GLOBAL COMPETITIVE RANKING FOR CONSTRAINTS HANDLING WITH MODIFIED DIFFERENTIAL EVOLUTION

Abul Kalam Azad, Edite M. G. P. Fernandes

2011

Abstract

Constrained nonlinear programming problems involving a nonlinear objective function with inequality and/or equality constraints introduce the possibility of multiple local optima. The task of global optimization is to find a solution where the objective function obtains its most extreme value while satisfying the constraints. Depending on the nature of the involved functions many solution methods have been proposed. Most of the existing population-based stochastic methods try to make the solution feasible by using a penalty function method. However, to find the appropriate penalty parameter is not an easy task. Population-based differential evolution is shown to be very efficient to solve global optimization problems with simple bounds. To handle the constraints effectively, in this paper, we propose a modified constrained differential evolution that uses self-adaptive control parameters, a mixed modified mutation, the inversion operation, a modified selection and the elitism in order to progress efficiently towards a global solution. In the modified selection, we propose a fitness function based on the global competitive ranking technique for handling the constraints. We test 13 benchmark problems. We also compare the results with the results found in literature. It is shown that our method is rather effective when solving constrained problems.

References

  1. Ali, M. M., Khompatraporn, C. and Zabinsky, Z. B. (2005). A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. Journal of Global Optimization, 31, 635- 672.
  2. Barbosa, H. J. C. and Lemonge, A. C. C. (2003). A new adaptive penalty scheme for genetic algorithms. Information Sciences, 156, 215-251.
  3. Brest, J., Greiner, S., Bos?kovic, B., Mernik, M. and Z?umer, V. (2006). Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation, 10, 646-657.
  4. Coello Coello, C. A. (2000). Constraint-handling using an evolutionary multiobjective optimization technique. Civil Engineering and Environmental Systems, 17, 319-346.
  5. Coello Coello, C. A. and Cortés, N. C. (2004). Hybridizing a genetic algorithm with an artificial immune system for global optimization. Engineering Optimization, 36, 607-634.
  6. Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186, 311-338.
  7. Dolan, E. D. and Moré, J. J. (2002). Benchmarking optimization software with performance profiles. Mathematical Programming, 91, 201-213.
  8. Dong, Y., Tang, J., Xu, B. and Wang, D. (2005). An application of swarm optimization to nonlinear programming. Computers & Mathematics with Applications, 49, 1655-1668.
  9. Fletcher, R. and Leyffer, S. (2002). Nonlinear programming without a penalty function. Mathematical Programming, 91, 239-269.
  10. Fourer, R., Gay, D. M. and Kernighan, B. W. (1993). AMPL: A modelling language for matematical programming. Boyd & Fraser Publishing Co.: Massachusets.
  11. Hedar, A. R. and Fukushima, M. (2006). Derivative-free filter simulated annealing method for constrained continuous global optimization. Journal of Global Optimization, 35, 521-549.
  12. Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press: Ann Arbor.
  13. Kaelo, P. and Ali, M. M. (2006). A numerical study of some modified differencial evolution algorithms. European Journal of Operational Research, 169, 1176-1184.
  14. Ray, T. and Tai, K. (2001). An evolutionary algorithm with a multilevel pairing strategy for single and multiobjective optimization. Foundations of Computing and Decision Sciences, 26, 75-98.
  15. Ray, T. and Liew, K. M. (2003). Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Transactions on Evolutionary Computation, 7, 386-396.
  16. Rocha, A. M. A. C. and Fernandes, E.M.G.P. (2008). Feasibility and dominance rules in the electromagnetismlike algorithm for constrained global optimization. In Gervasi et al. (Eds.), Computational Science and Its Applications: Lecture Notes in Computer Science (vol. 5073, pp. 768-783). Springer: Heidelberg.
  17. Rocha, A. M. A. C. and Fernandes, E.M.G.P. (2009). Self adaptive penalties in the electromagnetism-like algorithm for constrained global optimization problems. In Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization (pp. 1-10).
  18. Runarsson, T. P. and Yao, X. (2000). Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation, 4, 284-294.
  19. Runarsson, T.P. and Yao, X. (2003). Constrained evolutionary optimization - the penalty function approach. In Sarker et al. (Eds.), Evolutionary Optimization: International Series in Operations Research and Management Science (vol. 48, pp. 87-113), Springer: New York.
  20. Silva, E. K., Barbosa, H. J. C. and Lemonge, A. C. C. (2011). An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization. Optimization and Engineering, 12, 31-54.
  21. Storn, R. and Price, K. (1997). Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11, 341-359.
  22. Vaz, A. I. F. and Vicente, L. N. (2007). A particle swarm pattern search method for bound constrained global optimization. Journal of Global Optimization, 39, 197-219.
  23. Zahara, E. and Hu, C.-H. (2008). Solving constrained optimization problems with hybrid particle swarm optimization. Engineering Optimization, 40, 1031-1049.
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Paper Citation


in Harvard Style

Kalam Azad A. and M. G. P. Fernandes E. (2011). GLOBAL COMPETITIVE RANKING FOR CONSTRAINTS HANDLING WITH MODIFIED DIFFERENTIAL EVOLUTION . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011) ISBN 978-989-8425-83-6, pages 42-51. DOI: 10.5220/0003672200420051


in Bibtex Style

@conference{ecta11,
author={Abul Kalam Azad and Edite M. G. P. Fernandes},
title={GLOBAL COMPETITIVE RANKING FOR CONSTRAINTS HANDLING WITH MODIFIED DIFFERENTIAL EVOLUTION},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)},
year={2011},
pages={42-51},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003672200420051},
isbn={978-989-8425-83-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)
TI - GLOBAL COMPETITIVE RANKING FOR CONSTRAINTS HANDLING WITH MODIFIED DIFFERENTIAL EVOLUTION
SN - 978-989-8425-83-6
AU - Kalam Azad A.
AU - M. G. P. Fernandes E.
PY - 2011
SP - 42
EP - 51
DO - 10.5220/0003672200420051