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Genetic Programming Theory and Practice IV pp 237–256Cite as

Phase Transitions in Genetic Programming Search

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Part of the book series: Genetic and Evolutionary Computation ((GEVO))

Abstract

Phase transitions occur in computational, as well as thermodynamic systems. Of particular interest is the possibility that phase transitions occur as a consequence of GP search. If this were so, it would allow for a statistical mechanics approach and quantitative comparisons of GP with a broad variety of rigorously described systems. This chapter summarizes our research group’s work in this area and describes a case study that illustrates what is involved in establishing the existence of phase transitions in GP search.

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References

  • Achlioptas, D., Naor, A., and Peres, Y. (2005). Rigorous location of phase transitions in hard optimization problems. Nature, 435(7043):759–754.

    Article  Google Scholar 

  • Adamic, L.A., Lukose, R.M., Puniyani, A.R., and Huberman, B.A. (2001). Search in power-law networks. Phys Rev E, 64(4):046135/1–8.

    Article  Google Scholar 

  • Barabási, A.L. (2003). Emergence of scaling in complex networks. In Bornholdt, S. and Schuster, P., editors, Handbook of Graphs and Networks, pages 69–84. Wiley-VCH, Weinheim.

    Google Scholar 

  • Beottcher, S. and Percus, A.G. (2000). Combining local search with co-evolution in a remarkably simple way. In CEC, pages 1578–1584, La Jolla, CA, USA. IEEE.

    Google Scholar 

  • Beottcher, S. and Percus, A.G. (2001). External optimization for graph partioning. Phys Rev E, 64(2 II):26114/1–13.

    Google Scholar 

  • Bianconi, G. and Barabási, A.L. (2001). Bose-einstein condensation in complex networks. Physical Review Letters, 86(24):5632–5635.

    Article  Google Scholar 

  • Chan, M.H.W. (2001). Critical Phenomena. McGraw-Hill.

    Google Scholar 

  • Cheeseman, P., Kanefsky, B., and Taylor, W. (1991). Where the really hard problems are. In Proc lnt Joint Conf on AI, pages 331–337. Morgan Kaufmann.

    Google Scholar 

  • Clearwater, S.H. and Hogg, T. (1996). Problem structure heuristics and scaling behavior for genetic algorithms. AI, 81(1–2):327.

    MathSciNet  Google Scholar 

  • Correale, L., Leone, M., Pagnani, A., Weight, M., and Zecchina, R (2006). Core percolation and onset of complexity in boolean networks. Phys Rev Letters, 96(1):018101/1–4.

    Article  Google Scholar 

  • Crutchfield, J.P. and Mitchell, M. (1995). The evolution of emergent computation. Proceedings of the National Academy of Sciences of the United States of America, 92(23): 10742–10746.

    Article  MATH  Google Scholar 

  • Crutchfield, J.P. and Schuster, P. (2003). Evolutionary Dynamics: Exploring the Interplay of Selection, Accident, Neutrality, and function. Oxford University Press, New York.

    MATH  Google Scholar 

  • Daida, Jason (2004). Considering the roles of structure in problem solving by a computer. In O’Reilly, Una-May, Yu, Tina, Riolo, Rick L., and Worzel, Bill, editors, Genetic Programming Theory and Practice II, chapter 5, pages 67–86. Springer, Ann Arbor.

    Google Scholar 

  • Daida, Jason, Ward, David, Hilss, Adam, Long, Stephen, and Hodges, Mark (2004). Visualizing the loss of diversity in genetic programming. In Proceedings of the 2004 IEEE Congress on Evolutionary Computation, pages 1225–1232, Portland, Oregon. IEEE Press.

    Chapter  Google Scholar 

  • Daida, Jason M. (2003). What makes a problem GP-hard? A look at how structure affects content. In Riolo, Rick L. and Worzel, Bill, editors, Genetic Programming Theory and Practice, chapter 7, pages 99–118. Kluwer.

    Google Scholar 

  • Daida, Jason M. (2005). Towards identifying populations that increase the likelihood of success in genetic programming. In Beyer, Hans-Georg, O’Reilly, Una-May, Arnold, Dirk V., Banzhaf, Wolfgang, Blum, Christian, Bonabeau, Eric W., Cantu-Paz, Erick, Dasgupta, Dipankar, Deb, Kalyanmoy, Foster, James A., de Jong, Edwin D., Lipson, Hod, Llora, Xavier, Mancoridis, Spiros, Pelikan, Martin, Raidl, Guenther R., Soule, Terence, Tyrrell, Andy M., Watson, Jean-Paul, and Zitzler, Eckart, editors, GECCO 2005: Proceedings of the 2005 conference on Genetic and evolutionary computation, volume 2, pages 1627–1634, Washington DC, USA. ACM Press.

    Chapter  Google Scholar 

  • Daida, Jason M., Bertram, Robert R., Polito 2, John A., and Stanhope, Stephen A. (1999a). Analysis of single-node (building) blocks in genetic programming. In Spector, Lee, Langdon, William B., O’Reilly, Una-May, and Angeline, Peter J., editors, Advances in Genetic Programming 3, chapter 10, pages 217–241. MIT Press, Cambridge, MA, USA.

    Google Scholar 

  • Daida, Jason M. and Hilss, Adam M. (2003). Identifying structural mechanisms in standard genetic programming. In Cantú-Paz, E., Foster, J. A., Deb, K., Davis, D., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Standish, R., Kendall, G., Wilson, S., Harman, M., Wegener, J., Dasgupta, D., Potter, M. A., Schultz, A. C., Dowsland, K., Jonoska, N., and Miller, J., editors, Genetic and Evolutionary Computation — GECCO-2003, volume 2724 of LNCS, pages 1639–1651, Chicago. Springer-Verlag.

    Google Scholar 

  • Daida, Jason M., Hilss, Adam M., Ward, David J., and Long, Stephen L. (2003). Visualizing tree structures in genetic programming. In Cantú-Paz, E., Foster, J. A., Deb, K., Davis, D., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Standish, R., Kendall, G., Wilson, S., Harman, M., Wegener, J., Dasgupta, D., Potter, M. A., Schultz, A. C., Dowsland, K., Jonoska, N., and Miller, J., editors, Genetic and Evolutionary Computation — GECCO-2003, volume 2724 of LNCS, pages 1652–1664, Chicago. Springer-Verlag.

    Google Scholar 

  • Daida, Jason M., Polito, John A., Stanhope, Steven A., Bertram, Robert R., Khoo, Jonathan C., and Chaudhary, Shahbaz A. (1999b). What makes a problem GP-hard? analysis of a tunably difficult problem in genetic programming. In Banzhaf, Wolfgang, Daida, Jason, Eiben, Agoston E., Garzon, Max H., Honavar, Vasant, Jakiela, Mark, and Smith, Robert E., editors, Proceedings of the Genetic and Evolutionary Computation Conference, volume 2, pages 982–989, Orlando, Florida, USA. Morgan Kaufmann.

    Google Scholar 

  • Daida, Jason M., Samples, Michael E., and Byom, Matthew J. (2005). Probing for limits to building block mixing with a tunably-difficult problem for genetic programming. In Beyer, Hans-Georg, O’Reilly, Una-May, Arnold, Dirk V, Banzhaf, Wolfgang, Blum, Christian, Bonabeau, Eric W., Cantu-Paz, Erick, Dasgupta, Dipankar, Deb, Kalyanmoy, Foster, James A., de Jong, Edwin D., Lipson, Hod, Llora, Xavier, Mancoridis, Spiros, Pelikan, Martin, Raidl, Guenther R., Soule, Terence, Tyrrell, Andy M., Watson, Jean-Paul, and Zitzler, Eckart, editors, GECCO 2005: Proceedings of the 2005 conference on Genetic and evolutionary computation, volume 2, pages 1713–1720, Washington DC, USA. ACM Press.

    Chapter  Google Scholar 

  • Daida, J.M., Bertram, R.R., Stanhope, S.A., Khoo, J.C., Chaudhary, S.A., Chaudhri, O.A., and II, J.A. Polito (2001). What makes a problem gp-hard? analysis of a tunably difficult problem in genetic programming. GPEM, 2(2):165–191.

    MATH  Google Scholar 

  • Erdos, P. and Rényi, A. (1960). On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5:17–61.

    Google Scholar 

  • Gao, Y. and Culberson, J. (2002). An analysis of phase transitions in nk landscapes. JAIR, 17:309–332.

    MATH  MathSciNet  Google Scholar 

  • Hartmann, A. and Weight, M. (2005). Phase transitions in combinatory optimization problems. Wiley-VCH, Berlin.

    Google Scholar 

  • Hogg, T., Huberman, B.A., and Williams, C.P. (1996). Phase transitions and the search problem. AI, 81(1–2):1–15.

    Google Scholar 

  • Huberman, B.A. and Hogg, T. (1987). Phase transitions and ai systems. AI, 33(2): 155–177.

    Google Scholar 

  • Huberman, B.A., Lukose, R.M., and Hogg, T. (1997). An economics approach to hard computational problems. Science, 275(5296):51–54.

    Article  Google Scholar 

  • Izumi, K. and Ueda, K. (2001). Phase transition in a foreign exchange market-analysis based on an artificial market approach. IEE TEC, 5(5):456.

    Google Scholar 

  • Janson, S., Luczak, T., and Rucinski, A. (1999). Random Graphs. John Wiley, New York.

    Google Scholar 

  • Koza, John R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA.

    MATH  Google Scholar 

  • McPhee, Nicholas Freitag and Poli, Riccardo (2000). A schema theory analysis of the evolution of size in genetic programming with linear representations. Technical Report CSRP-00-22, University of Birmingham, School of Computer Science.

    Google Scholar 

  • Mitchell, D., Selman, B., and Levesque, H. (1992). Hard and easy distributions of sat problems. In Rosenbloom, P. and Szolovits, P., editors, Tenth National Conference on AI, pages 459–465, Menlo Park. AAAI.

    Google Scholar 

  • Mitchell, M., Hraber, P.T., and Crutchfield, J.P. (1993). Revisiting the edge of chaos: evolving cellular automata to perform computations. Complex Systems, 7(2):89–130.

    MATH  Google Scholar 

  • Mohamed, H.M., Munzir, S., Abdulmuin, M.Z., and Hameida, S. (2000). Fuzzy modeling and control of a spark ignition engine idle mode. In TENCON, pages II-586–II-591, Kuala Lumpur. IEEE.

    Google Scholar 

  • Naudts, B. and Schoofs, L. (2002). Ga performance distributions and randomly generated binary constraint satisfaction problems. Theoretical COmputer Science, 287(1):167–185.

    Article  MATH  MathSciNet  Google Scholar 

  • Oates, M.J., Corne, D.W., and Loader, R.J. (2000). Tri-phase performance profile of evolutionary search on uni-and multi-modal search spaces. In CEC, pages 357–364, La Jolla. IEEE.

    Google Scholar 

  • Oda, A., Nagao, H., Kitagawa, Y., Shigeta, Y., and Yamaguchi, K. (2000). Theoretical studies on magnetic behavior in clusters by the genetic algorithms. International Journal of Quantum Chemistry, 80(4–5):646–656.

    Article  Google Scholar 

  • Samples, M.E., Byom, M.J., and Daida, J.M. (2006). Parameter sweeps for exploring parameter spaces of evolutionary algorithms. In Lobo, F.G., Lima, C.F., and Michalewicz, Z., editors, Parameter Settings in Evolutionary Algorithms, New York. Springer.

    Google Scholar 

  • Sellmyer, D.J. and Jaswal, S.S. (2002). Phase transitions. McGraw-Hill, New York.

    Google Scholar 

  • Shimazaki, H. and Niebur, E. (2005). Phase transitions in multiplicative competitive processes. Physical Review E, 72(1):1–4.

    Article  Google Scholar 

  • Stanley, H.E. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, New York.

    Google Scholar 

  • Toulouse, M., Crainic, T., and Sansó, B. (2004). Systemic behavior of cooperative search algorithms. Parallel Computing, 30(1):57–79.

    Article  MathSciNet  Google Scholar 

  • van Hemert, J.I. and Urquhart, N.B. (2004). Phase transition properties of clustered traveling salesman problem instances generated with ec. In PPSN, pages 151–160, Birmingham. Springer-Verlag.

    Google Scholar 

  • Yamamoto, K. and Naito, S. (2002). A study on schema preservation by crossover. Systems and Computers in Japan, 33(2):64–76.

    Article  Google Scholar 

  • Zhang, F. and Dozier, G. (2004). A comparison of distributed restricted recombination operators for gec societies of hill-climbers: a disacsp perspective. In CEC, pages 1988–1995, Portland. IEEE.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Center for the Study of Complex Systems and Space Physics Research Laboratory, The University of Michigan, USA

    Jason M. Daida, Ricky Tang, Michael E. Samples & Matthew J. Byom

Authors
  1. Jason M. Daida
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  2. Ricky Tang
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  3. Michael E. Samples
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  4. Matthew J. Byom
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Editor information

Editors and Affiliations

  1. Center for the Study of Complex Systems, University of Michigan, USA

    Rick Riolo

  2. University of Idaho, USA

    Terence Soule

  3. Genetics Squared, Inc., USA

    Bill Worzel

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Daida, J.M., Tang, R., Samples, M.E., Byom, M.J. (2007). Phase Transitions in Genetic Programming Search. In: Riolo, R., Soule, T., Worzel, B. (eds) Genetic Programming Theory and Practice IV. Genetic and Evolutionary Computation. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-49650-4_15

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  • DOI: https://doi.org/10.1007/978-0-387-49650-4_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-33375-5

  • Online ISBN: 978-0-387-49650-4

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