A Pareto Strength Evolutionary Algorithm for Constrained Optimization

A new approach is presented to handle constraints optimization using evolutionary algorithms. It neither uses any penalty function nor makes distinction between feasible solutions and infeasible solutions. The new technique treats constrained optimization as a two-objective optimization. One objective is original objective function, the other is the degree violating the constraints. Individual抯 ranking procedure is based on its Pareto strength which appears first in multi-objective optimization. Pareto strength evaluates an individual抯 fitness dependent on the number of dominated points in the population. By combining Pareto strength ranking procedure with minimal generation gap modal, a new real-coded genetic algorithm is proposed. The new approach is compared against other evolutionary optimization techniques in several benchmark functions. The results obtained show that the new approach is a general, effective and robust method. Its performance outperforms some other techniques. Especially for some complicated optimization problems with inequality and equality constraints, the proposed method provides better numerical accuracy.

[1]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[2]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

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

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

[5]  Hajime Kita,et al.  A Comparison Study of Self-Adaptation in Evolution Strategies and Real-Coded Genetic Algorithms , 2001, Evolutionary Computation.

[6]  M. Yamamura,et al.  Multi-parent recombination with simplex crossover in real coded genetic algorithms , 1999 .

[7]  Shigenobu Kobayashi,et al.  A robust real-coded genetic algorithm using Unimodal Normal Distribution Crossover augmented by Uniform Crossover: effects of self-adaptation of crossover probabilities , 1999 .

[8]  K. Deb,et al.  Real-coded evolutionary algorithms with parent-centric recombination , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[10]  Kalyanmoy Deb,et al.  On self-adaptive features in real-parameter evolutionary algorithms , 2001, IEEE Trans. Evol. Comput..

[11]  Z. Michalewicz.  Genetic Algorithms , Numerical Optimization , and Constraints , 1995 .