Utilizing Symmetry in Evolutionary Design

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Vinod K. Valsalam: Utilizing Symmetry in Evolutionary Design. Dissertation and Technical Report AI-10-04 Department of Computer Sciences, The University of Texas at Austin, August 2010.



Can symmetry be utilized as a design principle to constrain evolutionary search, making it more effective? This dissertation aims to show that this is indeed the case, in two ways. First, an approach called ENSO is developed to evolve modular neural network controllers for simulated multilegged robots. Inspired by how symmetric organisms have evolved in nature, ENSO utilizes group theory to break symmetry systematically, constraining evolution to explore promising regions of the search space. As a result, it evolves effective controllers even when the appropriate symmetry constraints are difficult to design by hand. The controllers perform equally well when transferred from simulation to a physical robot. Second, the same principle is used to evolve minimal-size sort- ing networks. In this different domain, a different instantiation of the same principle is effective: building the desired symmetry step-by-step. This approach is more scalable than previous methods and finds smaller networks, thereby demonstrating that the principle is general. Thus, evolutionary viisearch that utilizes symmetry constraints is shown to be effective in a range of challenging applica- tions.

Extended Abstract


Used References

Ajtai, M., Koml ́os, J., and Szemer ́edi, E. (1983). Sorting in c log n parallel steps. Combinatorica, 3(1):1–19.

Alden, M. E. (2007). MARLEDA: Effective Distribution Estimation Through Markov Random Fields. PhD thesis, Department of Computer Sciences, The University of Texas at Austin. Tech- nical Report AI07-349. http://nn.cs.utexas.edu/keyword?alden:phd07

Baddar, S. W. A. (2009). Finding Better Sorting Networks. PhD thesis, Kent State University. http://rave.ohiolink.edu/etdc/view?acc_num

Bastert, O. (2001). Stabilization Procedures and Applications. PhD thesis, Technische Universit ̈at M ̈uchen.

Batcher, K. E. (1968). Sorting networks and their applications. In AFIPS Spring Joint Computing Conference, 307–314.

Beer, R. D., Chiel, H. J., and Sterling, L. S. (1989). Heterogeneous neural networks for adaptive behavior in dynamic environments. In Advances in Neural Information Processing Systems 1, 577–585. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.

Beer, R. D., and Gallagher, J. C. (1992). Evolving dynamical neural networks for adaptive behavior. Adaptive Behavior, 1(1):91–122.

Beineke, L., Wilson, R., and Cameron, P. (2004). Introduction. In Beineke, L. W., and Wilson, R. J., editors, Topics in Algebraic Graph Theory, 1–29. New York, NY, USA: Cambridge University Press.

Bengoetxea, E., Larranaga, P., Bloch, I., and Perchant, A. (2001). Estimation of distribution al- gorithms: A new evolutionary computation approach for graph matching problems. In Energy Minimization Methods in Computer Vision and Pattern Recognition, 454–469. Springer. http://dx.doi.org.ezproxy.lib.utexas.edu/10.1007/3-540-44745-8_30

Berryman, M. J., Allison, A., and Abbott, D. (2004). Optimizing genetic algorithm strategies for evolving networks. In White, L. B., editor, Noise in Communication, vol. 5473 of Proceedings of SPIE, 122–130. Bellingham, WA, USA: SPIE.

Billard, A., and Ijspeert, A. J. (2000). Biologically inspired neural controllers for motor control in a quadruped robot. In Proceedings of the International Joint Conference on Neural Networks (IJCNN 2000), 637–641.

Boers, E. J. W., and Kuiper, H. (1992). Biological Metaphors and the Design of Modular Artifi- cial Neural Networks. Master’s thesis, Departments of Computer Science and Experimental and Theoretical Psychology at Leiden University, The Netherlands. http://citeseer.nj.nec.com/boers92biological.html

Bongard, J. C., and Lipson, H. (2004). Once more unto the breach: Co-evolving a robot and its simulator. In Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems (ALIFE9), 57–62. MIT Press.

Bongard, J. C., and Pfeifer, R. (2001). Repeated structure and dissociation of genotypic and pheno- typic complexity in artificial ontogeny. In Spector, L., Goodman, E. D., Wu, A., Langdon, W. B., Voigt, H.-M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M. H., and Burke, E., editors, Proceedings of the Genetic and Evolutionary Computation Conference, 829–836. San Francisco: Morgan Kaufmann. http://www-illigal.ge.uiuc.edu:8080/gecco-2001/

Bongard, J. C., and Pfeifer, R. (2003). Evolving complete agents using artificial ontogeny. In Morpho-Functional Machines: The New Species (Designing Embodied Intelligence), 237–258. Springer-Verlag, Berlin.

Brading, K., and Castellani, E. (2008). Symmetry and symmetry breaking. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.

Brooks, R. A. (1989). A robot that walks; emergent behaviors from a carefully evolved network. Technical Report AIM-1091, Massachusetts Institute of Technology, Cambridge, MA, USA.

Brooks, R. A. (1992). Artificial life and real robots. In Proceedings of the First European Confer- ence on Artificial Life, 3–10. MIT Press.

Brooks, R. A., and Maes, P., editors (1994). Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems (Artificial Life IV). Cambridge, MA: MIT Press.

Bull, L., Fogarty, T. C., and Snaith, M. (1995). Evolution in multi-agent systems: Evolving commu- nicating classifier systems for gait in a quadrupedal robot. In Proceedings of the 6th International Conference on Genetic Algorithms, 382–388. San Francisco, CA, USA: Morgan Kaufmann Pub- lishers Inc.

Cangelosi, A., Parisi, D., and Nolfi, S. (1994). Cell division and migration in a ‘genotype’ for neural networks. Network: Computation in Neural Systems, 5:497–515. http://kant.irmkant.rm.cnr.it/econets/cangelosi.migration.ps.Z

Chakrabarti, C., and Wang, L.-Y. (1994). Novel sorting network-based architectures for rank order filters. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2(4):502–507.

Chan, A., and Godsil, C. (1997). Symmetry and eigenvectors. In Hahn, G., and Sabidussi, G., editors, Graph Symmetry: Algebraic Methods and Applications, 75–106. Springer.

Chauvin, Y., and Rumelhart, D. E., editors (1995). Backpropagation: Theory, Architectures, and Applications. Hillsdale, NJ: Erlbaum.

Chung, K.-L., and Lin, Y.-K. (1997). A generalized pipelined median filter network. Signal Pro- cessing, 63(1):101 – 106. http://www.sciencedirect.com/science/article/B6V18-3SNYT5C-1B/2/38110bb682311c8cc6169b64b233dac5

Clark, J. E. (2004). Design, Simulation, and Stability of a Hexapedal Running Robot. PhD thesis, Department of Mechanical Engineering, Stanford University.

Clune, J., Beckmann, B. E., Ofria, C., and Pennock, R. T. (2009). Evolving coordinated quadruped gaits with the HyperNEAT generative encoding. In Proceedings of the Eleventh conference on Congress on Evolutionary Computation (CEC’09), 2764–2771. Piscataway, NJ, USA: IEEE Press.

Collins, J. J., and Stewart, I. N. (1993). Coupled nonlinear oscillators and the symmetries of animal gaits. Journal of Nonlinear Science, 3(1):349–392.

Cornell Computational Synthesis Lab (2010). Cornell Computational Synthesis Lab (CCSL). http://ccsl.mae.cornell.edu/.

Deb, K., Agrawal, S., Pratab, A., and Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. PPSN VI, 849–858.

Dellaert, F., and Beer, R. D. (1996). A developmental model for the evolution of complete au- tonomous agents. In Maes, P., Mataric, M. J., Meyer, J.-A., Pollack, J., and Wilson, S. W., editors, From Animals to Animats 4: Proceedings of the Fourth International Conference on Simulation of Adaptive Behavior. Cambridge, MA: MIT Press. http://citeseer.nj.nec.com/dellaert96developmental.html

Edwards, R., and Glass, L. (2000). Combinatorial explosion in model gene networks. Chaos, 10:691–704.

Fahlman, S. E., and Lebiere, C. (1990). The cascade-correlation learning architecture. In Touretzky (1990), 524–532.

Ferrell, C. (1994). Failure recognition and fault tolerance of an autonomous robot. Adaptive Behav- ior, 2(4):375–398.

Filliat, D., Kodjabachian, J., and Meyer, J.-A. (1999). Evolution of neural controllers for locomotion and obstacle avoidance in a six-legged robot. Connection Science, 11(3/4):225–242.

Floreano, D., and Mondada, F. (1998). Evolutionary neurocontrollers for autonomous mobile robots. Neural Networks, 11:1461–1478.

Gao, L., Liu, S., and Dougal, R. A. (2002). Dynamic lithium-ion battery model for system simula- tion. IEEE Transactions on Components and Packaging Technologies, 25(3):495 – 505.

Gao, L., Sun, P., and Song, J. (2009). Clustering algorithms for detecting functional modules in protein interaction networks. Journal of Bioinformatics and Computational Biology, 07(01):217. http://www.worldscinet.com/jbcb/07/0701/S0219720009004023.html

GAP (2007). GAP – groups, algorithms, and programming. http://www.gap-system.org.

Garcia-Bellido, A. (1996). Symmetries throughout organic evolution. PNAS, 93(25):14229–14232.

Golubitsky, M., Shiau, L. J., and T ̈or ̈ok, A. (2003). Bifurcation on the visual cortex with weakly anisotropic lateral coupling. SIAM Journal on Applied Dynamical Systems, 2(2):97–143.

Golubitsky, M., and Stewart, I. (2002). Patterns of oscillation in coupled cell systems. In Newton, P., Holmes, P., and Weinstein, A., editors, Geometry, Mechanics, and Dynamics: Volume in Honor of the 60th Birthday of J. E. Marsden, chapter 8, 243–286. Springer.

Gomez, F., and Miikkulainen, R. (2004). Transfer of neuroevolved controllers in unstable domains. In Proceedings of the Genetic and Evolutionary Computation Conference. Berlin: Springer. http://nn.cs.utexas.edu/keyword?gomez:gecco04

Graham, L., and Oppacher, F. (2006). Symmetric comparator pairs in the initialization of genetic algorithm populations for sorting networks. IEEE Congress on Evolutionary Computation, 2006 (CEC 2006), 2845–2850.

Gruau, F. (1994a). Automatic definition of modular neural networks. Adaptive Behavior, 3(2):151– 183.

Gruau, F. (1994b). Neural Network Synthesis Using Cellular Encoding and the Genetic Algorithm. PhD thesis, Ecole Normale Superieure de Lyon, France. http://citeseer.nj.nec.com/frederic94neural.html

Gruau, F., and Whitley, D. (1993). Adding learning to the cellular development of neural networks: Evolution and the Baldwin effect. Evolutionary Computation, 1:213–233.

Gruau, F., Whitley, D., and Pyeatt, L. (1996). A comparison between cellular encoding and direct encoding for genetic neural networks. In Koza, J. R., Goldberg, D. E., Fogel, D. B., and Riolo, R. L., editors, Genetic Programming 1996: Proceedings of the First Annual Conference, 81–89. Cambridge, MA: MIT Press.

Gunter, C. A., Ngair, T.-H., and Subramanian, D. (1996). Sets as anti-chains. In ASIAN ’96: Pro- ceedings of the Second Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security, 116–128. London, UK: Springer-Verlag.

Heylighen, F. (1999). The growth of structural and functional complexity during evolution. In Heylighen, F., Bollen, J., Riegler, A., and Riegler, A., editors, The Evolution of Complexity: The Violet Book of ’Einstein Meets Magritte’, chapter 2, 17–44. Springer.

Hiasat, A., and Hasan, O. (2003). Bit-serial architecture for rank order and stack filters. Integration, the VLSI Journal, 36(1-2):3 – 12. http://www.sciencedirect.com/science/article/B6V1M-48NKGY5-1/2/53c0e6c9dfb4ef44292e616c4eab3356

Hillis, W. D. (1991). Co-evolving parasites improve simulated evolution as an optimization pro- cedure. In Farmer, J. D., Langton, C., Rasmussen, S., and Taylor, C., editors, Artificial Life II. Reading, MA: Addison-Wesley.

Holmes, P., Full, R. J., Koditschek, D., and Guckenheimer, J. (2006). The dynamics of legged locomotion: Models, analyses, and challenges. SIAM Review, 48(2):207–304.

Hornby, G. S., Fujita, M., Takamura, S., Yamamoto, T., and Hanagata, O. (1999). Autonomous evolution of gaits with the sony quadruped robot. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), 1297–1304.

Hornby, G. S., and Pollack, J. B. (2002). Creating high-level components with a generative repre- sentation for body-brain evolution. Artificial Life, 8(3). http://www.demo.cs.brandeis.edu/papers/hornby_alife02.pdf

Hornby, G. S., Takamura, S., Yokono, J., Hanagata, O., Yamamoto, T., and Fujita, M. (2000). Evolv- ing robust gaits with AIBO. In Proceedings of the IEEE International Conference on Robotics and Automation, vol. 3, 3040–3045.

Ijspeert, A. J. (2008). Central pattern generators for locomotion control in animals and robots: A review. Neural Networks, 21(4):642–653.

Jakobi, N. (1998). Minimal Simulations for Evolutionary Robotics. PhD thesis, School of Cognitive and Computing Sciences, University of Sussex.

Jakobi, N., Husbands, P., and Harvey, I. (1995). Noise and the reality gap: The use of simulation in evolutionary robotics. In Moran, F., Moreno, A., Merelo, J., and Chacon, P., editors, Advances in Artificial Life, vol. 929 of Lecture Notes in Computer Science, 704–720. Springer Berlin / Heidelberg. http://dx.doi.org/10.1007/3-540-59496-5_337

Juill ́e, H. (1995). Evolution of non-deterministic incremental algorithms as a new approach for search in state spaces. In Proceedings of the 6th International Conference on Genetic Algorithms, 351–358. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.

Kauffman, S. A. (1993). The Origins of Order. New York: Oxford University Press. Kepes, F., editor (2007). Biological Networks. World Scientific.

Kimura, H., Akiyama, S., and Sakurama, K. (1999). Realization of dynamic walking and running of the quadruped using neural oscillator. Autonomous Robots, 7(3):247–258.

Kipfer, P., Segal, M., and Westermann, R. (2004). Uberflow: A gpu-based particle engine. In HWWS ’04: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware, 115–122. New York, NY, USA: ACM.

Kitano, H. (1990). Designing neural networks using genetic algorithms with graph generation system. Complex Systems, 4:461–476.

Knuth, D. E. (1998). Art of Computer Programming: Sorting and Searching, vol. 3. Addison- Wesley Professional. Second edition.

Koditschek, D. E., Full, R. J., and Buehler, M. (2004). Mechanical aspects of legged locomotion control. Arthropod Structure and Development, 33(3):251–272.

Kodjabachian, J., and Meyer, J.-A. (1998). Evolution and development of modular control architec- tures for 1D locomotion in six-legged animats. Connection Science, 10:211–237.

Kohl, N., and Stone, P. (2004a). Machine learning for fast quadrupedal locomotion. In Nineteenth National Conference on Artificial Intelligence.

Kohl, N., and Stone, P. (2004b). Policy gradient reinforcement learning for fast quadrupedal lo- comotion. In Proceedings of the IEEE International Conference on Robotics and Automation, vol. 3, 2619–2624.

Koos, S., Mouret, J.-B., and Doncieux, S. (2010). Crossing the reality gap in evolutionary robotics by promoting transferable controllers. In GECCO ’10: Proceedings of the 12th annual conference on Genetic and evolutionary computation, 119–126. New York, NY, USA: ACM.

Korenek, J., and Sekanina, L. (2005). Intrinsic evolution of sorting networks: A novel complete hardware implementation for FPGAs. In Evolvable Systems: From Biology to Hardware, 46–55. Springer. http://dx.doi.org.ezproxy.lib.utexas.edu/10.1007/11549703_5

Korshunov, A. D. (2003). Monotone boolean functions. Russian Mathematical Surveys, 58(5):929. http://stacks.iop.org/0036-0279/58/i=5/a=R02

Kovacs, A. (1986). Spontaneous symmetry breaking in biological systems. Origins of Life and Evolution of Biospheres, 16:429–430. http://dx.doi.org/10.1007/BF02422114

Koza, J. R., Goldberg, D. E., Fogel, D. B., and Riolo, R. L., editors (1996). Genetic Programming 1996. Cambridge, MA: MIT Press.

Koza, J. R., Koza, J. R., Forest H. Bennett, I., Forest H. Bennett, I., Hutchings, J. L., Bade, S. L., Keane, M. A., and Andre, D. (1998). Evolving computer programs using rapidly reconfigurable field-programmable gate arrays and genetic programming. In FPGA ’98: Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays, 209–219. New York, NY, USA: ACM.

le Cun, Y., Denker, J. S., and Solla, S. A. (1990). Optimal brain damage. In Touretzky (1990), 598–605.

Leighton, T., and Plaxton, C. G. (1990). A (fairly) simple circuit that (usually) sorts. In SFCS ’90: Proceedings of the 31st Annual Symposium on Foundations of Computer Science, 264–274 vol.1. Washington, DC, USA: IEEE Computer Society.

Lindenmayer, A. (1968). Mathematical models for cellular interaction in development parts I and II. Journal of Theoretical Biology, 18:280–299 and 300–315.

Lipson, H., Bongard, J., Zykov, V., and Malone, E. (2006). Evolutionary robotics for legged ma- chines: From simulation to physical reality. In Proceedings of the 9th International Conference on Intelligent Autonomous Systems., 11–18.

Luke, S., and Spector, L. (1996). Evolving graphs and networks with edge encoding: Preliminary report. In Koza, J. R., editor, Late-Breaking Papers of Genetic Programming 1996. Stanford Bookstore. http://citeseer.nj.nec.com/128010.html

Martindale, M. Q., and Henry, J. Q. (1998). The development of radial and biradial symmetry: The evolution of bilaterality. American Zoologist, 38(4):672–684.

Mataric, M., and Cliff, D. (1996). Challenges in evolving controllers for physical robots. Robotics and Autonomous Systems, 19(1):67–83.

McFarlane, D. (1998). Modular distributed manufacturing systems and the implications for inte- grated control. In IEE Colloquium on Choosing the Right Control Structure for Your Process (Digest No. 1998/280).

Mehta, D. P., and Sahni, S. (2005). Handbook of data structures and applications. CRC Press.

Miglino, O., Lund, H. H., and Nolfi, S. (1995). Evolving mobile robots in simulated and real environments. Artificial Life, 2:417–434. http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=retrieve&db=pubmed&dopt=abstract&list_uids=8942055

Miller, J. F. (2004). Evolving a self-repairing, self-regulating, French flag organism. In Proceed- ings of the Genetic and Evolutionary Computation Conference (GECCO-2004). Berlin: Springer Verlag. http://www.elec.york.ac.uk/intsys/users/jfm7/gecco2004.pdf

M ̈uhlenbein, H., and H ̈ons, R. (2005). The estimation of distributions and the minimum relative entropy principle. Evolutionary Computation, 13(1):1–27.

Murtagh, F. (2002). Clustering in massive data sets. In Abello, J., Pardalos, P. M., and Resende, M. G. C., editors, Handbook of Massive Data Sets, chapter 14, 501–543. Norwell, MA, USA: Kluwer Academic Publishers.

Nolfi, S., Floreano, D., Miglino, O., and Mondada, F. (1994). How to evolve autonomous robots: Different approaches in evolutionary robotics. In Brooks and Maes (1994), 190–197. Objet Eden 260V (2010). Objet Eden 260V. http://www.mpi-sb.mpg.de/services/library/proceedings/contents/alife94.html


ODE (2007). ODE: Open dynamics engine. http://www.ode.org/.

OGRE (2007). OGRE: Object-oriented graphics rendering engine. http://www.ogre3d.org/.

OPAL (2007). OPAL: Open physics abstraction layer. http://opal.sourceforge.net/.

Open BEAGLE (2007). Open BEAGLE. http://beagle.gel.ulaval.ca/.

Palmer, A. R. (2004). Symmetry breaking and the evolution of development. Science, 306:828–833. Pinto, C. M. A., and Golubitsky, M. (2006). Central pattern generators for bipedal locomotion. Journal of Mathematical Biology, 53(3):474–489.

Raibert, M. H. (1986). Legged robots. Communications of the ACM, 29(6):499–514.

103Raibert, M. H., Chepponis, M., and H. Benjamin Brown, J. (1986). Running on four legs as though they were one. IEEE Journal of Robotics and Automation, 2(2):70–82.

Righetti, L., and Ijspeert, A. J. (2008). Pattern generators with sensory feedback for the control of quadruped locomotion. In Proceedings of the 2008 IEEE International Conference on Robotics and Automation (ICRA 2008), 819–824.

Robotis (2010). Robotis. http://www.robotis.com/.

Rumelhart, D. E., Hinton, G. E., and Williams, R. J. (1986). Learning internal representations by error propagation. In Rumelhart, D. E., and McClelland, J. L., editors, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1: Foundations, 318–362. Cambridge, MA: MIT Press.

Seo, K., and Slotine, J. J. E. (2007). Models for global synchronization in CPG-based locomotion. In Proceedings of the 2007 IEEE International Conference on Robotics and Automation, 281– 286.

Seo, S.-W., yun Feng, T., and Kim, Y. (1993). A simulation scheme in rearrangeable networks. In Proceedings of the 36th Midwest Symposium on Circuits and Systems, 177 – 180 vol. 1.

Shastri, S. V. (1997). A biologically consistent model of legged locomotion gaits. Biological Cybernetics, 76(6):429–440.

Shmulevich, I., Sellke, T. M., Gabbouj, M., and Coyle, E. J. (1995). Stack filters and free distributive lattices. In Proceedings of the 1995 IEEE Workshop on Nonlinear Signal and Image Processing, 927–930. IEEE Computer Society.

Siebel, N. T., and Sommer, G. (2007). Evolutionary reinforcement learning of artificial neural networks. International Journal of Hybrid Intelligent Systems, 4(3):171–183.

Sims, K. (1994a). Evolving 3D morphology and behavior by competition. In Brooks and Maes (1994), 28–39.

Sims, K. (1994b). Evolving 3D morphology and behavior by competition. In Brooks, R. A., and Maes, P., editors, Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems (Artificial Life IV), 28–39. Cambridge, MA: MIT Press. SolidWorks (2010). SolidWorks. http://www.solidworks.com/.

Stanley, K. (2007). Compositional pattern producing networks: A novel abstraction of development. Genetic Programming and Evolvable Machines, 8(2):131–162.

Stanley, K. O., D’Ambrosio, D. B., and Gauci, J. (2009). A Hypercube-Based encoding for evolving Large-Scale neural networks. Artificial Life, 15(2):185–212.

Stanley, K. O., and Miikkulainen, R. (2003). A taxonomy for artificial embryogeny. Artificial Life, 9(2):93–130. http://nn.cs.utexas.edu/keyword?stanley:alife03

Stanley, K. O., and Miikkulainen, R. (2004). Competitive coevolution through evolutionary com- plexification. Journal of Artificial Intelligence Research, 21:63–100. http://nn.cs.utexas.edu/keyword?stanley:jair04

Steiner, T., Jin, Y., and Sendhoff, B. (2009). Vector field embryogeny. PLoS ONE, 4(12):e8177. Stone, P., and Veloso, M. (2000). Multiagent systems: A survey from a machine learning perspec- tive. Autonomous Robots, 8(3):345–383.

T ́ellez, R. A., Angulo, C., and Pardo, D. E. (2006). Evolving the walking behaviour of a 12 DOF quadruped using a distributed neural architecture. In Biologically Inspired Approaches to Advanced Information Technology, Lecture Notes in Computer Science 3853, 5–19. Berlin: Springer.

Touretzky, D. S., editor (1990). Advances in Neural Information Processing Systems 2. San Fran- cisco: Morgan Kaufmann.

Watson, R. A., Ficici, S. G., and Pollack, J. B. (2002). Embodied evolution: Distributing an evolu- tionary algorithm in a population of robots. Robotics and Autonomous Systems, 39(1):1 – 18.

Watson, R. A., and Jansen, T. (2007). A building-block royal road where crossover is provably essential. In Proceedings of the 9th annual conference on Genetic and evolutionary computation (GECCO ’07), 1452–1459. New York, NY, USA: ACM.

Yeh, Y.-M., and Feng, T.-y. (1992). On a class of rearrangeable networks. IEEE Transactions on Computers, 41(11):1361–1379.

Zagal, J. C., and Ruiz-Del-Solar, J. (2007). Combining simulation and reality in evolutionary robotics. Journal of Intelligent and Robotic Systems, 50(1):19–39.

Zhang, S. S., Xu, K., and Jow, T. R. (2003). The low temperature performance of li-ion batteries. Journal of Power Sources, 115(1):137 – 140. http://www.sciencedirect.com/science/article/B6TH1-47JCRT5-2/2/ba618d9d10f2bc31473b7aca3bdfb151

Zykov, V., Bongard, J., and Lipson, H. (2004). Evolving dynamic gaits on a physical robot. In Proceedings of the Genetic and Evolutionary Computation Conference, Late-Breaking Papers.


Full Text


intern file

Sonstige Links