Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-22T01:59:30.373Z Has data issue: false hasContentIssue false
  • English
  • Français

Intelligent Genetic Algorithm with a Gradient-Based Local Search Applied to Supersonic Wing Planform Optimization

Published online by Cambridge University Press:  05 May 2011

J.-L. Liu  and
J.-L. Chen
J.-L. Liu*
Affiliation:
Department of Information Management, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, R.O.C.
J.-L. Chen*
Affiliation:
Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, Taiwan 84001, R.O.C.
*
*Doctoral student
**Assistant Professor
Get access

Abstract

This study proposes an efficiently evolutionary algorithm, termed IGA-LS, which combines an intelligent genetic algorithm (IGA) with a gradient-based local search (LS). The IGA performs a crossover operation and uses a fractional factorial design to determine the optimal combination of design variables. That is, in the proposed IGA, the chromosomes of children are generated via an intelligent crossover process with factorial experiments after the execution of the selection operation of the GA. This gene mating process differs from that of the traditional GA, in which each chromosome of child exchange genes randomly. The gradient-based optimization approach seeks feasible and usable directions in which to minimize a specified objective function. The initial conditions are provided by the IGA in each generation. Therefore, the IGA-LS offers fast convergence and high numerical accuracy. Several multi-modal test functions are introduced herein to examine the algorithmic capacity and efficiency of finding the global optima. Moreover, the proposed IGA-LS algorithm is applied to optimize the design of a supersonic wing planform for supersonic airplane. The objective function is to minimize the drag during supersonic cruising. From the numerical results, the presented algorithm outperforms the traditional GA, the micro-GA and the intelligent GA in terms of convergence rate and value of the optimal function.

Keywords

Intelligent genetic algorithmGradient-based local searchSupersonic wing planform.
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 4 , December 2007 , pp. 285 - 294
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Vanderplaats, G. N., “Efficient Algorithm for Numerical Airfoil Optimization,” Journal of Aircraft, 16, pp. 842–847 (1979).CrossRefGoogle Scholar
2.Oyama, A., Obayashi, S. and Nakahashi, K., “Euler/Navier-Stokes Optimization of Supersonic Wing Design Based on Evolutionary Algorithm,” AIAA Journal, 37, pp. 1327–1328 (1999).CrossRefGoogle Scholar
3.Gould, A. R. B., “Automated Surface Shape Optimisation in the MDO Project,” The Aeronautical Journal, pp. 363–372 (1999).CrossRefGoogle Scholar
4.Obayashi, S. and Takeguchi, Y., “Multipoint Aerodynamic Design of Supersonic Wing Planform Using MOGA,” Proc. of the 7th Annual Conference of the Computational Fluid Dynamics Society of Canada, Halifax (1999).Google Scholar
5.Sasaki, D., Obayashi, S., Sawada, K. and Himeno, R., “Multiobjective Aerodynamic Optimization of Supersonic Wings Using Navier-Stokes Equations,” European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, Spain (2000).Google Scholar
6.Pulliam, T. H., Nemec, M., Holst, T. and Zingg, D.W., “Comparison of Evolutionary (Genetic) Algorithm and Adjoint Methods for Multi-objective Viscous Airfoil Optimizations,” AIAA Paper, pp. 2003–0298 (2003).CrossRefGoogle Scholar
7.Griewank, A. O., “Generalized Descent for Global Optimization,” J. Optimization Theory and Applications, 34, pp. 11–39(1981).CrossRefGoogle Scholar
8.Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design, 3rd Edition, McGraw-Hill, New York (1999).Google Scholar
9.Storm, R. and Price, K., “Differential Evolution— A Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous Spaces,” TR–95–012, ICSI, University of California, Berkeley (1995).Google Scholar
10.Ahmed, Q., Krishnakumar, K. and Neidhoefer, J., “Applications of Evolutionary Algorithms to Aerospace Problems—A Survey,” Computational Methods in Applied Sciences ‘96, Wiley, London, pp. 236–242 (1996).Google Scholar
11.Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, 1st Edition, Addison-Wesley, Reading, MA (1989).Google Scholar
12.Michalewicz, Z., Genetic Algorithms +Data Structures = Evolution Programs, 3rd Edition, Springer-Verlag, Berlin Heidelberg (1999).Google Scholar
13.Coley, D. A., An Introduction to Genetic Algorithms for Scientists and Engineering, reprinted Edition, World Scientific, Singapore (2001).Google Scholar
14.Vicini, A. and Quagliarella, D., “Airfoil and Wing Design Through Hybrid Optimization Strategy,” AIAA Journal, 37, pp. 634–641 (1999).CrossRefGoogle Scholar
15.Yen, J., Liao, J. C., Lee, B. and Randolph, D., “A Hybrid Approach to Modeling Metabolic Systems Using a Genetic Algorithm and Simplex Method,” IEEE Transactions on Systems, Man and Cybernetics, pp. 173–191 (1998).CrossRefGoogle Scholar
16.Liaw, C. F., “A Hybrid Genetic Algorithm for Open Shop Scheduling Problem,” European Journal of Operational Research, 124, pp. 28–42, (2000).CrossRefGoogle Scholar
17.Ho, S. Y., Shu, L. S. and Chen, H. M., “Intelligent Genetic Algorithm with a New Intelligent Crossover Using Orthogonal Array,” Proceedings of 1999 Genetic and Evolutionary Computation Conference, 1, pp. 289–296 (1999).Google Scholar
18.Tsai, J. T., Liu, T. K. and Chou, J. H., “Hybrid Taguchi-Genetic Algorithm for Global Numerical Optimization,” IEEE Transactions on Evolutionary Computation, 8, pp. 365–377 (2004).CrossRefGoogle Scholar
19.Bui, T. N. and Moon, B. R., “A Fast and Stable Hybrid Genetic Algorithm for the Ratio-Cut Partitioning Problem on Hypergraphs,” Proceedings of ACM/IEEE Design Automation Conference, 1, pp. 664–669 (1994).Google Scholar
20.Krishnakumar, K., “Micro-Genetic Algorithms for Stationary and Non-Stationary Function Optimization,” SPIE: Intelligent Control and Adaptive Systems, 1196, Philadelphia PA (1989).Google Scholar
21.Bhote, K. R., World Class Quality: Using Design of Experiments to Make It Happen, 1st Edition, American Management Association, New York (1991).Google Scholar
22.Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design, 3rd Edition, Mcgraw-Hill, New York (1999).Google Scholar
23.Hsu, U. K., Tai, C. H. and Tsai, C. H.“All Speed and High-Resolution Scheme Applied to Three-Dimensional Multi-Block Complex Flowfield System,” Journal of Mechanics, 20, pp. 21–33 (2004).CrossRefGoogle Scholar
24.Tseng, J. B. and Lan, C. E., “Calculation of Aerodynamic Characteristics of Airplane Configurations at High Angles of Attack,” NASA Report, CR-4182 (1988).Google Scholar