EXPLICITLY SIMPLIFYING EVOLVED GENETIC PROGRAMS DURING EVOLUTION
Abstract
The genetic programming (GP) evolutionary process typically introduces a large amount of redundancy and unnecessary complexity into evolved programs. Quick growth of redundant and functionally useless sections of programs can quickly overcome a GP system, exhausting system resources and causing premature termination of the system before an acceptable solution can be found. Rather than implicitly controlling the redundancy and code growth/bloat as in most of the existing approaches, this paper investigates an algebraic simplification algorithm for explicitly removing the redundancy from the genetic programs and simplifying these programs online during the evolutionary process. The new GP system with the simplification is examined and compared with a standard GP system on two regression and three classification problems of varying difficulties. The results show that the GP system employing a simplification component can achieve superior efficiency with comparable or slightly superior effectiveness to the standard GP system on these problems. The programs evolved by the new GP approach with the explicit simplification contain ``hidden patterns'' for a particular problem and are relatively simple and easy to interpret.
References
-
J. R. Koza , Genetic Programming: On the Programming of Computers by Means of Natural Selection ( MIT Press , Cambridge, MA, USA , 1992 ) . Google Scholar - Pattern Recogn. Lett. 27(11), 1161 (2006). Crossref, Google Scholar
M. Zhang and V. Ciesielski , Genetic programming for multiple class object detection, 12th Australian Joint Conf. Artificial Intelligence,Lecture Notes in Artificial Intelligence 1747, ed.N. Foo (Springer-Verlag, 1999) pp. 180–192. Google ScholarJ. Busch , Automatic generation of control programs for walking robots using genetic programming, EuroGP '02: Proc. 5th Eur. Conf. Genetic Programming (2002) pp. 258–267. Google Scholar-
J. R. Koza , Genetic Programming IV: Routine Human–Competitive Machine Intelligence ( Kluwer Academic Publishers , 2003 ) . Google Scholar T. Soule , J. A. Foster and J. Dickinson , Code growth in genetic programming, Genetic Programming 1996: Proc. First Ann. Conf., eds.J. R. Koza (MIT Press, 1996) pp. 215–223. Google Scholar- T. Blickle and L. Thiele, Genetic programming and redundancy, in Genetic Algorithms Within the Framework of Evolutionary Computation, ed. J. Hopf, Workshop at KI-94, Saarbrücken, Im Stadtwald, Building 44, D-66123 Saarbrücken, Germany, Max-Planck-Institut für Informatik, MPI-I-94-241 (1994), pp. 33–38 . Google Scholar
P. Nordin and W. Banzhaf , Complexity compression and evolution, Genetic Algorithms: Proc. Sixth Int. Conf. (ICGA95), ed.L. Eshelman (Morgan Kaufmann, Pittsburgh, PA, USA) pp. 310–317. Google ScholarD. Parrott , X. Li and V. Ciesielski , Multi-objective techniques in genetic programming for evolving classifiers, Proc. 2005 IEEE Cong. Evolutionary Computation2, eds.D. Corne (IEEE Press) pp. 1141–1148. Google Scholar- Evol. Comput. 3(1), 17 (1995), DOI: 10.1162/evco.1995.3.1.17. Crossref, Google Scholar
M. Zhang and U. Bhowan , Program size and pixel statistics in genetic programming for object detection, Applications of Evolutionary Computing, EvoWorkshops2004: EvoBIO, EvoCOMNET, EvoHOT, EvoIASP, EvoMUSART, EvoSTOC,Lecture Notes in Computer Science 3005, eds.G. R. Raidl (Springer-Verlag, 2004) pp. 379–388. Google ScholarS. Luke and L. Panait , Lexicographic parsimony pressure, GECCO 2002: Proc. Genet. Evol. Comput. Conf., eds.W. B. Langdon (Morgan Kaufmann Publishers, New York) pp. 829–836. Google ScholarS. Luke , Code growth is not caused by introns, Late Breaking Papers, Proc. Genet. Evol. Comput. Conf. 2000 (2000) pp. 228–235. Google ScholarW. B. Langdon , Quadratic bloat in genetic programming, Proc. Genet. Evol. Comput. Conf. (GECCO-2000), eds.D. Whitley (Morgan Kaufmann) pp. 451–458. Google ScholarM. J. Streeter , The root causes of code growth in genetic programming, Genetic Programming, Proc. EuroGP'2003,Lecture Notes in Computer Science 2610, eds.C. Ryan (Springer-Verlag) pp. 443–454. Google Scholar- Genet. Program. Evol. Mach. 5(3), 271 (2004), DOI: 10.1023/B:GENP.0000030194.98244.e3. Crossref, Google Scholar
D. Jackson , Fitness evaluation avoidance in boolean GP problems, Proc. 2005 IEEE Congress on Evolutionary Computation3, eds.D. Corne (IEEE Press) pp. 2530–2536. Google Scholar- T. Soule, Code growth in genetic programming, Ph.D. thesis, University of Idaho, Moscow, Idaho, USA (15, May 1998) . Google Scholar
- Evol. Comput. 6(4), 293 (1998), DOI: 10.1162/evco.1998.6.4.293. Crossref, Google Scholar
A. Piszcz and T. Soule , Dynamics of evolutionary robustness, GECCO 2006: Proc. 8th Ann. Conf. Genetic and Evolutionary Computation1, eds.M. Keijzer (ACM Press) pp. 871–878. Google ScholarW. Ashlock and D. Ashlock , Single parent genetic programming, Proc. 2005 IEEE Congr. Evolutionary Computation2, eds.D. Corne (IEEE Press) pp. 1172–1179. Google ScholarW. B. Langdon and R. Poli , Fitness causes bloat: Mutation, Proc. First Eur. Workshop on Genetic Programming,Lecture Notes in Computer Science 1391, eds.W. Banzhaf (Springer-Verlag, 1998) pp. 37–48. Google Scholar- Soft Computing in Engineering Design and Manufacturing, eds.
P. K. Chawdhry , R. Roy and R. K. Pant (Springer-Verlag, London, 1997) pp. 13–22. Google Scholar , P. Nordin , F. Francone and W. Banzhaf , Explicitly defined introns and destructive crossover in genetic programming, Proc. Workshop on Genetic Programming: From Theory to Real-World Applications, ed.J. P. Rosca pp. 6–22. Google ScholarX. Zhong and T. Soule , Growth of self-canceling code in evolutionary systems, GECCO 2006: Proc. 8th Ann. Conf. Genetic and Evolutionary Computation1, eds.M. Keijzer (ACM Press) pp. 223–228. Google ScholarS. Silva and E. Costa , Comparing tree depth limits and resource-limited GP, Proc. 2005 IEEE Congress on Evolutionary Computation1, eds.D. Corne (IEEE Press) pp. 920–927. Google ScholarC. Skinner , P. J. Riddle and C. Triggs , Mathematics prevents bloat, Proc. 2005 IEEE Congress on Evolutionary Computation1, eds.D. Corne (IEEE Press) pp. 390–395. Google ScholarN. F. McPhee and J. D. Miller , Accurate replication in genetic programming, Genetic Algorithms: Proc. Sixth Int. Conf. (ICGA95), ed.L. Eshelman (Morgan Kaufmann) pp. 303–309. Google ScholarH. Stringer and A. S. Wu , Winnowing wheat from chaff: The chunking ga, Genetic and Evolutionary Computation — GECCO-2004,Lecture Notes in Computer Science 3013, eds.K. Deb (Springer-Verlag, 2004) pp. 198–209. Google ScholarD. Hooper and N. S. Flann , Improving the accuracy and robustness of genetic programming through expression simplification, Genetic Programming 1996: Proc. First Ann. Conf., eds.J. R. Koza (MIT Press) p. 428. Google ScholarA. Ekart , Shorter fitness preserving genetic programs, Artificial Evolution 4th European Conference, AE'99, Selected Papers,Lecture Notes in Computer Science 1829, eds.C. Fonlupt pp. 73–83. Google ScholarJ. F. Smith III , Genetic program based data mining for fuzzy decision trees, Intelligent Data Engineering and Automated Learning — IDEAL 2004, Proc. 5th Int. Conf.,Lecture Notes in Computer Science 3177, eds.Z. R. Yang , R. M. Everson and H. Yin (Springer, 2004) pp. 464–470. Google ScholarJ. F. Smith III , Evolving fuzzy decision tree structure that adapts in real-time, GECCO 2005: Proc. 2005 Conf. Genetic and Evolutionary Computation2, eds.H.-G. Beyer (ACM Press) pp. 1737–1744. Google ScholarM. Zhang , Y. Zhang and W. D. Smart , Program simplification in genetic programming for object classification, Knowledge-based Intelligent Information and Engineering Systems, Proc. 9th Int. Conf., KES 2005,Lecture Notes in Computer Science 3683, eds.R. Khosla , R. J. Howlett and L. C. Jain (Springer, 2005) pp. 988–996. Google Scholar-
W. B. Langdon and R. Poli , Foundations of Genetic Programming ( Springer-Verlag , 2002 ) . Crossref, Google Scholar - W. B. Langdon, Fitness causes bloat: Simulated annealing, hill climbing and populations, Technical Report CSRP-97-22, University of Birmingham, School of Computer Science (2, September 1997) . Google Scholar
-
W. Banzhaf , Genetic Programming: An Introduction on the Automatic Evolution of Computer Programs and Its Applications, San Francisco, CA ( Morgan Kaufmann Publishers , Dpunkt-Verlag, Heidelburg , 1998 ) . Crossref, Google Scholar - Artil. Intell. 2, 189 (1971), DOI: 10.1016/0004-3702(71)90010-5. Crossref, Google Scholar
- J. ACM 18(4), 549 (1971), DOI: 10.1145/321662.321668. Crossref, Google Scholar
G. H. Gonnet , Determining equivalence of expressions in random polynomial time, STOC '84: Proc. Sixteenth Ann. ACM Symp. Theory of Computing (ACM Press, New York, NY, USA, 1984) pp. 334–341. Google Scholar-
R. Lidl and H. Niederreiter , Introduction to Finite Fields and Their Applications ( Cambridge University Press , New York, NY, USA , 1986 ) . Google Scholar -
W. Trappe and L. C. Washington , Introduction to Cryptography with Coding Theory , 2nd edn. ( Prentice-Hall , 2006 ) . Google Scholar - B. Cherowitzo, Lecture Notes (2006), http://www-math.cudenver.edu/~wcherowi/courses/m5410/exeucalg.html, available online 7, January 2006 . Google Scholar
- Advances in Cognitive Science,
AAAS Selected Symposia Series, AAAS , eds.M. Kochen and H. M. Hastings (Washington, DC, 1986) pp. 210–227. Google Scholar , R. Solomonoff , A system for incremental learning based on algorithmic probability, Proc. Sixth Israeli Conf. Artificial Intelligence, Computer Vision and Pattern Recognition pp. 515–527. Google ScholarM. Anthony and N. Biggs , The Handbook of Brain Theory and Neural Networks (1995) pp. 694–697. Google Scholar- IEEE Trans. Pattern Anal. Mach. Intell. 23(6), 643 (2001), DOI: 10.1109/34.927464. Crossref, Google Scholar
- O. L. Mangasarian and W. H. Wolberg, Cancer diagnosis via linear programming (September 1990) . Google Scholar
M. Zhang and W. Smart , Multiclass object classification using genetic programming, Applications of Evolutionary Computing, EvoWorkshops2004,Lecture Notes in Computer Science 3003, eds.G. R. Raidl (Springer-Verlag) pp. 369–378. Google ScholarT. Loveard and V. Ciesielski , Representing classification problems in genetic programming, Proc. Congress on Evolutionary Computation2 (IEEE Press) pp. 1070–1077. Google Scholar-
M. L. Berenson and D. M. Levine , Applied Statistics: A First Course ( Prentice-Hall, Inc. , Upper Saddle River, NJ, USA , 1988 ) . Google Scholar -
J. R. Quinlan , C4.5: Programs for Machine Learning ( Morgan Kaufmann Publishers Inc. , San Francisco, CA , 1993 ) . Google Scholar
Remember to check out the Most Cited Articles! |
---|
Check out these titles in artificial intelligence! |