

Cent Eur J Oper Res

View full text Add to dashboard Cite

This paper presents a hybrid evolutionary algorithm for the two-dimensional non-guillotine packing problem. The problem consists of packing many rectangular pieces into a single rectangular sheet in order to maximize the total area of the pieces packed. Moreover, there is a constraint on the maximum number of times that a piece may be used in a packing pattern. The set of packing patterns is processed by an evolutionary algorithm. Three mutation operators and two types of quality functions are used in the algorithm. The best solution obtained by the evolutionary algorithm is used as the initial solution in a tree search improvement procedure. This approach is tested on a set of benchmark problems taken from the literature and compared with the results published by other authors.

show abstract

Developing a simulated annealing algorithm for the cutting stock problem

Cited by 131 publications

References 15 publications

A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem

A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem

A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems

A hybrid evolutionary algorithm for the two-dimensional packing problem

Contact Info

Product

Resources

About