An Approach Based on Evaluation Particle Swarm Optimization Algorithm for 2D Irregular Cutting Stock Problem

  • Yan-xin Xu
  • Gen-Ke Yang
  • Chang-chun Pan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7928)


Cutting stock problem is an important problem that arises in a variety of industrial applications. An irregular-shaped nesting approach for two-dimensional cutting stock problem is constructed and Evolution Particle Swarm Optimization Algorithm (EPSO) is utilized to search optimal solution in this research. Furthermore, the proposed approach combines a grid approximation method with Bottom-Left-Fill heuristic to allocate irregular items. We evaluate the proposed approach using 15 revised benchmark problems available from the EURO Special Interest Group on Cutting and Packing. The performance illustrates the effectiveness and efficiency of our approach in solving irregular cutting stock problems.


Cutting Stock Problem EPSO Grid Approximation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)zbMATHCrossRefGoogle Scholar
  2. 2.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  3. 3.
    Oliveira, J.F., Gomes, A.M., Ferreira, J.S.: TOPOS – a new constructive algorithm for nesting problems. OR Spektrum 22(2), 263–284 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Burke, E.K., Hellier, R.S.R., Kendall, G., Whitwell, G.: A new bottom-left-fill heuristic algorithm for the two-dimensional irregular packing problem. Operations Research 54(3), 587–601 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Gonçalves, J.: A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem. European Journal of Operational Research 183(3), 1212–1229 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: A tabu search algorithm for two-dimensional non-guillotine cutting problems. European Journal of Operational Research 183(3), 1167–1182 (2007)zbMATHCrossRefGoogle Scholar
  7. 7.
    Burke, E.K., Kendall, G., Whitwell, G.: A simulated annealing enhancement of the best-fit heuristic for the orthogonal stock-cutting problem. INFORMS Journal on Computing 21(3), 505–516 (2009)zbMATHCrossRefGoogle Scholar
  8. 8.
    Liu, D.S., Tan, K.C., Goh, C.K., Ho, W.K.: On solving multi-objective bin packing problems using particle swarm optimization. In: IEEE Congress on Evolutionary Computation, Vancouver, pp. 7448–7455 (2006)Google Scholar
  9. 9.
    Gomes, A.M., Oliveira, J.F.: Solving irregular strip packing problems by hybridizing simulated annealing and linear programming. European Journal of Operational Research 171(3), 811–829 (2006)zbMATHCrossRefGoogle Scholar
  10. 10.
    Bennell, J.A., Oliveira, J.F.: The geometry of nesting problems: A tutorial. Eur. J. Oper. Res. 184, 397–415 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Burke, E.K., Hellier, R.S.R., Kendall, G., Whitwell, G.: Complete and robust no-fit polygon generation for the irregular stock cutting problem. Eur. J. Oper. Res. 179(1), 27–49 (2007)zbMATHCrossRefGoogle Scholar
  12. 12.
    Burke, E.K., Hellier, R.S.R., Kendall, G., Whitwell, G.: Irregular Packing Using the Line and Arc No-Fit Polygon. Oper. Res. 58(4), 1–23 (2010)CrossRefGoogle Scholar
  13. 13.
    Bennell, J., Scheithauer, G., Stoyan, Y., Romanova, T.: Tools of mathematical modelling of arbitrary object packing problems. Annals of Operations Research 179, 343–368 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Jakobs, S.: On genetic algorithms for the packing of polygons. European Journal of Operational Research 88(1), 165–181 (1996)zbMATHCrossRefGoogle Scholar
  15. 15.
    Poshyanonda, P., Dagli, C.H.: Genetic neuro-nester. Journal of Intelligent Manufacturing 15(2), 201–218 (2004)CrossRefGoogle Scholar
  16. 16.
    Hopper, E., Turton, B.C.H.: An empirical investigation on meta-heuristic and heuristic algorithms for a 2d packing problem. European Journal of Operational Research 128, 34–57 (2001)zbMATHCrossRefGoogle Scholar
  17. 17.
    Dagli, C.H., Hajakbari, A.: Simulated annealing approach for solving stock cutting problem. In: Proceedings of IEEE International Conference on Systems, Man, and Cybernatics, pp. 221–223 (1990)Google Scholar
  18. 18.
    Wong, W.X., Guo, Z.X.: A hybrid approach for packing irregular patterns using evolutionary strategies and neural network. International Journal of Production Research 48(20), 6061–6084 (2010)zbMATHCrossRefGoogle Scholar
  19. 19.
    Liu, D., Tan, K., Huang, S., Goh, C., Ho, W.: On solving multi-objective bin packing problems using evolutionary particle swarm optimization. European Journal of Operational Research 190, 357–382 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Srinivasan, D., Seow, T.H.: Particle swarm inspired evolutionary algorithm (PS-EA) for multi-objective optimization problems. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 2292–2297 (2003)Google Scholar
  21. 21.
    Del Valle, A., De Queiroz, T., Miyazawa, F., Xavier, E.: Heuristics for twodimensional knapsack and cutting stock problems with items of irregular shape. Expert Systems with Applications 39(16), 12589–12598 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yan-xin Xu
    • 1
    • 2
  • Gen-Ke Yang
    • 1
    • 2
  • Chang-chun Pan
    • 1
    • 2
  1. 1.Department of AutomationShanghai JiaoTong UniversityChina
  2. 2.Key Laboratory of System Control and Information ProcessingMinistry of Education of ChinaShanghaiChina

Personalised recommendations