An Improved Best-First Branch and Bound Algorithm for Unconstrained Two-Dimensional Cutting Problems

무제한 2차원 절단문제에 대해 개선된 최적-우선 분지한계 해법

  • Published : 2005.12.01

Abstract

In this Paper, we develop an improved branch and bound algorithm for the (un)weighted unconstrained two-dimensional cutting problem. In the proposed algorithm, we improve the branching strategies of the existing exact algorithm and reduce the size of problem by removing the dominated pieces from the problem. We apply the newly Proposed definition of dominated cutting pattern and it can reduce the number of nodes that must be searched during the algorithm procedure. The efficiency of the proposed algorithm is presented through comparison with the exact algorithm known as the most efficient.

Keywords

References

  1. Beasley, J.E., 'Algorithms for Unconstrained Two-dimensional Guillotine Cutting,' Journal of the Operational Research Society, Vol.36(1985), pp.297-306 https://doi.org/10.1057/jors.1985.51
  2. Christofides, N. and C. Whitlock, 'An Algorithm for Two-dimensional Cutting Problems,' Operations Research, Vol.26(1977), pp.30-44
  3. Cung, V.D., M. Hifi, and B.L. Cun, 'Constrained Two-dimensional Cutting Stock Problems a Best-first Branch-and-bound Algorithm,' International Transactions in Operational Research, Vol.7(2000), pp.185-210 https://doi.org/10.1111/j.1475-3995.2000.tb00194.x
  4. G, Y.G., Y.J. Seong, and M.K. Kang, 'A Best-first Branch and Bound Algorithm for Unconstrained Two-dimensional Cutting Problems,' Operations Research Letters, Vol.31(2003), pp.301-307 https://doi.org/10.1016/S0167-6377(03)00002-6
  5. Gilmore, P.C. and R.E. Gomory, 'A Linear Programming approach to the Cutting-stock Problem,' Operations Research, Vol.9(1961), pp.849-859 https://doi.org/10.1287/opre.9.6.849
  6. Gilmore, P.C. and R.E. Gomory, 'The Theory and Computation of Knapsack Functions,' Operations Research, Vol.14(1969), pp.1045-1074 https://doi.org/10.1287/opre.14.6.1045
  7. Herz, J.C., 'A Recursive Computational Procedure for Two-dimensional Stock Cutting,' IBM Journal of Research and Development, Vol.16(1972), pp.462-469 https://doi.org/10.1147/rd.165.0462
  8. Hifi, M., 'The DH/KD Algorithm: A Hybrid approach for Unconstrained Two-dimensional Cutting Problems,' European Journal of Operational Research, Vol.97(1997), pp. 41-52 https://doi.org/10.1016/S0377-2217(96)00060-4
  9. Hifi, M. and V. Zissimopoulos, 'A Recursive Exact Algorithm for Weighted Two-dimensional Cutting,' European Journal of Operational Research, Vol.91(1996), pp.553-564 https://doi.org/10.1016/0377-2217(95)00343-6
  10. Morabito, R.N., M.N. Arenales, and V.F. Arcaro, 'An And-or-graph Approach for Two-dimensional Cutting Problems,' European Journal of Operational Research, Vol.58(1992), pp.263-271 https://doi.org/10.1016/0377-2217(92)90212-R
  11. Wang, P.Y., 'Two Algorithms for Constrained Two-dimensional Cutting Stock Problems,' Operations Research, Vol.31 (1983), pp.573-586 https://doi.org/10.1287/opre.31.3.573