Artículos regulares

 

Heurísticas de agrupación híbridas eficientes para el problema de empacado de objetos en contenedores

 

Efficient Hybrid Grouping Heuristics for the Bin Packing Problem

 

Laura Cruz-Reyes¹, Marcela Quiroz C.¹, Adriana C. F. Alvim², Héctor J. Fraire Huacuja¹, Claudia Gómez S.¹ y José Torres-Jiménez³

 

¹ Instituto Tecnológico de Ciudad Madero, México lauracruzreyes@itcm.edu.mx, qc.marcela@gmail.com, cggs71@hotmail.com

² Universidad Federal do Estado do Rio de Janeiro, Brasil adriana@uniriotec.br

³ Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, México jtj@tamps.cinvestav.mx, automatas2002@yahoo.com.mx

 

Artículo recibido el 03/01/2011;
aceptado el 08/11/2011.

 

Resumen

En este artículo se aborda un problema clásico muy conocido por su aplicabilidad y complejidad: el empacado de objetos en contenedores (Bin Packing Problem, BPP). Para la solución de BPP se propone un algoritmo genético híbrido de agrupación denominado HGGA-BP. El algoritmo propuesto está inspirado en el esquema de representación de grupos de Falkenauer, el cual aplica operadores evolutivos a nivel de contenedores. HGGA-BP incluye heurísticas eficientes para generar la población inicial y realizar mutación y cruzamiento de grupos; así como estrategias híbridas para el acomodo de objetos que quedaron libres al aplicar los operadores grupales. La efectividad del algoritmo es comparable con la de los mejores del estado del arte, superando los resultados publicados para el conjunto de instancias hard28, el cual ha mostrado el mayor grado de dificultad para los algoritmos de solución de BPP.

Palabras clave. Metodologías computacionales, inteligencia artificial, solución de problemas, problema de empacado de objeto en contenedores, algoritmo genético hibrido.

 

Abstract

This article addresses a classical problem known for its applicability and complexity: the Bin Packing Problem (BPP). A hybrid grouping genetic algorithm called HGGA-BP is proposed to solve BPP. The proposed algorithm is inspired by the Falkenauer grouping encoding scheme, which applies evolutionary operators at the bin level. HGGA-BP includes efficient heuristics to genérate the initial population and performs mutation and crossover for groups as well as hybrid strategies for the arrangement of objects that were released by the group operators. The effectiveness of the algorithm is comparable with the best state-of-the-art algorithms, outperforming the published results for the class of instances hard28, which has shown the highest difficulty for algorithms that solve BPP.

Keywords: Computer methodologies, artificial intelligence, problem solving, bin packing problem, hybrid genetic algorithm.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Referencias

1. Alvim, A.C.F., Ribeiro, C.C., Glover, F., & Aloise, D.J. (2004). A hybrid improvement heuristic for the one-dimensional bin packing problem. Journal of Heurístics, 10(2), 205-229.         [ Links ]

2. Baase, S. & Gelder, A.V. (2000). ComputerAlgorithms, Introduction to Design and Analysis(3^rded.). Reading, Mass.: Addison-WesleyLongman.         [ Links ]

3. Beasley, J.E. (1990). OR-library: Distributing test problems by electronic mail. Journal of the Operatlonal Research Society, 41(11), 1069-1072. Retrieved http://people.brunel.ac.uk/~mastjjb/jeb/orlib/binpackinfo.html.         [ Links ]

4. Belov, G. (1992). Problems, Models and Algorithms in One and Two Dimensional Cutting. Ph.D. Thesis, Technischen Universitat Dresden, St. Petersburg, Russland.         [ Links ]

5. Bhatia, A.K. & Basu, S.K. (2004). Packing Bins Using Multi-chromosomal Genetic Representation and Better-Fit Heuristic. Neural Information Processing, Lecture Notes in Computer Science, 3316, 181-186.         [ Links ]

6. CaPaD. Cutting and Packing at Dresden University: Test instances & results. Retrieved from http://www.math.tu-dresden.de/~capad/cpd-ti.html#pmp%2024.         [ Links ]

7. Coffman, E.G., Garey, M.R., & Johnson D.S. (1997). Approximation algorithms for bin packing: a survey. In Hochbaum D.S. (Ed.), Approximation algorithms for NP-hard problems (46-93). Boston: PWS Publishing.         [ Links ]

8. Crainic, T.G., Perboli, G., Rei, W., & Tadei, R. (2011). Efficient Lower Bounds and Heuristics for the Variable Cost and Size Bin Packing Problem. Computers and Operations Research, 38(11), 1474-1482.         [ Links ]

9. Cruz, L, Nieto-Yáñez, D.M., Rangel-Valdez, N., Herrera, J.A., González, J., Castilla, G., & Delgado-Orta, J.F. (2007). DiPro: An Algorithm for the Packing in Product Transportation Problems with Múltiple Loading and Routing Variants. 6^th Mexican International Conference on artificial Intelligence (MICAI2007:Advances in Artificial Intelligence), Lecture Notes in Artificial Intelligence, 4827, 1078-1088.         [ Links ]

10. Di Natale, M. & Bini, E. (2007). Optimizing the FPGA implementation of HRT systems. 13th IEEE Real Time and Embedded Technology and Applications Symposium (RTAS'07), Bellevue, Washington, USA, 22-31.         [ Links ]

11. ESICUP. Euro Especial Interest Group on Cutting and Packing. One Dimensional Cutting and Packing Data Sets. Retrieved from http://paginas.fe.up.pt/~esicup/tiki-list_file_gallery.php?galleryld=1%2023        [ Links ]

12. Falkenauer, E. & Delchambre, A. (1992). A Genetic Algorithm for Bin Packing and Line Balancing. 7992 IEEE International Conference on Robotics and Automation, Nice, France, 2, 1186— 1192.         [ Links ]

13. Falkenauer, E. (1996). A Hybrid Grouping Genetic Algorithm for Bin Packing. Journal of Heuristics, 2(1), 5-30.         [ Links ]

14. Fleszar, K. & Hindi, K. (2002). New heuristics for one-dimensional bin-packing. Computers & Operations Research, 29(7), 821-839.         [ Links ]

15. Fleszar, K. & Charalambous, C. (2011). Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem. European Journal of Operational Research. 210(2), 176-184.         [ Links ]

16. Garey, M.R. & Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP Completeness. San Francisco: W. H. Freeman        [ Links ]

17. Gómez-Meneses, P. & Randall, M.A. (2009). Hybrid Extremal Optimisation Approach for the Bin Packing Problem. Artificial Life: Borrowing from Biology, 4th Australian Conference, ACAL 2009, Lecture Notes in Computer Science, 5865, 242-251.         [ Links ]

18. Gupta, J.N.D. & Ho, J.C. (1999). A new heuristic algorithm for the one-dimensional bin-packing problem. Production Planning & Control: The Management of Operations, 10(6), 598-603. Retrieved from http://www.math.tu-dresden.de/~capad/cpd-ti.html#pmp%2024        [ Links ]

19. Johnson, D.S. (1974). Fast algorithms for bin packing. Journal of Computer and System Sciences, 8(3), 272-314.         [ Links ]

20. Levine, J. & Ducatelle, F. (2004). Ant colony optimization and local search for bin packing and cutting stock problems. Journal of the Operational Research Society, 55(7), 705-716.         [ Links ]

21. Lewis, R. (2009). A general-purpose hill-climbing method for order independent minimum grouping problems: A case study in graph colouring and bin packing. Computers & Operations Research, 36(7), 2295-2310.         [ Links ]

22. Loh, K.H., Golden, B., & Wasil, E. (2008). Solving the one-dimensional bin packing problem with a weight annealing heuristic. Computers & Operations Research, 35(7), 2283-2291.         [ Links ]

23. Martello, S. & Toth, P. (1990). Knapsack Problems: Algorithms and Computer Implementations. New York: J. Wiley & Sons.         [ Links ]

24. Martello, S. & Toth, P. (1990). Lower Bounds and Reduction Procedures for the Bin Packing Problem. Discrete Applied Mathematics, 28(1), 59-70.         [ Links ]

25. Quiroz, M. (2009). Caracterización de Factores de Desempeño de Algoritmos de Solución de BPP. Tesis de maestría, Instituto Tecnológico de Cd. Madero, Tamaulipas, México.         [ Links ]

26. Rohlfshagen, P. & Bullinaria, J.A. (2010).Nature inspired genetic algorithms for hard packing problems. Annals of Operations Research, 179(1), 393-419.         [ Links ]

27. Scholl, A. & Klein, R. (s.f.). Bin Packing. Retrieved from http://www.wiwi.uni-jena.de/Entscheidung/binpp/        [ Links ]

28. Scholl, A., Klein, R., & Jürgens, C. (1997). BISON: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem. Computers and Operations Research, 24(7), 627-645.         [ Links ]

29. Schwerin, P. & Wäscher, G. (1999). A new lower bound for the bin-packing problem and its integration to MTP. Pesquisa Operacional, 19(2), 111–130.         [ Links ]

30. Schwerin, P. & Wäscher, G. (1997). The bin packing problem: A problem generator and some numerical experiments with FFD packing and MTP. International Transactions in Operational Research, 4(5-6), 337–389.         [ Links ]

31. Singh, A. & Gupta, A.K. (2007). Two heuristics for the one-dimensional bin-packing problem. OR Spectrum, 29(4), 765–781.         [ Links ]

32. Stawowy, A. (2008). Evolutionary based heuristic for bin packing problem. Computers & Industrial Engineering, 55(2), 465–474.         [ Links ]

33. Wäscher, G. & Gau, T. (1996). Heuristics for the integer one-dimensional cutting stock problem: A computational study. OR Spektrum, 18(3), 131–144.         [ Links ]