Modularity and Regularity in Neural Networks Produced with Assembler Encoding
Institute of Naval Weapon, Polish Naval Academy
81-103 Gdynia, ul. Smidowicza 69
E-mail: t.praczyk@amw.gdynia.pl
Received:
Received: 18 February 2013; revised: 21 April 2013; accepted: 11 July 2013; published online: 5 September 2013
DOI: 10.12921/cmst.2013.19.03.145-155
OAI: oai:lib.psnc.pl:450
Abstract:
The main focus of the paper is on the ability of the neuro-evolutionary method called Assembler Encoding to repeatedly use the information included
in a genotype and to construct modular and/or regular neural networks. It
reports experiments whose the main goal was to test whether the method is
capable of adjusting topology of neural networks to a modular and regular
problem. In the experiments, the task of Assembler Encoding was to evolve
neuro-controllers responsible for balancing two or three inverted pendulums
instaled on separate carts. Since both the carts and the pendulums were
identical the task of neuro-controllers could be performed by means of
modular/regular neural networks.
Key words:
artificial neural networks, evolution, modularity/regularity
References:
[1] K. Balakrishnan, V. Honavar, Properties of Genetic Represen-
tations of Neural Architectures, Proc. of the World Congress
on Neural Networks (WCNN’95), 807-813, (1995).
[2] R. Calabretta, Genetic Interference reduces the evolvability
of modular and non-modular visual neural networks, Phil.
Trans. R. Soc. B 362, 403-410, doi:10.1098/rstb.2006.1967
(2007).
[3] S. Cho, K. Shimohara, Evolutionary Learning of Modular
Neural Networks with Genetic Programming, Applied Intelli-
gence 9, 191-200 (1998).
[4] F. Gruau, Neural network Synthesis Using Cellular Encod-
ing And The Genetic Algorithm, PhD Thesis, Ecole Normale
Superieure de Lyon (1994).
[5] F. Gruau, Automatic Definition of Modular Neural Networks,
Adaptive Behavior 3, Issue 2, 151-183 (1994).
[6] D.E. Goldberg, Genetic algorithms in search, optimization and
machine learning, Addison Wesley, Reading, Massachusetts,
(1989).
[7] F. Gomez, R. Miikkulainen, Incremental evolution of complex
general behavior, Adaptive Behavior, 5, 317-342 (1997).
[8] F. Gomez, J. Schmidhuber, R. Miikkulainen, Accelerated Neu-
ral Evolution through Cooperatively Coevolved Synapses,
Journal of Machine Learning Research, 9, 937-965 (2008).
[9] V.R. Khare, X. Yao, B. Sendhoff, Y. Jin, H. Wers-
ing, Co-evolutionary Modular Neural Networks for Au-
tomatic Problem Decomposition, in Proc. of The 2005
IEEE Congress on Evolutionary Computation, 3, 2691-2698,
doi:10.1109/CEC.2005.1555032 (2005).
[10] K. Krawiec, B. Bhanu, Visual Learning by Coevolutionary
Feature Synthesis, IEEE Trans. on Systems, Man, and Cyber-
netics, Part B: Cybernetics. 35, 409-425 (2005).
[11] S. Luke and L. Spector, Evolving Graphs and Networks with
Edge Encoding: Preliminary Report, In John R. Koza, ed.,
Late Breaking Papers at the Genetic Programming 1996 Con-
ference, (Stanford University, CA, USA, Stanford Bookstore,
1996) 117-124.
[12] G.F. Miller, P.M. Todd, S.U. Hegde, Designing Neural Net-
works Using Genetic Algorithms, Proceedings of the Third
International Conference on Genetic Algorithms. 379-384.
of Schaffer J.D. (1989).
[13] D.E. Moriarty, Symbiotic Evolution of Neural Networks in Se-
quential Decision Tasks, PhD thesis, The University of Texas
at Austin, TR UT-AI97-257 (1997).
[14] J. Mouret, S. Doncieux, Evolving modular neural-networks
through exaptation, Proc. of the Eleventh Conf. on Congress
on Evolutionary Computation, 1570-1577 (2009).
[15] P. Nordin, W. Banzhaf, F. Francone, Efficient Evolution of Ma-
chine Code for CISC Architectures using Blocks and Homolo-
gous Crossover, Advances in Genetic Programming III, MIT
Press, L. Spector and W. Langdon and U. O’Reilly and P.
Angeline, pages. 275-299 (1999).
[16] N. NourAshrafoddin, A.R. Vahdat, M.M. Ebadzadeh, Auto-
matic Design of Modular Neural Networks Using Genetic
Programming, Proc. of the 17th International Conference on
Artificial Neural Networks, 788-798 (2007).
[17] M. Potter, The Design and Analysis of a Computational Model
of Cooperative Coevolution, PhD thesis, George Mason Uni-
versity, Fairfax, Virginia (1997).
[18] M.A. Potter, K.A. De Jong, Cooperative coevolution: An archi-
tecture for evolving coadapted subcomponents, Evolutionary
Computation, 8(1), 1-29 (2000).
[19] T. Praczyk, Evolving co–adapted subcomponents in Assem-
bler Encoding, International Journal of Applied Mathematics
and Computer Science, 17(4) (2007).
[20] T. Praczyk, Modular networks in Assembler Encoding, Com-
putational Methods in Science and Technology, CMST 14(1),
27-38 (2008).
[21] T. Praczyk, Using assembler encoding to solve inverted pendu-
lum problem, Computing and Informatics 28, 895-912 (2009).
[22] T. Praczyk, Forming Neural Networks by Means of Assembler
Encoding, Intelligent Automation and Soft Computing 17, no.
3, 319-331 (2011).
[23] T. Praczyk, Assembler Encoding Improved, CMST 18(1), 11-
24, (2012).
[24] O. Stanley, Efficient Evolution of Neural Networks Through
Complexification, PhD thesis, Department of Computer Sci-
ence, The University of Texas at Austin, Technical Report
AI-TR-04-314 (2004).
The main focus of the paper is on the ability of the neuro-evolutionary method called Assembler Encoding to repeatedly use the information included
in a genotype and to construct modular and/or regular neural networks. It
reports experiments whose the main goal was to test whether the method is
capable of adjusting topology of neural networks to a modular and regular
problem. In the experiments, the task of Assembler Encoding was to evolve
neuro-controllers responsible for balancing two or three inverted pendulums
instaled on separate carts. Since both the carts and the pendulums were
identical the task of neuro-controllers could be performed by means of
modular/regular neural networks.
Key words:
artificial neural networks, evolution, modularity/regularity
References:
[1] K. Balakrishnan, V. Honavar, Properties of Genetic Represen-
tations of Neural Architectures, Proc. of the World Congress
on Neural Networks (WCNN’95), 807-813, (1995).
[2] R. Calabretta, Genetic Interference reduces the evolvability
of modular and non-modular visual neural networks, Phil.
Trans. R. Soc. B 362, 403-410, doi:10.1098/rstb.2006.1967
(2007).
[3] S. Cho, K. Shimohara, Evolutionary Learning of Modular
Neural Networks with Genetic Programming, Applied Intelli-
gence 9, 191-200 (1998).
[4] F. Gruau, Neural network Synthesis Using Cellular Encod-
ing And The Genetic Algorithm, PhD Thesis, Ecole Normale
Superieure de Lyon (1994).
[5] F. Gruau, Automatic Definition of Modular Neural Networks,
Adaptive Behavior 3, Issue 2, 151-183 (1994).
[6] D.E. Goldberg, Genetic algorithms in search, optimization and
machine learning, Addison Wesley, Reading, Massachusetts,
(1989).
[7] F. Gomez, R. Miikkulainen, Incremental evolution of complex
general behavior, Adaptive Behavior, 5, 317-342 (1997).
[8] F. Gomez, J. Schmidhuber, R. Miikkulainen, Accelerated Neu-
ral Evolution through Cooperatively Coevolved Synapses,
Journal of Machine Learning Research, 9, 937-965 (2008).
[9] V.R. Khare, X. Yao, B. Sendhoff, Y. Jin, H. Wers-
ing, Co-evolutionary Modular Neural Networks for Au-
tomatic Problem Decomposition, in Proc. of The 2005
IEEE Congress on Evolutionary Computation, 3, 2691-2698,
doi:10.1109/CEC.2005.1555032 (2005).
[10] K. Krawiec, B. Bhanu, Visual Learning by Coevolutionary
Feature Synthesis, IEEE Trans. on Systems, Man, and Cyber-
netics, Part B: Cybernetics. 35, 409-425 (2005).
[11] S. Luke and L. Spector, Evolving Graphs and Networks with
Edge Encoding: Preliminary Report, In John R. Koza, ed.,
Late Breaking Papers at the Genetic Programming 1996 Con-
ference, (Stanford University, CA, USA, Stanford Bookstore,
1996) 117-124.
[12] G.F. Miller, P.M. Todd, S.U. Hegde, Designing Neural Net-
works Using Genetic Algorithms, Proceedings of the Third
International Conference on Genetic Algorithms. 379-384.
of Schaffer J.D. (1989).
[13] D.E. Moriarty, Symbiotic Evolution of Neural Networks in Se-
quential Decision Tasks, PhD thesis, The University of Texas
at Austin, TR UT-AI97-257 (1997).
[14] J. Mouret, S. Doncieux, Evolving modular neural-networks
through exaptation, Proc. of the Eleventh Conf. on Congress
on Evolutionary Computation, 1570-1577 (2009).
[15] P. Nordin, W. Banzhaf, F. Francone, Efficient Evolution of Ma-
chine Code for CISC Architectures using Blocks and Homolo-
gous Crossover, Advances in Genetic Programming III, MIT
Press, L. Spector and W. Langdon and U. O’Reilly and P.
Angeline, pages. 275-299 (1999).
[16] N. NourAshrafoddin, A.R. Vahdat, M.M. Ebadzadeh, Auto-
matic Design of Modular Neural Networks Using Genetic
Programming, Proc. of the 17th International Conference on
Artificial Neural Networks, 788-798 (2007).
[17] M. Potter, The Design and Analysis of a Computational Model
of Cooperative Coevolution, PhD thesis, George Mason Uni-
versity, Fairfax, Virginia (1997).
[18] M.A. Potter, K.A. De Jong, Cooperative coevolution: An archi-
tecture for evolving coadapted subcomponents, Evolutionary
Computation, 8(1), 1-29 (2000).
[19] T. Praczyk, Evolving co–adapted subcomponents in Assem-
bler Encoding, International Journal of Applied Mathematics
and Computer Science, 17(4) (2007).
[20] T. Praczyk, Modular networks in Assembler Encoding, Com-
putational Methods in Science and Technology, CMST 14(1),
27-38 (2008).
[21] T. Praczyk, Using assembler encoding to solve inverted pendu-
lum problem, Computing and Informatics 28, 895-912 (2009).
[22] T. Praczyk, Forming Neural Networks by Means of Assembler
Encoding, Intelligent Automation and Soft Computing 17, no.
3, 319-331 (2011).
[23] T. Praczyk, Assembler Encoding Improved, CMST 18(1), 11-
24, (2012).
[24] O. Stanley, Efficient Evolution of Neural Networks Through
Complexification, PhD thesis, Department of Computer Sci-
ence, The University of Texas at Austin, Technical Report
AI-TR-04-314 (2004).
