Abstract
This article presents a method based on the multi-objective evolutionary algorithm NSGA-II to approximate hyper-heuristics for solving irregular 2D cutting stock problems under multiple objectives. In this case, additionally to the traditional objective of minimizing the number of sheets used to fit a finite number of irregular pieces, the time required to perform the placement task is also minimized, leading to a bi-objective minimization problem with a tradeoff between the number of sheets and the time required for placing all pieces. We solve this problem using multi-objective hyper-heuristics (MOHHs), whose main idea consists of finding a set of simple heuristics which can be combined to find a general solution for a wide range of problems, where a single heuristic is applied depending on the current condition of the problem, instead of applying a unique single heuristic during the whole placement process. The MOHHs are approximated after going through a learning process by mean of the NSGA-II, which evolves combinations of condition-action rules producing at the end a set of Pareto-optimal MOHHs. We tested the approximated MMOHHs on several sets of benchmark problems, having outstanding results for most of the cases.
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References
Burke, E., Hart, E., Kendall, G., Newall, J., Ross, P., Schulenburg, S.: Hyper-heuristics: An emerging direction in modern research technolology. In: Handbook of Metaheuristics, pp. 457–474. Kluwer Academic Publishers, Dordrecht (2003)
Cheng, C.H., Fiering, B.R., Chang, T.C.: The cutting stock problem. A survey. International Journal of Production Economics 36(3), 291–305 (1994)
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, Dordrecht (2002)
Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of Parallel Problem Solving From Nature VI Conference, pp. 849–858 (2000)
Dyckhoff, H.: A topology of cutting and packing problems. European Journal of Operational Research 44(2), 145–159 (1990)
Fujita, K., Akagji, S., Kirokawa, N.: Hybrid approach for optimal nesting using a genetic algorithm and a local minimisation algorithm. In: Proceedings of the Annual ASME Design Automation Conference 1993, Part 1 (of 2), pp. 477–484 (1993)
Geiger, M.J.: Bin packing under multiple objectives - a heuristic approximation approach. In: International Conference on Evolutionary Multi-Criterion Optimization 2008, pp. 53–56 (2008)
Golden, B.L.: Approaches to the cutting stock problem. AIIE Transactions 8(2), 256–274 (1976)
Hopper, E., Turton, B.C.: An empirical study of meta-heuristics applied to 2D rectangular bin packing. Studia Informatica Universalis 2(1), 77–106 (2001)
Kantorovich, L.V.: Mathematical methods of organizing and planning production. Management Science 6(4), 366–422 (1960)
Lodi, A., Martella, S., Monaci, M.: Two-dimensional packing problems: A survey. European Journal of Operational Research 141(2), 241–252 (2002)
Muñoz, C., Sierra, M., Puente, J., Vela, C.R., Varela, R.: Improving cutting-stock plans with multi-objective genetic algorithms. In: International Work-conference on the Interplay between Natural and Artificial Computation 2007, pp. 528–537 (2007)
Ross, P., Schulenburg, S., Blázquez, J.M., Hart, E.: Hyper-heuristics: learning to combine simple heuristics in bin-packing problems. In: Proceedings of the Genetic and Evolutionary Computation Conference 2002, pp. 942–948 (2002)
Ross, P.: Hyper-heuristics. In: Search Methodologies: Introductory Tutorials in Optimization and Decision Support Methodologies, ch.17, pp. 529–556. Springer, Heidelberg (2005)
Terashima-Marín, H., Flores-Álvarez, E.J., Ross, P.: Hyper-heuristics and classifier systems for solving 2D-regular cutting stock problems. In: Proceedings of the Genetic and Evolutionary Computation Conference 2005, pp. 637–643 (2005)
Terashima-Marín, H., Farías-Zárate, C.J., Ross, P., Valenzuela-Rendón, M.: A GA-based method to produce generalized hyper-heuristics for the 2D-regular cutting stock problem. In: Proceedings of the Genetic and Evolutionary Computation Conference 2006, pp. 591–598 (2006)
Terashima-Marín, H., Ross, P., Farías-Zárate, C.J., López-Camacho, E., Valenzuela-Rendón, M.: Generalized hyper-heuristics for solving 2D regular and irregular packing problems. Annals of Operations Research (2008)
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Gomez, J.C., Terashima-Marín, H. (2010). Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds) Advances in Soft Computing. MICAI 2010. Lecture Notes in Computer Science(), vol 6438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16773-7_30
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DOI: https://doi.org/10.1007/978-3-642-16773-7_30
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