Journal of Artificial Evolution and Applications

Journal of Artificial Evolution and Applications / 2009 / Article

Research Article | Open Access

Volume 2009 |Article ID 896595 | 11 pages | https://doi.org/10.1155/2009/896595

Viewing the Problem from Different Angles: A New Diversity Measure Based on Angular Distances

Academic Editor: Natalio Krasnogor
Received19 May 2009
Accepted01 Dec 2009
Published01 Mar 2010

Abstract

It is commonly believed that diversity is crucial for an evolutionary system to succeed, especially when the problem to be solved contains local optima from which the population cannot easily escape. There exist numerous methods to measure population diversity, but none of these have been shown to be consistently useful. In this paper, a new diversity measure is introduced, and it is shown that high diversity according to this new measure generally leads to a more successful overall evolution in most of the cases considered.

References

  1. B. Wyns, P. De Bruyne, and L. Boullart, “Characterizing diversity in genetic programming,” in Proceedings of the 9th European Conference on Genetic Programming, vol. 3905 of Lecture Notes in Computer Science, pp. 250–259, 2006. View at: Publisher Site | Google Scholar
  2. E. K. Burke, S. Gustafson, and G. Kendall, “Diversity in genetic programming: an analysis of measures and correlation with fitness,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 1, pp. 47–62, 2004. View at: Publisher Site | Google Scholar
  3. A. Toffolo and E. Benini, “Genetic diversity as an objective in multi-objective evolutionary algorithms,” Evolutionary Computation, vol. 11, no. 2, pp. 151–167, 2003. View at: Publisher Site | Google Scholar
  4. A. Ekárt and S. Z. Németh, “Maintaining the diversity of genetic programs,” in Proceedings of the 5th European Conference on Genetic Programming, pp. 162–171, 2002. View at: Google Scholar
  5. D. Curran and C. O'Riordan, “Increasing population diversity through cultural learning,” Adaptive Behavior, vol. 14, no. 4, pp. 315–338, 2006. View at: Publisher Site | Google Scholar
  6. J. P. Rosca, “Genetic programming exploratory power and the discovery of functions,” in Proceedings of the 4th Annual Conference on Evolutionary Programming, pp. 719–736, 1995. View at: Google Scholar
  7. J. P. Rosca, “Entropy-driven adaptive representation,” in Proceedings of the Workshop on Genetic Programming: From Theory to Real-World Applications, pp. 23–32, 1995. View at: Google Scholar
  8. T. M. Mitchell, Machine Learning, McGraw-Hill, Singapore, 1997.
  9. P. H. McQuesten, Cultural enhancement of neuroevolution, Ph.D. dissertation, Artificial Intelligence Laboratory, The University of Texas, Austin, Tex, USA, 2002.
  10. J. He and X. Yao, “From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 5, pp. 495–511, 2002. View at: Publisher Site | Google Scholar
  11. V. Nissen and J. Propach, “On the robustness of population-based versus point-based optimization in the presence of noise,” IEEE Transactions on Evolutionary Computation, vol. 2, no. 3, pp. 107–119, 1998. View at: Google Scholar
  12. D. V. Arnold and H.-G. Beyer, “On the benefits of populations for noisy optimization,” Evolutionary Computation, vol. 11, no. 2, pp. 111–127, 2003. View at: Publisher Site | Google Scholar
  13. T. Smith, P. Husbands, P. Layzell, and M. O'Shea, “Fitness landscapes and evolvability,” Evolutionary Computation, vol. 10, no. 1, pp. 1–34, 2002. View at: Google Scholar
  14. T. Bäck, “Selective pressure in evolutionary algorithms: a characterizationof selection mechanisms,” in Proceedings of the 1st IEEE Conference on Evolutionary Computation, pp. 57–62, 1994. View at: Google Scholar
  15. T. Blickle and L. Thiele, “A comparison of selection schemes used in evolutionary algorithms,” Evolutionary Computation, vol. 4, no. 4, pp. 361–394, 1996. View at: Google Scholar
  16. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman, Boston, Mass, USA, 1989.
  17. H.-P. Schwefel, Evolution and Optimum Seeking, John Wiley & Sons, New York, NY, USA, 1995.
  18. J. T. Alander, “On optimal population size of genetic algorithms,” in Proceedings of Computer Systems and Software Engineering (CompEuro '92), pp. 65–70, The Hague, The Netherlands, May 1992. View at: Publisher Site | Google Scholar
  19. D. E. Goldberg, “Genetic algorithms, noise, and the sizing of populations,” Complex Systems, vol. 6, pp. 333–362, 1992. View at: Google Scholar
  20. T. Jansen, K. A. De Jong, and I. Wegener, “On the choice of the offspring population size in evolutionary algorithms,” Evolutionary Computation, vol. 13, no. 4, pp. 413–440, 2005. View at: Publisher Site | Google Scholar
  21. M. Fuchs, “Large populations are not always the best choice in genetic programming,” in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '99), pp. 1033–1038, 1999. View at: Google Scholar
  22. J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge, Mass, USA, 1992.
  23. H. Shimodaira, “Dcga: a diversity control oriented genetic algorithm,” in Proceedings of the 9th International Conference on Tools with Artificial Intelligence, pp. 367–374, 1997. View at: Google Scholar
  24. U.-M. O'Reilly, “Using a distance metric on genetic programs to understand genetic operators,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, vol. 5, pp. 4092–4097, 1997. View at: Google Scholar
  25. M. Hutter and S. Legg, “Fitness uniform optimization,” IEEE Transactions on Evolutionary Computation, vol. 10, no. 5, pp. 568–589, 2006. View at: Publisher Site | Google Scholar
  26. E. Burke, S. Gustafson, and G. Kendall, “A survey and analysis of diversity measures in genetic programming,” in Proceedings of the Genetic and Evolutionary Computation Conference, pp. 716–723, 2002. View at: Google Scholar
  27. A. E. Magurran, Ecological Diversity and Its Measurement, Princeton University Press, Princeton, NJ, USA, 1988.
  28. R. Olsson, “Inductive functional programming using incremental program transformation,” Artificial Intelligence, vol. 74, no. 1, pp. 55–81, 1995. View at: Google Scholar
  29. L. B. Booker, D. E. Goldberg, and J. H. Holland, “Classifier systems and genetic algorithms,” Artificial Intelligence, vol. 40, no. 1–3, pp. 235–282, 1989. View at: Google Scholar
  30. N. R. Draper and H. Smith, Applied Regression Analysis, John Wiley & Sons, New York, NY, USA, 3rd edition, 1998.
  31. S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, Upper Saddle River, NJ, USA, 2nd edition, 1999.
  32. R. Olsson, “The art of writing specifications for the adate automatic programming system,” in Proceedings of the 3rd Annual Conference on Genetic Programmin, pp. 278–283, 1998. View at: Google Scholar
  33. S. Gustafson, E. K. Burke, and G. Kendall, “Sampling of unique structures and behaviours in genetic programming,” in Proceedings of the 7th European Conference on Genetic Programming, vol. 3003 of Lecture Notes in Computer Science, pp. 279–288, 2004. View at: Google Scholar
  34. G. Zenobi and P. Cunningham, “Using diversity in preparing ensembles of classifiers based on different feature subsets to minimize generalization error,” in Proceedings of the 12th European Conference on Machine Learning (ECML '01), pp. 576–587, Freiburg, Germany, September 2001. View at: Publisher Site | Google Scholar
  35. T. G. Dietterich, “Ensemble methods in machine learning,” in Proceedings of the 1st International Workshop on Multiple Classifier Systems, pp. 1–15, 2000. View at: Google Scholar
  36. O. Takahashi and S. Kobayashi, “An angular distance dependent alternation model for real-coded genetic algorithms,” in Proceedings of the Congress on Evolutionary Computation (CEC '04), vol. 2, pp. 2159–2165, 2004. View at: Google Scholar
  37. T. Bäck, Evolutionary Algorithms in Theory and Practice, Oxford University Press, Oxford, UK, 1996.
  38. O. W. Gilley and R. K. Pace, “On the harrison and rubinfeld data,” Journal of Environmental Economics and Management, vol. 31, no. 3, pp. 403–405, 1996. View at: Publisher Site | Google Scholar
  39. A. Asuncion and D. Newman, “UCI machine learning repository,” 2007, http://archive.ics.uci.edu/ml. View at: Google Scholar
  40. P. Vlachos, “The StatLib data set repository,” 2009, http://lib.stat.cmu.edu/datasets. View at: Google Scholar
  41. X. Yao, “Evolving artificial neural networks,” Proceedings of the IEEE, vol. 87, no. 9, pp. 1423–1447, 1999. View at: Publisher Site | Google Scholar
  42. C. Spearman, “The proof and measurement of association between two things,” The American Journal of Psychology, vol. 15, no. 1, pp. 72–101, 1904. View at: Google Scholar
  43. B. Sareni and L. Krähenbühl, “Fitness sharing and niching methods revisited,” IEEE Transactions on Evolutionary Computation, vol. 2, no. 3, pp. 97–106, 1998. View at: Google Scholar
  44. P. Darwen and X. Yao, “Every niching method has its niche: fitness sharing and implicit sharing compared,” in Parallel Problem Solving from Nature, vol. 1141 of Lecture Notes in Computer Science, pp. 398–407, Springer, Berlin, Germany, 1996. View at: Google Scholar
  45. C. D. Rosin and R. K. Belew, “New methods for competitive coevolution,” Evolutionary Computation, vol. 5, no. 1, pp. 1–29, 1997. View at: Google Scholar

Copyright © 2009 Henrik Berg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

127 Views | 47 Downloads | 1 Citation
 PDF  Download Citation  Citation
 Download other formatsMore
 Order printed copiesOrder

Related articles

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at help@hindawi.com to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.