Skip to main content
SpringerLink
Log in

Genetic neuro-nester

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

In this paper, the integration of artificial neural networks and genetic algorithms is explored for solving uncured composite stock cutting problem, which is an NP-complete problem. The input patterns can be either rectangular or irregular, and the proposed approach can accommodate any orientation and size restrictions. A genetic algorithm is used to generate sequences of the input patterns to be allocated. The scrap percentage of each allocation is used as an evaluation criterion. The allocation algorithm uses the sliding method integrated with an artificial neural network, based on the adaptive resonance theory (ART1) paradigm, to allocate the patterns according to the sequence generated by the genetic algorithm. The results obtained by this approach give packing densities on the order of 80–95%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adamowicz, M. and Albano, A. (1976) A solution of the rectangular cutting-stock problem. IEEE Transactions on Systems, Man, and Cybernatics, 6(4), 302–310.

    Google Scholar 

  • Adamowicz, M. and Albano, A. (1976) Nesting two-dimensional shapes in rectangular modules. Computer Aided Design, 8, 27–33.

    Google Scholar 

  • Albano, A. (1977) A method to improve two-dimensional layout. Computer Aided Design, 9, 48–52.

    Google Scholar 

  • Albano, A. and Orsini, R. (1980) A heuristic solution of the rectangular cutting stock problem. The Computer Journal, 23(4), 338–343.

    Google Scholar 

  • Albano, A. and Sapuppo, G. (1980) Optimal allocation of two dimensional irregular shapes using heuristic search methods. IEEE Transactions on Systems, Man, and Cybernatics, 10, 242–248.

    Google Scholar 

  • Beasley, J. E. (1985) An algorithm for the two-dimensional assortment problem. European Journal of Operation Research, 19(2), 253–261.

    Google Scholar 

  • Bengtsson, B. E. (1982) Packing rectangular pieces a heuristic approach. The Computer Journal, 25(3), 353–357.

    Google Scholar 

  • Carpenter, G. A. and Grossberg, S. (1987) A massively parallel architecture for a self-organizing neural pattern recognition machine. Computer Vision, Graphics, and Image Processing, 37, 54–115.

    Google Scholar 

  • Christofides, N. and Whitlock, C. (1977) An algorithm for two-dimensional cutting problems. Operations Research, 25(1), 30–44.

    Google Scholar 

  • Chung, J., Scott, D. and Hillman, D. J. (1990) An intelligent nesting system on 2–D highly irregular resources. Proceedings of Application of Artificial Intelligence VIII, pp. 472–483.

  • Dagli, C. H. (1988) Cutting stock problem: combined use of heuristics and optimization methods, in Recent Developments in Production Research, Mital, A. (ed), pp. 500–506.

  • Dagli, C. H. (1988) Integrating AI and OR in solving cutting stock problem, in Robotics and Manufacturing: Recent Trends in Research, Education and Applications, Jamsidi, M., Luh, J. Y. S., Seraji, H. and Starr, G. P. (eds), pp. 911–918.

  • Dagli, C. H. (1990) Neural networks in manufacturing: possible impacts on cutting stock problems. Second International Conference on Computer Integrated Manufacturing, pp. 531–537.

  • Dagli, C. H. (1994) Intelligent manufacturing systems. Artificial Neural Networks for Intelligent Manufacturing. Chapman & Hall, London, pp. 3–16.

    Google Scholar 

  • Dagli, C. H., Ashouri, M. R., Leininger, G. and McMillin, B. (1990) Composite stock cutting pattern classification through neocognitron. International Joint Conference on Neural Networks, 2, pp. II-587–590.

    Google Scholar 

  • Dagli, C. H. and Hajakbari, A. (1990) Simulated annealing approach for solving stock cutting problem. Proceedings of IEEE International Conference on Systems, Man, and Cybernatics, pp. 221–223.

  • Dagli, C. H. and Nisanci, I. H. (1981) A heuristic for cutting-stock problem. Sixth International Conference on Production Research, Vol. 1, pp. 9–16.

    Google Scholar 

  • Dagli, C. H. and Tatoglu, M. Y. (1983) A computer package for solving cutting stock problems. Seventh International Conference on Production Research, Vol. 1, pp. 175–190.

    Google Scholar 

  • Dagli, C. H. and Tatoglu, M. Y. (1987) An approach to two-dimensional cutting stock problems. International Journal of Production Research, 25(2), 175–190.

    Google Scholar 

  • Daniels, J. J. and Ghandforoush P. (1990) An improved algorithm for the non-guillotine cutting-stock problem. Journal of Operational Research Society, 41(2), 141–149.

    Google Scholar 

  • Dietrich, R. D. and Yakowitz, S. J. (1991) A rule-based approach to the trim-loss problem. International Journal of Production Research, 29(2), 401–415.

    Google Scholar 

  • Dowsland, K. A. (1992) Comments on an algorithm for the cutting stock problem. Journal of Operational Research Society, 43(12), 1189–1190.

    Google Scholar 

  • Duta, L. D. and Fabian, C. (1984) Solving cutting-stock problems through the Monte-Carlo method. Economic Computation and Economic Cybernetics Studies and Research, 35–54.

  • Dyckhoff, H. (1989) Approaches to cutting and packing problems. Tenth International Conference on Production Research, August.

  • Eisemann, K. (1957) the trim problem. Management Science, 3(3), 279–284.

    Google Scholar 

  • Farley, A. A. (1988) Mathematical programming models for cutting-stock problems in the clothing industry. Journal of Operational Research Society, 39(1), 41–53.

    Google Scholar 

  • Farley, A. A. (1990) The cutting stock problem in the canvas industry. European Journal of Operational Research, 44, 247–255.

    Google Scholar 

  • Ferreira, J. S., Neves, M. A. and Fonseca e Castro, P. (1990) A two-phase roll cutting problem. European Journal of Operational Research, 44, 185–196.

    Google Scholar 

  • Foronda, S. U. and Carino, H. F. (1991) A heuristic approach to the lumber allocation problem in hardwood dimension and furniture manufacturing. European Journal of Operational Research, 54(2), 151–162.

    Google Scholar 

  • Garey, M. R. and Johnson, D. S. (1979) Computers and Interactability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco.

    Google Scholar 

  • Gemmill, D. D. (1992) Solution to the assortment problem via the genetic algorithm. Mathematical and Computer Modeling, 16(1), 89–94.

    Google Scholar 

  • Gemmill, D. D. and Sanders, J. L. (1991) A comparison of solution methods for the assortment problem. International Journal of Production Research, 29(2), 2521–2527.

    Google Scholar 

  • George, J. A. (1992) A correction of the improved bounds for the non-guillotine constrained cutting stock problem. Journal of Operational Research Society, 43(12), 1187–1189.

    Google Scholar 

  • Ghandforoush, P. and Daniels, J. J. (1992) A heuristic algorithm for the guillotine constrained cutting stock problem. ORSA Journal on Computing, 4(3), 351–356.

    Google Scholar 

  • Gilmore, P. C. and Gomory, R. E. (1961) A linear programming approach to the cutting stock problem. Operations Research, 9(6), 849–859.

    Google Scholar 

  • Gilmore, P. C. and Gomory, R. E. (1965) Multistage cutting stock problems of two and more dimensions. Operations Research, 13(1), 94–120.

    Google Scholar 

  • Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization & Machine Learning, Addison Wesley, MA.

    Google Scholar 

  • Golden, B. L. (1976) Approaches to cutting stock problem. AIIE Transactions, 8(2), 256–274.

    Google Scholar 

  • Goulimis, C. (1990) Optimal solutions for the cutting stock problem. European Journal of Operational Research, 44, 197–208.

    Google Scholar 

  • Haessler, R. W. (1980) Multimachine roll trim: problem and solutions. TAPPI, 63(1), 71–74.

    Google Scholar 

  • Haessler, R. W. and Sweeney, P. E. (1991) Cutting stock problems and solution procedures. European Journal of Operational Research, 54, 141–150.

    Google Scholar 

  • Hahn, S. G. (1986) On the optimum cutting of defective sheets. Operations Research, 16(6), 1100–1114.

    Google Scholar 

  • Haims, M. J. and Freeman, H. (1970) A multistage solution of the template-layout problem. IEEE Transactions on Systems Science and Cybernetics, 6(2), 145–151.

    Google Scholar 

  • Harris, R. and Zinober, A. (1988) Practical microcomputer solutions of the cutting stock problem. IEEE Colloquium on Artificial Intelligence in Planning for Production Control, 8(1–4).

  • Hinxman, A. I. (1973) Two-dimensional trim-loss problem with sequencing constraints. International Joint Conference on Artificial Intelligence, pp. 859–864.

  • Hinxman, A. I. (1980) The trim loss and assortment problems: a survey. European Journal of Operational Research, 5, 8–18.

    Google Scholar 

  • Kampke, T. (1988) Simulated annealing: use of a new tool in bin packing. Annals of Operations Research, 16, 327–332.

    Google Scholar 

  • Kantorovich, L. V. (1960) Mathematical methods of organising and planning production. Management Science, 6, 366–422.

    Google Scholar 

  • Kirkpatrick, S., Gellatt, C. D. Jr. and Vecchi, M. P. (1982) Optimization by simulated annealing. IBM Research Report, RC 9355.

  • Lirov, Y. (1992) Knowledge based approach to the cutting stock problem. Mathematical and Computer Modeling, 16(1), 107–125.

    Google Scholar 

  • Lutfiyya, H., McMillin, B., Poshyanonda, P. and Dagli, C. (1992) Composite stock cutting through simulated annealing. Mathematical and Computer Modeling, 16(1), 57–74.

    Google Scholar 

  • Metzger, R. (1958) Stock slitting. Elementary Mathematical Programming, Wiley, New York.

    Google Scholar 

  • Oliveira, J. F. and Ferreira, J. S. (1990) An improved version of Wang's algorithm for two-dimensional cutting problems. European Journal of Operational Research, 44, 256–266.

    Google Scholar 

  • Oliver, I. M., Smith, D. J. and Holland J. R. C. (1987) A study of permutation crossover operators on the traveling salesman problem. Proceeding of the Second International Conference on Genetic Algorithms, pp. 224–230.

  • Paull, A. E. (1956) Linear programming: a key to optimum newsprint production. Pulp Paper Mag. Can., 57, 145–150.

    Google Scholar 

  • Pierce, J. F. (1966) On the solution of integer cutting stock problems by combinatorial programming, Part I. IBM Technical Report, 36.Y02, Cambridge Scientific Center, Cambridge, MA.

    Google Scholar 

  • Poshyanonda, P., Bahrami, A. and Dagli, C. (1992) Two dimensional nesting problem: artificial neural network and optimization approach. International Joint Conference of Neural Networks, pp. IV-572–IV-577.

  • Poshyanonda, P., Bahrami, A. and Dagli, C. (1992) Artificial neural networks in stock cutting problem. Neural Networks in Manufacturing and Robotics, ASME Press, New York, p. 143.

    Google Scholar 

  • Poshyanonda, P. and Dagli, C. (1992) A hybrid approach to composite stock cutting: artificial neural networks and genetic algorithms, in Robotics and Manufacturing: Recent Trends in Research Education and Applications, Vol. 4, Jamshidi, M., Lumia, R., Mulling, J. and Shahinpoor, M. (eds), ASME Press, New York, p. 775.

    Google Scholar 

  • Qu, W. and Sanders, J. L. (1989) Sequence selection of stock sheets in two-dimensional layout problems. International Journal of Production Research, 27(9), 1553–1571.

    Google Scholar 

  • Richter, K. (1992) Solving sequential interval cutting problems via dynamic programming. European Journal of Operational Research, 57, 332–338.

    Google Scholar 

  • Schollmeyer, M. and Lin, J. Q. et al. (1991) Hybrid expert system and operations research for solving nesting problems. The World Congress on Expert Systems Proceedings, Vol. 2, pp. 1223–1231.

    Google Scholar 

  • Vajda, S. (1958) Trim loss reduction. Readings in Linear Programming, Wiley, New York.

    Google Scholar 

  • Viswanathan, K. V. and Bagchi, A. (1993) Best-first search methods for constrainted two-dimensional cutting stock problems. Operations Research, 41(4), 768–776.

    Google Scholar 

  • Viswanathan, K. V. and Bagchi, A. (1988) An exact best-first search procedure for the constrainted rectangular Guillotine Knapsack problem. 7th National Conference on Artificial Intelligence, pp. 145–149.

  • Wang, P. Y. (1983) Two algorithms for constrained two-dimensional cutting stock problems. Operations Research, 31(3), 573–586.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Smart Engineering Systems Laboratory, Engineering Management Department, University of Missouri-Rolla, Rolla, MO, 65401, USA

    Pipatpong Poshyanonda & Cihan H. Dagli

Authors
  1. Pipatpong Poshyanonda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cihan H. Dagli
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Poshyanonda, P., Dagli, C.H. Genetic neuro-nester. Journal of Intelligent Manufacturing 15, 201–218 (2004). https://doi.org/10.1023/B:JIMS.0000018033.05556.65

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JIMS.0000018033.05556.65

Search

Navigation