Semantic Forward Propagation for Symbolic Regression

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9921)


In recent years, a number of methods have been proposed that attempt to improve the performance of genetic programming by exploiting information about program semantics. One of the most important developments in this area is semantic backpropagation. The key idea of this method is to decompose a program into two parts—a subprogram and a context—and calculate the desired semantics of the subprogram that would make the entire program correct, assuming that the context remains unchanged. In this paper we introduce Forward Propagation Mutation, a novel operator that relies on the opposite assumption—instead of preserving the context, it retains the subprogram and attempts to place it in the semantically right context. We empirically compare the performance of semantic backpropagation and forward propagation operators on a set of symbolic regression benchmarks. The experimental results demonstrate that semantic forward propagation produces smaller programs that achieve significantly higher generalization performance.


Genetic programming Program semantics Semantic backpropagation Problem decomposition Symbolic regression 



This work was supported by the National Aeronautics and Space Administration under grant number NNX15AH48G.


  1. 1.
    Beadle, L., Johnson, C.G.: Semantically driven crossover in genetic programming. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2008, pp. 111–116. IEEE (2008)Google Scholar
  2. 2.
    Beadle, L., Johnson, C.G.: Semantic analysis of program initialisation in genetic programming. Genet. Prog. Evol. Mach. 10(3), 307–337 (2009)CrossRefGoogle Scholar
  3. 3.
    Jackson, D.: Promoting phenotypic diversity in genetic programming. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6239, pp. 472–481. Springer, Heidelberg (2010)Google Scholar
  4. 4.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  5. 5.
    Krawiec, K.: Behavioral Program Synthesis with Genetic Programming, Studies in Computational Intelligence, vol. 618. Springer, Heidelberg (2016)CrossRefGoogle Scholar
  6. 6.
    Krawiec, K., O’Reilly, U.M.: Behavioral programming: a broader and more detailed take on semantic GP. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, GECCO 2014, pp. 935–942. ACM (2014)Google Scholar
  7. 7.
    Liskowski, P., Krawiec, K., Helmuth, T., Spector, L.: Comparison of semantic-aware selection methods in genetic programming. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1301–1307. ACM (2015)Google Scholar
  8. 8.
    McDermott, J., White, D.R., Luke, S., Manzoni, L., Castelli, M., Vanneschi, L., Jaskowski, W., Krawiec, K., Harper, R., De Jong, K., O’Reilly, U.M.: Genetic programming needs better benchmarks. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 791–798. ACM (2012)Google Scholar
  9. 9.
    McPhee, N.F., Hopper, N.J.: Analysis of genetic diversity through population history. In: Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 1112–1120. Morgan Kaufmann (1999)Google Scholar
  10. 10.
    Moraglio, A., Krawiec, K., Johnson, C.G.: Geometric semantic genetic programming. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 21–31. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Pawlak, T.P., Wieloch, B., Krawiec, K.: Review and comparative analysis of geometric semantic crossovers. Genet. Prog. Evol. Mach. 16(3), 351–386 (2015)CrossRefGoogle Scholar
  12. 12.
    Pawlak, T., Wieloch, B., Krawiec, K.: Semantic backpropagation for designing search operators in genetic programming. IEEE Trans. Evol. Comput. 19(3), 326–340 (2015)CrossRefGoogle Scholar
  13. 13.
    Uy, N.Q., Hoai, N.X., O’Neill, M., Mckay, R.I., Galván-López, E.: Semantically-based crossover in genetic programming: application to real-valued symbolic regression. Genet. Prog. Evol. Mach. 12(2), 91–119 (2011)CrossRefGoogle Scholar
  14. 14.
    Vanneschi, L., Castelli, M., Silva, S.: A survey of semantic methods in genetic programming. Genet. Prog. Evol. Mach. 15(2), 195–214 (2014)CrossRefGoogle Scholar
  15. 15.
    Wieloch, B., Krawiec, K.: Running programs backwards: instruction inversion for effective search in semantic spaces. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, GECCO 2013, pp. 1013–1020. ACM, New York (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.University of VermontBurlingtonUSA
  2. 2.University of CaliforniaSanta CruzUSA
  3. 3.NASA Ames Research CenterMoffett FieldUSA
  4. 4.Bay Area Environmental Research InstitutePetalumaUSA

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