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Emergence of genomic self-similarity in location independent representations

Favoring positive correlation between the form and quality of candidate solutions

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Abstract

A key property for predicting the effectiveness of stochastic search techniques, including evolutionary algorithms, is the existence of a positive correlation between the form and the quality of candidate solutions. In this paper we show that when the ordering of genomic symbols in a genetic algorithm is completely independent of the fitness function and therefore free to evolve along with the candidate solutions it encodes, the resulting genomes self-organize into self-similar structures that favor this key stochastic search property.

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References

  1. J. D. Bagley, “The behavior of adaptive systems which employ genetic and correlation algorithms,” PhD thesis, University of Michigan, 1967.

  2. W. Banzhaf, P. Dittrich, and B. Eller, “Selforganization in a system of binary strings with topological interactions,” Physica D, vol. 125, pp. 85–104, 1999.

  3. P. J. Bentley, “Natural Design by Computer,” in Proceedings of the 2003 AAAI Spring Symposioum: Computational Synthesis: From Basic Building Blocks to High Level Functionality, American Association for Artificial Intelligence, AAAI Press, 2003, pp. 1–2. Technical Report SS-03-02.

  4. P. J. Bentley, “Fractal proteins,” Genetic Programming and Evolvable Machines Journal, vol. 5, pp. 71–101, 2004

  5. D. S. Burke, K. A. De Jong, J. J. Grefenstette, C. L. Ramsey and A. S. Wu, “Putting more genetics into genetic algorithms.” Evolutionary Computation, vol. 6, pp. 387–410, 1998.

  6. M. Conrad, “Computation: evolutionary, neural, molecular,” in 2000 IEEE Symposium on Combinations of Evolutionary Computation and Neural Networks 2000, pp. 1–9.

  7. L. J. Eshelman, R. A. Caruana and J. D. Schaffer, “Biases in the crossover landscape,” in Proc. 3rd Int’l Conference on Genetic Algorithms, J. D. Schaffer (ed.). 1989, pp. 10–19.

  8. R. W. Franceschini, A. S. Wu and A. Mukherjee, “Computational strategies for disaggregation,” in Proc. 9th Conf. on Computer Generated Forces and Behavioral Representation, Simulation Interoperability Standards Organization (SISO), 2000, pp. 543–554.

  9. D. R. Frantz, “Non-linearities in genetic adaptive search,” PhD thesis, University of Michigan, 1972.

  10. I. Garibay, “The proteomics approach to evolutionary computation: an analysis of proteome-based location independent representations based on the proportional genetic algorithm,” PhD thesis, University of Central Florida, 2004.

  11. M. Garzon, D. Blain, K. Bobba, A. Neel, and M. West, “Self-assembly of DNA-like structures in Silico,” Genetic Programming and Evolvable Machines vol. 4, pp.185–200, 2003.

  12. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, 1989.

  13. D. E. Goldberg, K. Deb, H. Kargupta, and G. Harik, “Rapid accurate optimization of difficult problems using fast messy genetic algorithms.” in Proc. 5th Int’l Conference on Genetic Algorithms, S. Forrest, (ed.), 1993, pp. 56–64.

  14. D. E. Goldberg, B. Korb, and K. Deb, “Messy genetic algorithms: Motivation, analysis, and first results,” Complex Systems, vol. 3, pp. 493–530, 1989.

  15. J. Grefenstette, C. L. Ramsey and A. C. Schultz, “Learning sequential decision rules using simulation models and competition,” Machine Learning, vol. 5, pp. 355–381, 1990.

  16. G. R. Harik, “Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms,” Ph. D thesis, University of Michigan, 1997.

  17. J. H. Holland, “Adaptation in Natural and Artificial Systems,” University of Michigan Press, Ann Arbor, MI, 1975.

  18. J. H. Holland, Emergence: From Chaos to Order, Addison-Wesley, 1998.

  19. G. S. Hornby, H. Lipson, and J. B. Pollack, “Generative representations for the automated design of modular physical robots,” IEEE Transactions on Robotics and Automation, vol. 19, pp. 703–719, 2003.

  20. G. S. Hornby, and J. B. Pollack, “Creating high-level components with a generative representation for body-brain evolution,” Artificial Life, vol. 8, pp. 223–246, 2002.

  21. H. Kargupta, “The gene expression messy genetic algorithm,” in Proc. IEEE Int’l Conference on Evolutionary Computation, IEEE Press, pp. 814–819, 1996.

  22. J. R. Koza, F. H Bennett III, D. Andre, and M. A. Keane, Genetic Programming III, Morgan Kaufmann Publishers, 1999.

  23. J. R. Koza, M. A. Keane, M. J. Streeter, W. Mydlowec, J. Yu, and G. Lanza, Genetic Programming IV: Routine Human-Competitive Machine Intelligence, Kluwer Academic Publishers, 2003. ISBN 1-4020-7446-8.

  24. J. R. Koza, M. J. Streeter, and M. A. Keane, “Automated synthesis by means of genetic programming of human-competitive designs employing reuse, hierarchies, modularities, development, and parameterized topologies,” in Proceedings of the 2003 AAAI Spring Symposioum: Computational Synthesis: From basic Building Blocks to High Level Functionality, American Association for Artificial Intelligence, AAAI Press, pp. 138–145, 2003. Technical Report SS-03-02.

  25. S. Kumar, “Multicellular development, self-organization, and differentiation,” in Proc. GECCO 2004 Workshop on Self-organization in Representations for Evolutionary Algorithms: Building Complexity from Simplicity, 2004.

  26. S. Kumar and P. J Bentley, (eds.) On Growth, Form and Computers, Academic Press, 2003.

  27. B. B. Mandelbrot, The Fractal Geometry of Nature, San Francisco : W.H. Freeman, 1982.

  28. B. B. Mandelbrot, Multifractals and 1/f Noise. Springer, 1999.

  29. H. A. Mayer, “Genetic algorithms evolving noncoding segments by means of promoter/terminator sequences,” Evolutionary Computation, vol. 6, pp. 361–386, 1998.

  30. J. Miller and P. Thomson, “Beyond the complexity ceiling: evolution, emergence and regeneration,” in Proc. GECCO 2004 Workshop on Regeneration and Learning in Developmental Systems, 2004.

  31. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, 1984.

  32. N. J. Radcliffe, “Schema processing. handbook of evolutionary computation,” in Iop Institute of Physics, T. Back, D. Fogel, and Z. Michalewicz, (eds.), 1997. pp. B2.5:1–B2.5:10.

  33. F. Reif, Fundamentals of Statistical and Thermal Physics, Chapter Irreversible Processes and Fluctuations, McGraw-Hill, 1965.

  34. H. S. Robertson, Statistical Thermophysics, chapter Fluctuations. Prentice-Hall, 1993.

  35. L. Mateus Rocha, “Evolving Memory: logical tasks for cellular automata,” in Proc. Ninth International Conference on the Simulation and Synthesis of Living Systems (ALIFE9), J. Pollack, M. Bedau, P. Husbands, T. Ikegami, and R. Watson (eds.), Cambridge, Massachusetts, pp. 256–261, 2004, MIT Press.

  36. T. Soule and A. E. Ball, “A genetic algorithm with multiple reading frames,” in Proc. Genetic and Evolutionary Computation Conference, L. Spector, E. D. Goodman, A. S. Wu, W. B. Langdon, H. M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, and E. Burke (eds), pp. 615–622, 2001.

  37. G. Syswerda, “Uniform crossover in genetic algorithms,” in Proc. 3rd Int’l Conference on Genetic Algorithms, H. Schaffer (ed.), San Mateo, Morgan Kaufmannm, pp. 2–9, 1989.

  38. R. F. Voss, “Evolution of long-range fractal correlations and 1/f noise in DNA base sequences,” Physical Review Letters, vol. 68, pp. 3805–3808, 1992.

  39. R. F. Voss, “1/f Noise and Fractals in DNA-base Sequences,” in Applications of Fractals and Chaos, Crilly, Earnshaw and Jones (eds.), pp. 7–20, Springer-Verlag, 1993.

  40. A. S. Wu and I. Garibay, “The proportional genetic algorithm: Gene expression in a genetic algorithm,” Genetic Programming and Evolvable Hardware, vol. 3, pp. 157–192, 2002.

  41. A. S. Wu and I. Garibay, “Intelligent automated control of life support systems using proportional representations,” in IEEE Transactions on Systems Man, and Cybernetics—Part B vol. 34, pp. 1423–1434, 2004.

  42. A. S. Wu and R. K. Lindsay, “A comparison of the fixed and floating building block representation in the genetic algorithm,” Evolutionary Computation, vol. 4, pp. 169–193, 1996.

  43. A. S. Wu, A. C. Schultz, and A. Agah, “Evolving control for distributed micro air vehicles,” in Proc. IEEE Int’l Symp. Computational Intelligence in Robotics and Automation, Monterey, California, IEEE Robotics and Automation Society, 1999, pp. 174–179

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Correspondence to Ivan Garibay.

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Garibay, I., Wu, A.S. & Garibay, O. Emergence of genomic self-similarity in location independent representations. Genet Program Evolvable Mach 7, 55–80 (2006). https://doi.org/10.1007/s10710-006-7011-4

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  • DOI: https://doi.org/10.1007/s10710-006-7011-4

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