# GLOBAL COMPETITIVE RANKING FOR CONSTRAINTS HANDLING WITH MODIFIED DIFFERENTIAL EVOLUTION

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

#### 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.

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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