Handling equality constraints by adaptive relaxing rule for swarm algorithms

The adaptive constraints relaxing rule for swarm algorithms to handle with the problems with equality constraints is presented. The feasible space of such problems may be similiar to ridge function class, which is hard for applying swarm algorithms. To enter the solution space more easily, the relaxed quasi feasible space is introduced and shrinked adaptively. The experimental results on benchmark functions are compared with the performance of other algorithms, which show its efficiency.

[1]  Xiao-Feng Xie,et al.  DEPSO: hybrid particle swarm with differential evolution operator , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[2]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[3]  Xiaohui Hu,et al.  Engineering optimization with particle swarm , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

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

[5]  Eric Bonabeau,et al.  Agent-based modeling: Methods and techniques for simulating human systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

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

[7]  L. N. de Castro Immune, swarm, and evolutionary algorithms. Part II: philosophical comparisons , 2002 .

[8]  J. Lampinen A constraint handling approach for the differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..

[10]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[11]  Hans-Georg Beyer,et al.  On the performance of (1,l)-Evolution Strategies at the ridge function class , 2001 .

[12]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

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

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

[15]  R. Salomon Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms. , 1996, Bio Systems.

[16]  James Kennedy,et al.  Bare bones particle swarms , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[17]  Hans-Georg Beyer,et al.  On the performance of (1, Lambda)-evolution strategies for the ridge function class , 2001, IEEE Trans. Evol. Comput..

[18]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .