CULTURAL SWARMS - Knowledge-driven Framework for Solving Nonlinearly Constrained Global Optimization Problems

Mostafa Z. Ali, Yaser Khamayseh, Robert G. Reynolds

Abstract

In this paper we investigate how diverse knowledge sources interact to direct individuals in a swarm population influenced by a social fabric approach to efficiently solve nonlinearly constrained global minimization problems. We identify how knowledge sources used by Cultural Algorithms are combined to direct the decisions of the individual agents in solving optimization problems using an influence function family based upon a Social Fabric metaphor. The interaction of these knowledge sources with the population swarms produced emergent phases of problem solving. This reflected an algorithmic process that emerged from the interaction of the knowledge sources under the influence of a social fabric using different configurations. This suggests that the social interaction of individuals coupled with their interaction with a culture within which they are embedded provides a powerful vehicle for the solution of nonlinearly constrained optimization problems. The algorithm can escape from the previously converged local minimizers, and can converge to an approximate global minimizer of the problem asymptotically. Numerical experiments show that it is better than many other well-known recent methods for constrained global optimization.

References

  1. Cheng, L., Patterson, J., Rohall S., Hupfer S., Ross S., 2005. Weaving a Social Fabric into Existing Software AOSD 2005 - Fourth International Conference on Aspect-Oriented Software Development, March 2005, Chicago, IL. RC23485.
  2. Coelho, L., Souza R., Mariani V., 2009. Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems, Mathematics and Computers in Simulation, Vol. 79 , Issue 10.
  3. Coello, C., 2002. Theoretical and numerical constrainthandling techniques used with evolutionary algorithms: A survey of the state of the art, Computer Methods in Applied Mechanics and Engineering 191, 1245-1287.
  4. Coello, C., Mezura-Montes, E., 2002. Handling Constraints in Genetic Algorithms Using Dominance-Based Tournaments. In I. Parmee, editor, Proceedings of the Fifth International Conference on Adaptive Computing Design and Manufacture (ACDM 2002), volume 5, pages 273- 284, University of Exeter, Devon, UK, April 2002. Springer-Verlag.
  5. Deb, K., Goldberg, D., 1989. An Investigation of Niche and Species Formation in Genetic Function Optimization. In J. D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 42-50, San Mateo, California. Morgan Kaufmann Publishers.
  6. Deb, K., Goyal, M., 1996. A Combined Genetic Adaptive Search GeneAS for Engineering Design. Computer Science and Informatics, 26(4):30-45.
  7. Hedar, A., Fukushima, M., 2006. Derivative-free filter simulated annealing method for constrained continuous global optimization, Journal of Global Optimization 35 521_549.
  8. Hock, W., Schittkowski, K., 1981. Test Examples for Nonlinear Programming Codes, Springer-Verlag, Berlin, Heidelberg.
  9. Horn, J., Nafpliotis, N., Goldberg, D., 1994. A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In Proceedings of the First IEEE Conference on Evolutionary Computation, WCCI volume 1, pages 82-87, Piscataway, New Jersey, June 1994. IEEE Service Center.
  10. Koziel, S., Michalewicz, Z., 1999. Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization, Evolutionary Computation 7 (1) 19_44.
  11. Michalewicz, Z., Schoenauer, M., 1996. Evolutionary algorithms for constrained parameter optimization problems, Evolutionary Computation 4 (1) 1_32.
  12. North, M., Collier, N., and Vos, J., 2006. 'Experiences Creating Three Implementations of the Repast Agent Modelling Toolkit', ACM Transactions on Modelling and Computer Simulation, 16(1): 1-25.
  13. Reynolds, R., 1986. "A Metrics-Based System to Monitor the Stepwise Refinement of Program Modules", Fourth Conference on Intelligent Systems and Machines, Oakland University, April 29-30.
  14. Reynolds, R., Saleem, S., 2003, “The Impact of Environmental Dynamics on Cultural Emergence”. Festschrift, in Honor of John Holland, to appear, Oxford University Press, pp.1-10.
  15. Reynolds, R., Peng, B., 2005. Cultural algorithms: computational modeling of how cultures learn to solve problems: an engineering example. Cybernetics and Systems 36(8): 753-771.
  16. Reynolds, R., Ali, M., 2007. "Exploring knowledge and population swarms via an agent-based Cultural Algorithms Simulation Toolkit (CAT)," Evolutionary Computation, 2007. CEC 2007. IEEE Congress on, vol., no., pp.2711-2718, 25-28.
  17. Wenxing Z., Ali, M., 2009. Solving nonlinearly constrained global optimization problem via an auxiliary function method, Journal of computational and applied mathematics.
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Paper Citation


in Harvard Style

Z. Ali M., Khamayseh Y. and G. Reynolds R. (2009). CULTURAL SWARMS - Knowledge-driven Framework for Solving Nonlinearly Constrained Global Optimization Problems . In Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009) ISBN 978-989-674-014-6, pages 103-110. DOI: 10.5220/0002282301030110


in Bibtex Style

@conference{icec09,
author={Mostafa Z. Ali and Yaser Khamayseh and Robert G. Reynolds},
title={CULTURAL SWARMS - Knowledge-driven Framework for Solving Nonlinearly Constrained Global Optimization Problems},
booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)},
year={2009},
pages={103-110},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002282301030110},
isbn={978-989-674-014-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)
TI - CULTURAL SWARMS - Knowledge-driven Framework for Solving Nonlinearly Constrained Global Optimization Problems
SN - 978-989-674-014-6
AU - Z. Ali M.
AU - Khamayseh Y.
AU - G. Reynolds R.
PY - 2009
SP - 103
EP - 110
DO - 10.5220/0002282301030110