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What Makes a Problem GP-Hard?

A Look at How Structure Affects Content

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Part of the book series: Genetic Programming Series ((GPEM,volume 6))

Abstract

This chapter summarizes theoretical work at The University of Michigan concerning the question: “What makes a problem difficult for genetic programming to solve?” It specifically describes linkages between content, tree structures, and problem difficulty in genetic programming. It focuses on the significance of structure in influencing problem difficulty.

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References

  • Banzhaf, W., et al., (1998).GP: An Introduction. San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Banzhaf, W. and Langdon, W. B. (2002). Some Considerations on the Reason for Bloat.Genetic Programming and Evolvable Machines 3: 81–91

    Article  MATH  Google Scholar 

  • Bickle T. and Thiele L. (1995). A Mathematical Analysis of Tournament Selection. In Proceedings of ICGA ’95, San Francisco: Morgan Kaufmann; 9–16

    Google Scholar 

  • Daida, J. M. (2002). Limits to Expression in GP: Lattice-Aggregate Modeling. In Proceedings of ICEC 2002, Piscataway: IEEE; 273–278

    Google Scholar 

  • Daida J. M., et al., (1999). Analysis of Single-Node (Building) Blocks in GP.Advances in GP 3, pp. 217–241. Cambridge: MIT Press

    Google Scholar 

  • Daida J. M., et al., (2001). What Makes a Problem GP-Hard? Analysis of a Tunably Difficult Problem in GP. 2001; Genetic Programming and Evolvable Machines 2: 165–191

    Article  MATH  Google Scholar 

  • Daida, J. M., et al. (2003a). Visualizing Tree Structures in GP. In Proceedings in GECCO 2003. Berlin: Springer-Verlag

    Google Scholar 

  • Daida, J. M., et al, (2003b). What Makes a Problem GP-Hard? Validating a Hypothesis of Structural Causes. In Proceedings in GECCO 2003. Berlin: Springer-Verlag

    Google Scholar 

  • Daida, J. M. and Hilss, A. (2003). Identifying Structural Mechanisms in Standard GP. In Proceedings in GECCO 2003. Berlin: Springer-Verlag

    Google Scholar 

  • Deb, K., et al. (1997). Fitness Landscapes. In Handbook of Evolutionary Computation, Bristol: Institute of Physics Publishing; B2. 7:1-B2. 7:25

    Google Scholar 

  • Dobzhansky, T. (1941).Genetics and the Origin of the Species, Second ed. New York: Columbia University Press

    Google Scholar 

  • Fogel, D. B. (1997). “Principles of Evolutionary Process. ” In Handbook of Evolutionary Computation, Bristol: Institute of Physics Publishing; A2. 1:1-A2. 1:3.

    Google Scholar 

  • Gathercole, C. and Ross, P. (1996). An Adverse Interaction Between Crossover and Restricted Tree Depth in GP. In Proceedings in GP ’96, Cambridge: MIT Press; 291–296

    Google Scholar 

  • Goldberg, D. E. and O’Reilly, U. -M. (1998). Where Does the Good Stuff Go, and Why? In Proceedings in EuroGP ’98, Berlin: Springer-Verlag

    Google Scholar 

  • Knuth, D. E. (1997). The Art of Computer Programming Vol 1, Third ed. Reading: Addison-Wesley

    MATH  Google Scholar 

  • Koza, J. R. (1992).Genetic Programming. Cambridge: MIT Press

    MATH  Google Scholar 

  • Koza, J. R. (1994).Genetic Programming II. Cambridge: MIT Press

    MATH  Google Scholar 

  • Koza J. R., et al., (1999).Genetic Programming III. San Francisco: Morgan Kaufmann

    MATH  Google Scholar 

  • Langdon, W. B. (2000a). Size Fair and Homologous Tree Crossovers for Tree GP.GPEM; 7:95–119

    Google Scholar 

  • Langdon, W. B. (2000b). Quadratic Bloat in GP. In Proceedings of GECCO 2000, San Francisco: Morgan Kaufmann; 451–458

    Google Scholar 

  • Langdon, W. B., et al. (1999). The Evolution of Size and Shape. In Advances in GP 3, Cambridge: MIT Press; 163–190

    Google Scholar 

  • Langdon, W. B. and Poli, R. (1997). “Fitness Causes Bloat. ” In Soft Computing in Engineering Design and Manufacturing, London: Springer-Verlag; 23–27

    Google Scholar 

  • Langdon, W. B. and Poli, R. (2002).Foundations of GP. Berlin: Springer-Verlag

    Google Scholar 

  • McPhee, N. F. and Hopper, N. J. (1999). Analysis of Genetic Diversity through Population History. In Proceedings of GECCO ’99, pp. 1112–1120. San Francisco: Morgan Kaufmann

    Google Scholar 

  • Mitchell, M., et al. (1992). The Royal Road for Genetic Algorithms: Fitness Landscapes and GA Performance. In Proceedings in ECAL ’92, pp. 245–254. Cambridge: MIT Press.

    Google Scholar 

  • Mitchell, M. (1996).An Introduction to GA. Cambridge: MIT Press

    Google Scholar 

  • Ogden H. G. (1888). The Survey of the Coast.National Geographic 1: 59–77

    Google Scholar 

  • O’Reilly, U. -M. and Goldberg, D. E. (1998). How Fitness Structure Affects Subsolution Acquisition in GP. In Proceedings in GP ’98, pp. 269–77. San Francisco: Morgan Kaufmann

    Google Scholar 

  • Poli, R. (2000). Exact Schema Theorem and Effective Fitness for GP with One-Point Crossover. In Proceedings in GECCO 2000, pp. 469–476. San Francisco: Morgan Kaufmann

    Google Scholar 

  • Poli, R. and Langdon, W. B. (1997). A New Schema Theory for GP with One-Point Crossover and Point Mutation. In Proceedings in GP ’97, pp. 279–85. San Francisco: Morgan Kaufmann

    Google Scholar 

  • Poli, R. and Langdon, W. B. (1998). Schema Theory for GP with One-Point Crossover and Point Mutation.Evolutionary Computation 6: 231–252

    Article  Google Scholar 

  • Punch, W., et al. (1996). The Royal Tree Problem, A Benchmark for Single and Multiple Population GP. In Advances in GP 2, pp. 299–316. Cambridge: MIT Press

    Google Scholar 

  • Rosca, J. P. (1997). Analysis of Complexity Drift in GP. In Proceedings in GP ’97, pp. 286–94. San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Rosca, J. P. and Ballard, D. H. (1999). Rooted-Tree Schemata in GP. In Advances in GP 3, pp. 243–271. Cambridge: MIT Press

    Google Scholar 

  • Simpson, G. G. (1944).Tempo and Mode in Evolution. New York: Columbia University Press.

    Google Scholar 

  • Soule, T., et al. (1996). Code Growth in GP. In Proceedings in GP ’96, pp. 215–223. Cambridge: MIT Press

    Google Scholar 

  • Soule, T. and Foster, J. A. (1997). Code Size and Depth Flows in GP. In Proceedings of GP ’97, pp. 313–320. San Francisco: Morgan Kaufmann

    Google Scholar 

  • Soule, T. and Foster, J. A. (1998). Removal Bias: A New Cause of Code Growth in Tree Based Evolutionary Programming. In Proceedings in ICEC ’98, vol. 1, pp. 781–786. Piscataway: IEEE Press

    Google Scholar 

  • Witten, T. A. and Sander, L. M. (1981). Diffusion-Limited Aggregation: A Kinetic Critical Phenomenon.Physics Review Letters 47: 1400–1403

    Article  Google Scholar 

  • Witten, T. A. and Sander, L. M. (1983). Diffusion-Limited Aggregation.Physics Review B: 27: 5686–5697

    Article  MathSciNet  Google Scholar 

  • Wright S. (1932). The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution. In Proceedings of the Sixth International Congress of Genetics, 1: 356–366

    Google Scholar 

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Daida, J.M. (2003). What Makes a Problem GP-Hard?. In: Riolo, R., Worzel, B. (eds) Genetic Programming Theory and Practice. Genetic Programming Series, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8983-3_7

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  • DOI: https://doi.org/10.1007/978-1-4419-8983-3_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4747-7

  • Online ISBN: 978-1-4419-8983-3

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