An Analysis of Geometric Semantic Crossover: A Computational Geometry Approach

Mauro Castelli, Luca Manzoni, Ivo Gonçalves, Leonardo Vanneschi, Leonardo Trujillo, Sara Silva

2016

Abstract

Geometric semantic operators have recently shown their ability to outperform standard genetic operators on different complex real world problems. Nonetheless, they are affected by drawbacks. In this paper, we focus on one of these drawbacks, i.e. the fact that geometric semantic crossover has often a poor impact on the evolution. Geometric semantic crossover creates an offspring whose semantics stands in the segment joining the parents (in the semantic space). So, it is intuitive that it is not able to find, nor reasonably approximate, a globally optimal solution, unless the semantics of the individuals in the population ``contains'' the target. In this paper, we introduce the concept of convex hull of a genetic programming population and we present a method to calculate the distance from the target point to the convex hull. Then, we give experimental evidence of the fact that, in four different real-life test cases, the target is always outside the convex hull. As a consequence, we show that geometric semantic crossover is not helpful in those cases, and it is not even able to approximate the population to the target. Finally, in the last part of the paper, we propose ideas for future work on how to improve geometric semantic crossover.

References

  1. Bonnans, J. F., Gilbert, J. C., Lemaréchal, C., and Sagastizábal, C. A. (2006). Numerical Optimization: Theoretical and Practical Aspects (Universitext). SpringerVerlag New York, Inc., Secaucus, NJ, USA.
  2. Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press, New York, NY, USA.
  3. Castelli, M., Castaldi, D., Giordani, I., Silva, S., Vanneschi, L., Archetti, F., and Maccagnola, D. (2013a). An efficient implementation of geometric semantic genetic programming for anticoagulation level prediction in pharmacogenetics. In Progress in Artificial Intelligence, pages 78-89. Springer Berlin Heidelberg.
  4. Castelli, M., Silva, S., and Vanneschi, L. (2015a). A c++ framework for geometric semantic genetic programming. Genetic Programming and Evolvable Machines, 16(1):73-81.
  5. Castelli, M., Vanneschi, L., and Felice, M. D. (2015b). Forecasting short-term electricity consumption using a semantics-based genetic programming framework: The south italy case. Energy Economics, 47:37 - 41.
  6. Castelli, M., Vanneschi, L., and Popovic?, A. (2015c). Parameter evaluation of geometric semantic genetic programming in pharmacokinetics. International journal of bio-inspired computation, pages 1 - 10. To appear.
  7. Castelli, M., Vanneschi, L., and Silva, S. (2014). Prediction of the unified parkinson's disease rating scale assessment using a genetic programming system with geometric semantic genetic operators. Expert Systems with Applications, 41(10):4608 - 4616.
  8. de Berg, M., Cheong, O., van Kreveld, M., and Overmars, M. (2008). Computational geometry. In Computational Geometry, pages 1-17. Springer Berlin Heidelberg.
  9. Koza, J. R. (1992). Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge, MA, USA.
  10. Krawiec, K. and Lichocki, P. (2009). Approximating geometric crossover in semantic space. In GECCO 7809: Proceedings of the 11th Annual conference on Genetic and evolutionary computation, pages 987-994, Montreal. ACM.
  11. Lichman, M. (2013). UCI machine learning repository.
  12. Moraglio, A. (2011). Abstract convex evolutionary search. In Proceedings of the 11th Workshop Proceedings on Foundations of Genetic Algorithms, FOGA 7811, pages 151-162, New York, NY, USA. ACM.
  13. Moraglio, A., Krawiec, K., and Johnson, C. (2012). Geometric semantic genetic programming. In Parallel Problem Solving from Nature - PPSN XII, volume 7491 of Lecture Notes in Computer Science, pages 21-31. Springer Berlin Heidelberg.
  14. Moraglio, A. and Mambrini, A. (2013). Runtime analysis of mutation-based geometric semantic genetic programming for basis functions regression. In Proceedings of the annual international conference on Genetic and Evolutionary Computation, GECCO 7813, pages 989- 996, New York, NY, USA. ACM.
  15. Vanneschi, L., Castelli, M., Manzoni, L., and Silva, S. (2013). A new implementation of geometric semantic GP and its application to problems in pharmacokinetics. In Proceedings of the 16th European Conference on Genetic Programming, EuroGP 2013, volume 7831 of LNCS, pages 205-216, Vienna, Austria. Springer Verlag.
  16. Vanneschi, L., Castelli, M., and Silva, S. (2014a). A survey of semantic methods in genetic programming. Genetic Programming and Evolvable Machines, 15(2):195- 214.
Download


Paper Citation


in Harvard Style

Castelli M., Manzoni L., Gonçalves I., Vanneschi L., Trujillo L. and Silva S. (2016). An Analysis of Geometric Semantic Crossover: A Computational Geometry Approach . In Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016) ISBN 978-989-758-201-1, pages 201-208. DOI: 10.5220/0006056402010208


in Bibtex Style

@conference{ecta16,
author={Mauro Castelli and Luca Manzoni and Ivo Gonçalves and Leonardo Vanneschi and Leonardo Trujillo and Sara Silva},
title={An Analysis of Geometric Semantic Crossover: A Computational Geometry Approach},
booktitle={Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016)},
year={2016},
pages={201-208},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006056402010208},
isbn={978-989-758-201-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016)
TI - An Analysis of Geometric Semantic Crossover: A Computational Geometry Approach
SN - 978-989-758-201-1
AU - Castelli M.
AU - Manzoni L.
AU - Gonçalves I.
AU - Vanneschi L.
AU - Trujillo L.
AU - Silva S.
PY - 2016
SP - 201
EP - 208
DO - 10.5220/0006056402010208