Abstract
Binary Decision Diagrams (BDDs) have become the data structure of choice for representing discrete functions in some design and verification applications: They are compact and efficient to manipulate with strong theoretical underpinnings. However, and despite many appealing characteristics, BDDs are not a representation commonly considered for evolutionary computation (EC). The inherent difficulties associated with evolving graphs combined with the variable ordering problem poses a significant challenge which is yet to be overcome. This work addresses this challenge and presents a new approach to evolving BDDs that exhibits good variable orderings as an emergent property.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akers, S.B.: Binary Decision Diagrams. IEEE Transactions on Computers C-27(6), 509–516 (1978)
Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-complete. IEEE Transactions on Computers 45(9), 993–1002 (1996)
Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24(3), 293–318 (1992)
Downing, R.M.: Evolving Binary Decision Diagrams using implicit neutrality. In: Corne, D., Michalewicz, Z., Dorigo, M., Eiben, G., Fogel, D., Fonseca, C., Greenwood, G., Chen, T.K., Raidl, G., Zalzala, A., Lucas, S., Paechter, B., Willies, J., Guervos, J.J.M., Eberbach, E., McKay, B., Channon, A., Tiwari, A., Volkert, L.G., Ashlock, D., Schoenauer, M. (eds.) Proceedings of the 2005 IEEE Congress on Evolutionary Computation, Edinburgh, September 2-5, 2005, vol. 3, pp. 2107–2113. IEEE Press, Los Alamitos (2005)
Downing, R.M.: Neutrality and gradualism: encouraging exploration and exploitation simultaneously with Binary Decision Diagrams. In: Proceedings of the 2006 IEEE Congress on Evolutionary Computation, Vancouver, Canada (to appear, 2006)
Droste, S.: Efficient genetic programming for finding good generalizing boolean functions. In: Koza, J.R., Deb, K., Dorigo, M., Fogel, D.B., Garzon, M., Iba, H., Riolo, R.L. (eds.) Genetic Programming 1997. Proceedings of the Second Annual Conference, Stanford University, July 13-16, 1997, pp. 82–87. Morgan Kaufmann, San Francisco (1997)
Droste, S., Heutelbeck, D., Wegener, I.: Distributed hybrid genetic programming for learning boolean functions. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 181–190. Springer, Heidelberg (2000)
Kimura, M.: The neutral theory of molecular evolution. Cambridge University Press, Cambridge (1983)
Krause, M., Savický, P., Wegener, I.: Approximations by OBDDs and the variable ordering problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 493–502. Springer, Heidelberg (1999)
Lee, C.Y.: Representation of Switching Circuits by Binary-Decision Programs. Bell Systems Technical Journal 38, 985–999 (1959)
Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proceedings of the International Conference on CAD (ICCAD), pp. 42–47 (1993)
Sakanashi, H., Higuchi, T., Iba, H., Kakazu, Y.: Evolution of binary decision diagrams for digital circuit design using genetic programming. In: International Conference on Evolvable Systems, pp. 470–481 (1996)
Sieling, D.: On the existence of polynomial time approximation schemes for OBDD-Minimization. LNCS, vol. 1373, pp. 205–215. Springer, Heidelberg (1998)
van Remortel, P., Lenaerts, T., Manderick, B.: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, July 19-21, pp. 249–254. IEEE Computer Society, Los Alamitos
Yanagiya, M.: Efficient genetic programming based on binary decision diagrams. In: 1995 IEEE Conference on Evolutionary Computation, Perth, November 29 - December 1, 1995, vol. 1, pp. 234–239. IEEE Press, Los Alamitos (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Downing, R.M. (2006). Evolving Binary Decision Diagrams with Emergent Variable Orderings. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_81
Download citation
DOI: https://doi.org/10.1007/11844297_81
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38990-3
Online ISBN: 978-3-540-38991-0
eBook Packages: Computer ScienceComputer Science (R0)