¹Universidad Nacional Experimental del Táchira, Departamento de Ing. Informática, San Cristóbal, Venezuela. Associate Professor. Email: drodri@unet.edu.ve
²Universidad Nacional de Colombia, Facultad de Ciencias Agrarias, Departamento de Agronomía, Bogotá, Colombia. Assistant Professor. Email: aqedarghanco@unal.edu.co
³Universidad de Pamplona, Facultad de Ciencias Básicas, Departamento de Matemáticas, Pamplona, Colombia. Associate Professor. Email: julio.monroy@unipamplona.edu.co

The problem with designing balanced incomplete blocks (BIBD) is enclosed within the combinatorial optimization approach that has been extensively used in experimental design. The present proposal addresses this problem by using local search techniques known as Hill Climbing, Tabu Search, and an approach based considerable sized the use of Multi-Agents, which allows the exploration of diverse areas of search spaces. Furthermore, the use of a vector vision for the consideration associated with vicinity is presented. The experimental results prove the advantage of this technique compared to other proposals that are reported in the current literature.

Key words: Balanced incomplete block design, Vector process, Computer search, Experimental design.

El problema del diseño de bloques incompletos equilibrados (BIBD) se enmarca dentro del enfoque de optimización combinatoria que ha sido utilizado ampliamente en el diseño de experimentos. La presente propuesta aborda este problema utilizando técnicas de búsqueda local conocidas como Ascenso a la Colina (Hill Climbing), Búsqueda Tabú (Tabu Search) y un enfoque basado en el uso de Multi-Agentes que permiten la exploración de diversas áreas de espacios de búsqueda de tamaño considerable, además se presenta el uso de una visión vectorial para la consideración asociada a la vecindad. Los resultados experimentales evidencian la ventaja de esta técnica frente a otras propuestas mostradas en la literatura actual.

Palabras clave: diseño de bloques incompletos equilibrados, proceso vectorial, búsqueda por computador, diseño de experimentos.

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References

1. Anderson, I. (1997), Combinatorial designs and tournaments, Clarendon Press, Oxford University Press.         [ Links ]

2. Bofill, P., Guimerà, R. & Torras, C. (2003), 'Comparison of simulated annealing and mean field annealing as applied to the generation of block designs', Neural Networks 16(10), 1421-1428.         [ Links ]

3. Buratti, M. (1999), 'Some (17q, 17, 2) and (25q, 25, 3)BIBD constructions', Designs, Codes and Cryptography 16(2), 117-120.         [ Links ]

4. Colbourn, C. & Dinitz, J., eds (1996), The CRC handbook of combinatorial designs, CRC Press, Boca Raton.         [ Links ]

5. Corneil, D. G. & Mathon, R. (1978), 'Algorithmic techniques for the generation and analysis of strongly regular graphs and other combinatorial configurations', Annals of Discrete Mathematics 2, 1-32.         [ Links ]

6. Daisuke Yokoya, T. Y. (2009), 'A mathematical programming approach to the construction of bibds', International Journal of Computer Mathematics, 1-16.         [ Links ]

7. Fisher, R. A. (1926), 'The arrangement of field experiments', Journal of the Ministry of Agriculture Great Britain 33.         [ Links ]

8. Fisher, R. A. (1940), 'An examination of the different possible solutions of a problem in incomplete blocks', Annals of Eugenics 10, 52-75.         [ Links ]

9. Flener, P., Frisch, A. M., Hnich, B., Kzltan, Z., Miguel, I. & Walsh, T. (2001), Matrix modelling, 'CP-01 Workshop on Modelling and Problem Formulation. International Conference on the Principles and Practice of Constraint Programming'.         [ Links ]

10. Gibbons, P. B. & Ostergard, P. R. J. (2007), Computational methods in design theory, 'Handbook of Combinatorial Designs', Chapman & Hall/CRC Press, Boca Raton, p. 755-783.         [ Links ]

11. Hall, M. J. (1998), Combinatorial Theory, 2 edn, John Wiley & Sons, Inc., New York, USA.         [ Links ]

12. Hinkelman, K. & Kempthorne, O. (1994), Design and analysis of experiments, Vol. 1, John Wiley and Sons, Inc., New York.         [ Links ]

13. John, J. A., Whitaker, D. & Triggs, C. M. (1993), 'Construction of cyclic designs using integer programming', Journal of statistical planning and inference 36(2), 357-366.         [ Links ]

14. Lan, L., Tai, Y. Y., Lin, S., Memari, B. & Honary, B. (2008), 'New constructions of quasi-cyclic LDPC codes based on special classes of BIDBs for the AWGN and binary erasure channels', IEEE Transactions on Communications 56(1), 39-48.         [ Links ]

15. Mead, R. (1993), Design of Experiments: Statistical Principles for Practical Applications, Cambridge University Press.         [ Links ]

16. Meseguer, P. & Torras, C. (2001), 'Exploiting symmetries within constraint satisfaction search', Artificial Intelligence 129(1-2), 133-163.         [ Links ]

17. Prestwich, S. (2003a), A local search algorithm for balanced incomplete block designs, '9th International Conference on Principles and Practices of Constraint Programming (CP2003)', LNCS, Springer, p. 53-64.         [ Links ]

18. Prestwich, S. (2003b), 'Negative effects of modeling techniques on search performance', Annals of Operations Research 18, 137-150.         [ Links ]

19. Puget, Jean-Francois (2002), Symmetry breaking revisited, '8th International Conference on Principles and Practice of Constraint Programming (CP 2002)', Vol. 2470 of LNCS, Springer, Ithaca, NY, USA, p. 446-461.         [ Links ]

20. Raghavarao, D. (1988), Constructions and Combinatorial Problems in Design of Experiments (Paperback), Dover Publications.         [ Links ]

21. Rodriguez, D., Cotta,. & Leiva, A. José Fernandez (2011), 'A memetic algorithm for designing balanced incomplete blocks', IJCOPI 2(1), 14-22.         [ Links ]

22. Rodriguez, D., Cotta, C. & Fernandez, A. (2009), Finding balanced incomplete block designs with metaheuristics, 'Evolutionary Computation in Combinatorial Optimization 2009', Vol. 5482 of Lecture Notes in Computer Science, Springer, p. 156-167.         [ Links ]

23. Whitaker, D., Triggs, C. M. & John, J. A. (1990), 'Construction of block designs using mathematical programming', Journal of the Royal Statistical Society, Series B 52(3), 497-503.         [ Links ]

24. Yates, F. (1936), 'Incomplete randomized blocks', Annals of Eugenics 7, 121-140.         [ Links ]

25. van Lint, J. & Wilson, R. (1992), A Course in Combinatorics, Cambridge University Press.         [ Links ]

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