Approximate and exact algorithms for the double-constrained two-dimensional guillotine cutting stock problem
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In this paper, we propose approximate and exact algorithms for the double constrained two-dimensional guillotine cutting stock problem (DCTDC). The approximate algorithm is a two-stage procedure. The first stage attempts to produce a starting feasible solution to DCTDC by solving a single constrained two dimensional cutting problem, CDTC. If the solution to CTDC is not feasible to DCTDC, the second stage is used to eliminate non-feasibility. The exact algorithm is a branch-and-bound that uses efficient lower and upper bounding schemes. It starts with a lower bound reached by the approximate two-stage algorithm. At each internal node of the branching tree, a tailored upper bound is obtained by solving (relaxed) knapsack problems. To speed up the branch and bound, we implement, in addition to ordered data structures of lists, symmetry, duplicate, and non-feasibility detection strategies which fathom some unnecessary branches. We evaluate the performance of the algorithm on different problem instances which can become benchmark problems for the cutting and packing literature.
KeywordsCombinatorial optimization Cutting problems Dynamic programming Single constrained knapsack problem
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- 4.Blazewicz, J., Moret-Salvador, A., Walkowiak, R.: Parallel tabu search approaches for two-dimensional cutting. Parallel Process. Lett. 14, 23–32 Google Scholar
- 5.Bortfeldt, A.: A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces. Eur. J. Oper. Res. (2005), available online Google Scholar
- 11.Cung, V.-D., Hifi, M.: Handling lower bound constraints in two-dimensional cutting problems. In: ISMP 2000, The 17th Symposium on Mathematical Programming, Atlanta, 7–11 August 2000 Google Scholar
- 13.Cung, V.-D., Hifi, M., Le Cun, B.: Constrained two-dimensional cutting stock problems: the NMVB approach and the duplicate test revisited. Working Paper, Série Bleue No 2000.127 (CERMSEM), Maison des Sciences Economiques, Université Paris 1 (2000) Google Scholar
- 30.Mumford-Valenzuela, C.L., Vick, J., Wang, P.Y.: Heuristics for large strip packing problems with guillotine patterns: An empirical study. In: Metaheuristics: Computer Decision-Making, pp. 501–522. Kluwer Academic, Dordrecht (2003) Google Scholar