Abstract
Reaction-diffusion systems contribute to various morphogenetic processes, and can also be used as computation models in real and artificial chemistries. Evolving reaction-diffusion solutions automatically is interesting because it is otherwise difficult to engineer them to achieve a target pattern or to perform a desired task. However most of the existing work focuses on the optimization of parameters of a fixed reaction network. In this paper we extend this state of the art by also exploring the space of alternative reaction networks, with the help of GPU hardware. We compare parameter optimization and reaction network optimization on the evolution of reaction-diffusion solutions leading to simple spot patterns. Our results indicate that these two optimization modes tend to exhibit qualitatively different evolutionary dynamics: in the former, the fitness tends to improve continuously in gentle slopes, while the latter tends to exhibit large periods of stagnation followed by sudden jumps, a sign of punctuated equilibria.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adamatzky, A., Costello, B.D.L., Asai, T.: Reaction-Diffusion Computers. Elsevier Science Inc., New York (2005)
Banzhaf, W., Harding, S., Langdon, W.B., Wilson, G.: Accelerating Genetic Programming through Graphics Processing Units. In: Genetic Programming Theory and Practice VI, pp. 1–19. Springer, US (2009)
Breyer, J., Ackermann, J., McCaskill, J.: Evolving Reaction-Diffusion Ecosystems with Self-Assembling Structures in Thin Films. Artificial Life 4(1), 25–40 (1998)
Calabretta, R., Nolfi, S., Parisi, D., Wagner, G.P.: Duplication of Modules Facilitates the Evolution of Functional Specialization. Artificial Life 6(1), 69–84 (2000)
Dale, K., Husbands, P.: The Evolution of Reaction-Diffusion Controllers for Minimally Cognitive Agents. Artificial Life 16(1), 1–20 (2010)
Deutsch, A., Dormann, S.: Cellular automaton modeling of biological pattern formation: characterization, applications, and analysis. Birkhäuser (2005)
Fujita, H., Mochizuki, A.: The Origin of the Diversity of Leaf Venation Pattern. Developmental Dynamics 235(10), 351–361 (2006)
Fukagata, K., Kern, S., Chatelain, P., Koumoutsakos, P., Kasagi, N.: Evolutionary optimization of an anisotropic compliant surface for turbulent friction drag reduction. Journal of Turbulence 9(35), 1–17 (2008)
Graván, C.P., Lahoz-Beltra, R.: Evolving morphogenetic fields in the zebra skin pattern based on Turing’s morphogen hypothesis. Int. J. Appl. Math. Comp. Sci. 14(3), 351–361 (2004)
Gray, P., Scott, S.: Chemical Oscillations and Instabilities: Nonlinear Chemical Kinetics. Oxford Science Publications, Oxford (1990)
Grzybowski, B.A., Bishop, K.J.M., Campbell, C.J., Fialkowski, M., Smoukov, S.K.: Micro-and nanotechnology via reaction-diffusion. Soft Matter 1, 114–128 (2005)
Hohm, T., Zitzler, E.: A Hierarchical Approach to Model Parameter Optimization for Developmental Systems. BioSystems 102, 157–167 (2010)
Koch, A.J., Meinhardt, H.: Biological pattern formation: from basic mechanisms to complex structures. Reviews of Modern Physics 66 (1994)
Lenser, T., Hinze, T., Ibrahim, B., Dittrich, P.: Towards Evolutionary Network Reconstruction Tools for Systems Biology. In: Marchiori, E., Moore, J.H., Rajapakse, J.C. (eds.) EvoBIO 2007. LNCS, vol. 4447, pp. 132–142. Springer, Heidelberg (2007)
Lowe, D., Miorandi, D., Gomez, K.: Activation- inhibition-based data highways for wireless sensor networks. In: Proc. Bionetics. ICST (2009)
Maitre, O., Baumes, L.A., Lachiche, N., Corma, A., Collet, P.: Coarse grain parallelization of evolutionary algorithms on GPGPU cards with EASEA. In: Proc. GECCO, pp. 1403–1410 (2009)
Meinhardt, H.: Models of biological pattern formation. Academic Press, London (1982)
Meinhardt, H.: The Algorithmic Beauty of Sea Shells, 4th edn. Springer, Heidelberg (2009)
Meng, Y., Zhang, Y., Jin, Y.: Autonomous self-reconfiguration of modular robots by evolving a hierarchical mechanochemical model. IEEE Computational Intelligence Magazine 6(1), 43–44 (2011)
Molnár Jr., F., Izsák, F., Mészáros, R., Lagzi, I.: Simulation of reaction-diffusion processes in three dimensions using CUDA. ArXiv e-prints (April 2010)
Murray, J.D.: Mathematical Biology: Spatial Models and Biomedical Applications, vol. 2. Springer, Heidelberg (2003)
Neglia, G., Reina, G.: Evaluating activator-inhibitor mechanisms for sensors coordination. In: Proc. Bionetics. ICST (2007)
Pearson, J.E.: Complex patterns in a simple system. Science 261(5118), 189–192 (1993)
Sanderson, A.R., Meyer, M.D., Kirby, R.M., Johnson, C.R.: A framework for exploring numerical solutions of advection-reaction-diffusion equations using a GPU-based approach. Computing and Visualization in Science 12(4), 155–170 (2009)
Shen, W.M., Will, P., Galstyan, A., Chuong, C.M.: Hormone-inspired self-organization and distributed control of robotic swarms. Autonomous Robots 17(1), 93–105 (2004)
Streichert, F., Spieth, C., Ulmer, H., Zell, A.: How to evolve the head-tail pattern from reaction-diffusion systems. In: NASA/DoD Conference on Evolvable Hardware, pp. 261–268. IEEE Computer Society Press, Los Alamitos (2004)
Turing, A.M.: The chemical basis of morphogenesis. Phil. Trans. Royal Soc. London B 327, 37–72 (1952)
Yamamoto, L., Miorandi, D.: Evaluating the Robustness of Activator-Inhibitor Models for Cluster Head Computation. In: Dorigo, M., Birattari, M., Di Caro, G.A., Doursat, R., Engelbrecht, A.P., Floreano, D., Gambardella, L.M., Groß, R., Şahin, E., Sayama, H., Stützle, T. (eds.) ANTS 2010. LNCS, vol. 6234, pp. 143–154. Springer, Heidelberg (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yamamoto, L., Banzhaf, W., Collet, P. (2011). Evolving Reaction-Diffusion Systems on GPU. In: Antunes, L., Pinto, H.S. (eds) Progress in Artificial Intelligence. EPIA 2011. Lecture Notes in Computer Science(), vol 7026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24769-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-24769-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24768-2
Online ISBN: 978-3-642-24769-9
eBook Packages: Computer ScienceComputer Science (R0)