Abstract
Structured grammatical evolution (SGE) is a new genotypic representation for grammatical evolution (GE). It comprises a hierarchical organization of the genes, where each locus is explicitly linked to a non-terminal of the grammar being used. This one-to-one correspondence ensures that the modification of a gene does not affect the derivation options of other non-terminals. We present a comprehensive set of optimization results obtained with problems from three different categories: symbolic regression, path finding, and predictive modeling. In most of the situations SGE outperforms standard GE, confirming the effectiveness of the new representation. To understand the reasons for SGE enhanced performance, we scrutinize its main features. We rely on a set of static measures to model the interactions between the representation and variation operators and assess how they influence the interplay between the genotype-phenotype spaces. The study reveals that the structured organization of SGE promotes an increased locality and is less redundant than standard GE, thus fostering an effective exploration of the search space.
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Notes
In the previous problems, optimization designates the step where the GE algorithms are applied. For predictive modeling tasks we adopt the standard terms from the ML community: training/generalization.
References
F. Archetti, S. Lanzeni, E. Messina, L. Vanneschi, Genetic programming for computational pharmacokinetics in drug discovery and development. Genet. Program. Evol. Mach. 8(4), 413–432 (2007)
R.M.A. Azad, A position independent representation for evolutionary automatic programming algorithms—the chorus system. Ph.D. thesis, University of Limerick, Ireland (2003)
M. Brameier, W. Banzhaf, Explicit control of diversity and effective variation distance in linear genetic programming. In Genetic Programming, Lecture notes in computer science, vol. 2278 (Springer, 2002), pp. 37–49
J. Byrne, M. O’Neill, A. Brabazon, Structural and nodal mutation in grammatical evolution. In Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation (New York, NY, USA, 2009), pp. 1881–1882
J. Byrne, M. O’Neill, J. McDermott, A. Brabazon, An analysis of the behaviour of mutation in grammatical evolution. In Genetic Programming, Lecture notes in computer science, vol. 6021 (Springer, 2010), pp. 14–25
T. Castle, C. Johnson, Positional effect of crossover and mutation in grammatical evolution. In Genetic Programming, Lecture notes in computer science, vol. 6021 (Springer, 2010), pp. 26–37
I. Dempsey, M. O’Neill, A. Brabazon, Foundations in Grammatical Evolution for Dynamic Environments (Springer, Berlin, 2009)
D. Fagan, Analysing the Genotype-Phenotype Map in Grammatical Evolution, PhD Thesis, University College Dublin (2014)
D. Fagan, M. O’Neill, E. Galván-López, A. Brabazon, S. McGarraghy, An analysis of genotype-phenotype maps in grammatical evolution. In Genetic Programming, Lecture notes in computer science, vol. 6021 (Springer, 2010), pp. 62–73
A. Field, Discovering Statistics Using IBM SPSS Statistics (Sage, Beverley Hills, 2013)
I. Gonçalves, S. Silva, Balancing learning and overfitting in genetic programming with interleaved sampling of training data. In Genetic Programming, Lecture notes in computer science, vol. 7831 (Springer, 2013), pp. 73–84
J. Gottlieb, C. Eckert, A comparison of two representations for the fixed charge transportation problem. In Parallel Problem Solving from Nature PPSN VI, Lecture notes in computer science, vol. 1917 (Springer, 2000), pp. 345–354
J. Gottlieb, G. Raidl, Characterizing locality in decoder-based eas for the multidimensional knapsack problem. In Artificial Evolution, Lecture notes in computer science, vol. 1829 (Springer, 2000), pp. 38–52
R. Harper, Spatial co-evolution: quicker, fitter and less bloated. In Proceedings of the 14th annual conference on Genetic and evolutionary computation (ACM, 2012), pp. 759–766
J. Hugosson, E. Hemberg, A. Brabazon, M. O’Neill, Genotype representations in grammatical evolution. Appl. Soft Comput. 10(1), 36–43 (2010)
T. Jones, S. Forrest, Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In Proceedings of the 6th International Conference on Genetic Algorithms (Morgan Kaufmann Publishers Inc., San Francisco, 1995), pp. 184–192
M. Keijzer, M. O’Neill, C. Ryan, M. Cattolico, Grammatical evolution rules: the mod and the bucket rule. In Genetic Programming, Lecture notes in computer science, vol. 2278 (Springer, 2002), pp. 123–130
R. Keller, W. Banzhaf, Genetic programming using genotype-phenotype mapping from linear genomes into linear phenotypes. In: Proceedings of the 1st Annual Conference on Genetic Programming (MIT Press, Cambridge, 1996), pp. 116–122
J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, 1992)
N. Lourenço, F.B. Pereira, E. Costa, SGE : a structured representation for grammatical evolution. In 12th International Conference Evolution Artificielle, EA 2015 (Lyon, 2015)
R.I. McKay, N.X. Hoai, P. Whigham, Y. Shan, M. O’Neill, Grammar-based genetic programming: a survey. Genetic programming and evolvable machines, 11(3–4), 365–396 (2010)
M. O’Neill, A. Brabazon, Grammatical differential evolution. In H.R. Arabnia (ed.) Proceedings of the 2006 International Conference on Artificial Intelligence, ICAI 2006, vol. 1 (2006), pp. 231–236
M. O’Neill, A. Brabazon, Grammatical swarm: the generation of programs by social programming. Nat. Comput. 5(4), 443–462 (2006)
M. O’Neill, A. Brabazon, M. Nicolau, S. McGarraghy, P. Keenan, Pigrammatical evolution. In Genetic and Evolutionary Computation, vol. 3103 (Springer, 2004), pp. 617–629
M. O’Neill, E. Hemberg, C. Gilligan, E. Bartley, J. McDermott, A. Brabazon, Geva—grammatical evolution in java (v 2.0). Technical report, UCD School of Computer Science (2008)
M. O’Neill, C. Ryan, Grammatical Evolution: Evolutionary Automatic Programming in an Arbitrary Language (Kluwer Academic Publishers, Norwell, 2003)
U.M. O’Reilly, Using a distance metric on genetic programs to understand genetic operators. In IEEE International Conference on Systems, Man, and Cybernetics, vol. 5 (1997), pp. 4092–4097
J. O’Sullivan, C. Ryan, An investigation into the use of different search strategies with grammatical evolution. In Genetic Programming (Springer, 2002), pp. 268–277
G. Raidl, J. Gottlieb, Empirical analysis of locality, heritability and heuristic bias in evolutionary algorithms: a case study for the multidimensional knapsack problem. Evol. Comput. 13(4), 441–475 (2005)
F. Rothlauf, On the locality of representations. In Genetic and Evolutionary Computation, Lecture notes in computer science, vol. 2724 (Springer, 2003), pp. 1608–1609
F. Rothlauf, Representations for Genetic and Evolutionary Algorithms (Springer, Berlin, 2006)
F. Rothlauf, M. Oetzel, On the locality of grammatical evolution. In Genetic Programming, Lecture notes in computer science (Springer, 2006), pp. 320–330
C. Ryan, A. Azad, Sensible initialisation in grammatical evolution. In A.M. Barry (ed.) GECCO 2003: Proceedings of the Bird of a Feather Workshops, Genetic and Evolutionary Computation Conference (AAAI, 2003), pp. 142–145
C. Ryan, A. Azad, A. Sheahan, M. O’Neill, No coercion and no prohibition, a position independent encoding scheme for evolutionary algorithms—the chorus system. In Genetic Programming (Springer, 2002), pp. 131–141
C. Ryan, J. Collins, M. O’Neill, Grammatical evolution: evolving programs for an arbitrary language. In W. Banzhaf, R. Poli, M. Schoenauer, T. Fogarty (eds.) Genetic Programming, Lecture notes in computer science, vol. 1391 (Springer, 1998), pp. 83–96
A. Thorhauer, F. Rothlauf, On the locality of standard search operators in grammatical evolution. In Parallel Problem Solving from Nature—PPSN XIII, Lecture notes in computer science, vol. 8672 (Springer International Publishing, 2014), pp. 465–475
P.A. Whigham, G. Dick, J. Maclaurin, C.A. Owen, Examining the best of both worlds of grammatical evolution. In Proceedings of the 2015 on Genetic and Evolutionary Computation Conference (ACM, 2015), pp. 1111–1118
D. White, J. McDermott, M. Castelli, L. Manzoni, B. Goldman, G. Kronberger, W. Jaskowski, U.M. O’Reilly, S. Luke, Better gp benchmarks: community survey results and proposals. Genet. Program. Evol. Mach. 14(1), 3–29 (2013)
K. Zhang, D. Shasha, Simple fast algorithms for the editing distance between trees and related problems. SIAM J. Comput. 18(6), 1245–1262 (1989)
Acknowledgments
The first author is funded by Fundação para a Ciência e Tecnologia (FCT), Portugal, under the Grant SFRH/BD/79649/2011. The authors would like to thank the anonymous reviewers for their insightful comments that helped to improve our work.
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Lourenço, N., Pereira, F.B. & Costa, E. Unveiling the properties of structured grammatical evolution. Genet Program Evolvable Mach 17, 251–289 (2016). https://doi.org/10.1007/s10710-015-9262-4
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DOI: https://doi.org/10.1007/s10710-015-9262-4