An Evolutionary Computing Approach to Robust Design in the Presence of Uncertainties

This paper sets forth a new approach to robust evolutionary computing. In particular, the proposed approach allows users to specify the probability of success in meeting design specifications in the presence of uncertainties. Three benchmark problems have been considered to demonstrate the proposed approach. In addition, a robust electromagnet design example is also considered. The results illustrate quantitative correspondence between the prescribed and the computed robustness.

[1]  Bernhard Sendhoff,et al.  Trade-off between Optimality and Robustness: An Evolutionary Multiobjective Approach , 2003 .

[2]  Jürgen Branke,et al.  Creating Robust Solutions by Means of Evolutionary Algorithms , 1998, PPSN.

[3]  S.D. Sudhoff,et al.  Evolutionary Optimization of PowerElectronics Based Power Systems , 2008, IEEE Transactions on Power Electronics.

[4]  J. Fitzpatrick,et al.  Genetic Algorithms in Noisy Environments , 2005, Machine Learning.

[5]  Jürgen Branke,et al.  Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation , 2006, IEEE Transactions on Evolutionary Computation.

[6]  J. Cale,et al.  Accurately modeling EI core inductors using a high-fidelity magnetic equivalent circuit approach , 2006, IEEE Transactions on Magnetics.

[7]  Kay Chen Tan,et al.  An Investigation on Noisy Environments in Evolutionary Multiobjective Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[8]  S. D. Sudhoff,et al.  Evolutionary Optimization of Power Electronics Based Power Systems , 2007, APEC 07 - Twenty-Second Annual IEEE Applied Power Electronics Conference and Exposition.

[9]  Evan J. Hughes Evolutionary algorithm with a novel insertion operator for optimising noisy functions , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[10]  S.D. Sudhoff,et al.  Evolutionary Design of Electromagnetic and Electromechanical Devices , 2007, 2007 IEEE Electric Ship Technologies Symposium.

[11]  E. J. Hughes,et al.  Constraint handling with uncertain and noisy multi-objective evolution , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[12]  S. Leigh,et al.  Probability and Random Processes for Electrical Engineering , 1989 .

[13]  Ignacio J. Ramirez-Rosado,et al.  Genetic algorithms applied to the design of large power distribution systems , 1998 .

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

[15]  Russell C. Eberhart,et al.  Utilizing particle swarm optimization to label a structured beam matrix , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[16]  I. Miller Probability, Random Variables, and Stochastic Processes , 1966 .

[17]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

[18]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[19]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[20]  Bernhard Sendhoff,et al.  Trade-Off between Performance and Robustness: An Evolutionary Multiobjective Approach , 2003, EMO.

[21]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[22]  H. Kita,et al.  Genetic algorithms for optimization of uncertain functions and their applications , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[23]  Shigeyoshi Tsutsui,et al.  Genetic algorithms with a robust solution searching scheme , 1997, IEEE Trans. Evol. Comput..

[24]  T. Ray Constrained robust optimal design using a multiobjective evolutionary algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[25]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .