Replicator Dynamic Inspired Differential Evolution Algorithm for Global Optimization

Shichen Liu, Qiwei Lu, Wenchao huang, Yan Xiong

2012

Abstract

Differential Evolution (DE) has been shown to be a simple yet efficient evolutionary algorithm for solving optimization problems in continuous search domain. However the performance of the DE algorithm, to a great extent, depends on the selection of control parameters. In this paper, we propose a Replicator Dynamic Inspired DE algorithm (RDIDE), in which replicator dynamic, a deterministic monotone game dynamic generally used in evolutionary game theory, is introduced to the crossover operator. A new population is generated for an applicable probability distribution of the value of Cr, with which the parameter is evolving as the algorithm goes on and the evolution is rather succinct as well. Therefore, the end-users do not need to find a suitable parameter combination and can solve their problems more simply with our algorithm. Different from the rest of DE algorithms, by replicator dynamic, we obtain an advisable probability distribution of the parameter instead of a certain value of the parameter. Experiment based on a suite of 10 bound-constrained numerical optimization problems demonstrates that our algorithm has highly competitive performance with respect to several conventional DE and parameter adaptive DE variants. Statistics of the experiment also show that our evolution of the parameter is rational and necessary.

References

  1. Friedberg, R. M., (1958). A learning machine: Part I. IBM Journal of Research and Development, 2, 2-13.
  2. Box, G. E. P., (1957). Evolutionary operation: A method for increasing industrial productivity. Applied Statistics, 6, 81-101.
  3. Holland, J. H., (1962). Outline for a logical theory of adaptive systems. Journal of the Association for Computing Machinery, 3, 297-314.
  4. Fogel, L. J., (1962). Autonomous automata. Industrial Research, 4, 14-19.
  5. Storn, R. and Price, K., (1995). Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, International Computer Science Institute, Berkeley.
  6. Storn, R., (1996). Differential evolution design of an IIRfilter. In Proceedings of IEEE International Conference on Evolutionary Computation (pp. 268- 273).
  7. Storn, R., (2005). Designing nonstandard filters with differential evolution. IEEE Signal Processing Magazine, 22, 103-106.
  8. Lakshminarasimman, L. and Subramanian, S., (2008). Applications of differential evolution in power system optimization. Studies in Computational Intelligence, 143, 257-273.
  9. Lobo, F. G. and Goldberg, D. E., (2001). The parameterless genetic algorithm in practice. Technical Report 2001022, University of Illinois at Urbana-Champaign, Urbana, IL.
  10. Harik, G. R. and Lobo, F. G. (1999). A parameter-less genetic algorithm. In Banzhaf et al. (Eds.), Proceedings of the 1999 genetic and evolutionary computation conference (vol. 1, pp. 258-265.), Morgan Kaufmann: Orlando.
  11. Gämperle, R., Müller, S. D. and Koumoutsakos, P., (2002). A parameter study for differential evolution. In Grmela, and Mastorakis (Eds.), Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation (pp. 293-298). WSEAS Press: Interlaken.
  12. Omran, M. G. H., Salman, A. and Engelbrecht, A. P., (2005). Self-adaptive differential evolution. In Lecture Notes in Artificial Intelligence (pp. 192-199), Springer-Verlag: Berlin.
  13. Brest, J., Greiner, S., Boskovic, B., Mernik, M. and Zumer, V., (2006). Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation, 10, 646-657.
  14. Teo, J., (2006). Exploring dynamic self-adaptive populations in differential evolution. Soft ComputingA Fusion of Foundations, Methodologies and Applications, 10, 637-686.
  15. Qin, A. K., Huang, V. L, and Suganthan, P. N., (2009). Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation, 13, 398 - 417.
  16. Price, K., Storn, R., and Lampinen, J., (2005). Differential Evolution-A Practical Approach to Global Optimization. Springer-Verlag: New York.
  17. Rogalsky, T., Derksen, R. W., and Kocabiyik, S., (1999). Differential evolutionin aerodynamic optimization. In Proceedings of the 46th Annual Conference of the Canadian Aeronautics and Space Institute (pp. 29-36), Montreal.
  18. Zaharie, D., (2003). Control of population diversity and adaptation in differential evolution algorithms. In Matousek and Osmera (Eds.), Proceedings of 9th International Conference on Soft Computing (pp. 41- 46), Brno.
Download


Paper Citation


in Harvard Style

Liu S., Xiong Y., Lu Q. and huang W. (2012). Replicator Dynamic Inspired Differential Evolution Algorithm for Global Optimization . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 133-143. DOI: 10.5220/0004053401330143


in Bibtex Style

@conference{ecta12,
author={Shichen Liu and Yan Xiong and Qiwei Lu and Wenchao huang},
title={Replicator Dynamic Inspired Differential Evolution Algorithm for Global Optimization},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)},
year={2012},
pages={133-143},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004053401330143},
isbn={978-989-8565-33-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)
TI - Replicator Dynamic Inspired Differential Evolution Algorithm for Global Optimization
SN - 978-989-8565-33-4
AU - Liu S.
AU - Xiong Y.
AU - Lu Q.
AU - huang W.
PY - 2012
SP - 133
EP - 143
DO - 10.5220/0004053401330143