Self-adaptive penalties in the electromagnetism-like algorithm for constrained global optimization problems

1. Abstract A well-known approach for solving constrained optimization problems is based on penalty functions. A penalty technique transforms the constrained problem into an unconstrained problem by penalizing the objective function when constraints are violated and then minimizing the penalty function using methods for unconstrained problems. In this paper, we analyze the implementation of a self-adaptive penalty approach, within the electromagnetism-like population-based algorithm, in which the constraints that are more difficult to be satisfied will have relatively higher penalty values. The penalties depend upon the level of constraint violation scaled by the average of the objective function values. Numerical results obtained with a collection of well-known global optimization problems are presented and a comparison with other stochastic methods is also reported. 2.

[1]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[2]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[3]  Jiann-Horng Lin,et al.  Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization , 2007 .

[4]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[5]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[6]  Masao Fukushima,et al.  Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization , 2006, J. Glob. Optim..

[7]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[8]  Shu-Cherng Fang,et al.  An Electromagnetism-like Mechanism for Global Optimization , 2003, J. Glob. Optim..

[9]  Angel Eduardo Muñoz Zavala,et al.  Constrained optimization via particle evolutionary swarm optimization algorithm (PESO) , 2005, GECCO '05.

[10]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[11]  Ana Maria A. C. Rocha,et al.  Implementation of the Electromagnetism-Like Algorithm with a Constraint-Handling Technique for Engineering Optimization Problems , 2008, 2008 Eighth International Conference on Hybrid Intelligent Systems.

[12]  Sevket Ilker Birbil,et al.  Stochastic Global Optimization Techniques , 2002 .

[13]  Afonso C. C. Lemonge,et al.  An Adaptive Penalty Method for Genetic Algorithms in Constrained Optimization Problems , 2008 .

[14]  Helio J. C. Barbosa,et al.  An adaptive penalty scheme for genetic algorithms in structural optimization , 2004 .

[15]  Michael N. Vrahatis,et al.  Memetic particle swarm optimization , 2007, Ann. Oper. Res..