ICSI 2013: Advances in Swarm Intelligence pp 168-175 | Cite as
An Approach Based on Evaluation Particle Swarm Optimization Algorithm for 2D Irregular Cutting Stock Problem
Conference paper
Abstract
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.
Keywords
Cutting Stock Problem EPSO Grid ApproximationPreview
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References
- 1.Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)MATHCrossRefGoogle Scholar
- 2.Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)MATHGoogle Scholar
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 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)MATHCrossRefGoogle Scholar
- 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)MATHCrossRefGoogle Scholar
- 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.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)MATHCrossRefGoogle Scholar
- 10.Bennell, J.A., Oliveira, J.F.: The geometry of nesting problems: A tutorial. Eur. J. Oper. Res. 184, 397–415 (2008)MathSciNetMATHCrossRefGoogle Scholar
- 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)MATHCrossRefGoogle Scholar
- 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.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)MathSciNetMATHCrossRefGoogle Scholar
- 14.Jakobs, S.: On genetic algorithms for the packing of polygons. European Journal of Operational Research 88(1), 165–181 (1996)MATHCrossRefGoogle Scholar
- 15.Poshyanonda, P., Dagli, C.H.: Genetic neuro-nester. Journal of Intelligent Manufacturing 15(2), 201–218 (2004)CrossRefGoogle Scholar
- 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)MATHCrossRefGoogle Scholar
- 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.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)MATHCrossRefGoogle Scholar
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 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.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
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