Research Papers

A Novel Global Optimization Algorithm and Its Application to Airfoil Optimization

[+] Author and Article Information
B. Yang

Gas Turbine Institute,
Shanghai Jiaotong University,
No. 800 Dongchuan Road,
Shanghai 200000, China
e-mail: byang0626@sjtu.edu.cn

Q. Xu

Shanghai Electric Power Generation
R & D Center,
1st Floor, Building A,
No. 333, West Yindu Road,
Shanghai 201612, China
e-mail: xuqiang@shanghai-electric.com

L. He

Shanghai Electric Power Generation
R & D Center,
1st Floor, Building A,
No. 333, West Yindu Road,
Shanghai 201612, China
e-mail: helei@shanghai-electric.com

L. H. Zhao

Shanghai Electric Power Generation
R & D Center,
1st Floor, Building A,
No. 333, West Yindu Road,
Shanghai 201612, China
e-mail: zhaolh@shanghai-electric.com

Ch. G. Gu

School of Mechanical Engineering,
Shanghai Jiaotong University,
No. 800 Dongchuan Road,
Shanghai 200000, China
e-mail: cggu2006@126.com

P. Ren

Shanghai Electric Power Generation
R & D Center,
1st Floor, Building A,
No. 333, West Yindu Road,
Shanghai 201612, China
e-mail: renping2@shanghai-electric.com

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 15, 2014; final manuscript received September 22, 2014; published online November 26, 2014. Editor: Ronald Bunker.

J. Turbomach 137(4), 041011 (Apr 01, 2015) (10 pages) Paper No: TURBO-14-1242; doi: 10.1115/1.4028712 History: Received September 15, 2014; Revised September 22, 2014; Online November 26, 2014

In this paper, a novel global optimization algorithm has been developed, which is named as particle swarm optimization combined with particle generator (PSO–PG). In PSO–PG, a PG was introduced to iteratively generate the initial particles for PSO. Based on a series of comparable numerical experiments, it was convinced that the calculation accuracy of the new algorithm as well as its optimization efficiency was greatly improved in comparison with those of the standard PSO. It was also observed that the optimization results obtained from PSO–PG were almost independent of some critical coefficients employed in the algorithm. Additionally, the novel optimization algorithm was adopted in the airfoil optimization. A special fitness function was designed and its elements were carefully selected for the low-velocity airfoil. To testify the accuracy of the optimization method, the comparative experiments were also carried out to illustrate the difference of the aerodynamic performance between the optimized and its initial airfoil.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Chen, X., and Agarwal, R. K., 2013, “Shape Optimization of Airfoil in Transonic Flow Using a Multi-Objective Genetic Algorithm,” AIAA Paper No. 2013-2907. [CrossRef]
Cocke, T., Moscicki, Z., and Agarwa, R., 2012, “Optimization of Hydrofoils Using a Genetic Algorithm,” AIAA Paper No. 2012-3120. [CrossRef]
Mazaheri, K., Khayatzadeh, P., and Nezhad, S. T., 2008, “Laminar Airfoil Shape Optimization Using an Improved Genetic Algorithm,” AIAA Paper No. 2008-913. [CrossRef]
Liu, J., 2005, “A Novel Taguchi-Simulated Annealing Method and Its Application to Airfoil Design Optimization,” AIAA Paper No. 2005-4858. [CrossRef]
Quagliarella, D., Periauz, J., Poloni, C., and Winter, G., 1997, Genetic Algorithm in Engineering and Computer Science, 1st ed., John Wiley and Sons, Chichester, UK.
Ingber, L., and Rosen, B., 1992, “Genetic Algorithms and Very Fast Simulated Annealing: A Comparison,” Math. Comput. Model., 16(11), pp. 87–100. [CrossRef]
Vicini, A., and Quagliarella, D., 1999, “Airfoil and Wing Design Through Hybrid Optimization Strategy,” AIAA J., 37(5), pp. 634–641. [CrossRef]
Zingg, D. W., Nemec, M., and Pulliam, T. H., 2008, “A Comparative Evaluation of Genetic and Gradient-Based Algorithms Applied to Aerodynamic Optimization,” Eur. J. Comput. Mech., 17(1), pp. 103–126. [CrossRef]
Kennedy, J., and Eberhart, R. C., 1995, “Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, Perth, Australia, Nov. 27–Dec. 1, pp. 1942–1948. [CrossRef]
Khurana, M. S., Winarto, H., and Sinha, A. K., 2008, “Application of Swarm Approach and Artificial Neural Networks for Airfoil Shape Optimization,” AIAA Paper No. 2008-5954. [CrossRef]
Pontani, M., and Conway, B. A., 2010, “Particle Swarm Optimization Applied to Space Trajectories,” J. Guidance, Control Dynam., 33(5), pp. 1429–1441. [CrossRef]
Shi, Y. H., and Eberhart, R. C., 1998, “Parameter Selection in Particle Swarm Optimization,” Evolutionary Programming VII: 7th International Conference (EP98), San Diego, CA, Mar. 25–27, pp. 591–600. [CrossRef]
Fourie, P. C., and Groenwold, A. A., 2002, “The Particle Swarm Optimization Algorithm in Size and Shape Optimization,” Struct. Multidisc. Optim., 23(4), pp. 259–267. [CrossRef]
Clerc, M., and Kennedy, J. E., 2002, “The Particle Swarm–Explosion, Stability in a Multidimensional Complex Space,” IEEE Trans. Evol. Comput., 6(1), pp. 259–267. [CrossRef]
Dong, C., and Qiu, Z., 2006, “Particle Swarm Optimization Algorithm Based on the Idea of Simulated Annealing,” Int. J. Comput. Sci. Network Secur., 6(10), pp. 152–157, available at: http://paper.ijcsns.org/07_book/200610/200610B03.pdf
Wu, X., Wang, Y., and Zhang, T., 2009, “An Improved GAPSO Hybrid Programming Algorithm,” International Conference on Information Engineering and Computer Science, Wuhan, China, Dec. 19–20.
Xie, X., and Wu, P., 2010, “Research on the Optimal Combination of ACO Parameters Base on PSO,” 2nd International Conference on Networking and Digital Society (ICNDS), Wenzhou, China, May 30–31.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E., 1953, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys., 21(6), pp. 1087–1092. [CrossRef]
Kirpatrick, S., Gelatt, C. D., and Vecchi, M. P., 1982, “Optimization by Simulated Annealing,” IBM Thomas J Watson Research Center, Yorktown Heights, NY, Research Report No. RC 9355.
Szu, H., and Hartley, R., 1987, “Fast Simulated Annealing,” Phys. Lett. A, 122(3–4), pp. 157–162. [CrossRef]
Kennedy, J., 1997, “The Particle Swarm: Social Adaptation of Knowledge,” IEEE International Conference on Evolutionary Computation, Indianapolis, IN, Apr. 13–16, pp. 303–308. [CrossRef]
Pohlheim, H., 2007, “GEATbx: Genetic and Evolutionary Algorithm Toolbox for Use With Matlab,” H. Pohlheim, Berlin, http://www.geatbx.com/
Shu, X., Gu, C., Wang, T., and Yang, B., 2007, “Aerodynamic Optimization for Turbine Blades Based on Hierarchical Fair Competition Genetic Algorithms With Dynamic Niche,” Chin. J. Mech. Eng., 20(6), pp. 38–42. [CrossRef]
Shu, X., Gu, C., Xiao, J., and Gao, C., 2008, “Centrifugal Compressor Blade Optimization Based on Uniform Design and Genetic Algorithms,” Front. Energy Power Eng. China, 2(4), pp. 453–456. [CrossRef]
Sieverding, F., Ribi, B., Casey, M., and Meyer, M., 2004, “Design of Industrial Axial Compressor Blade Sections for Optimal Range and Performance,” ASME J. Turbomach., 126(2), pp. 323–331. [CrossRef]
Wilcox, D. C., 1993, “Comparison of Two-Equation Turbulence Models for Boundary Layers With Pressure Gradient,” AIAA J., 31(8), pp. 1414–1421. [CrossRef]
Wilcox, D. C., 1994, “Simulation of Transition With a Two-Equation Turbulence Model,” AIAA J., 32(2), pp. 247–255. [CrossRef]
Menter, F. R., 1992, “Performance of Popular Turbulence Models for Attached and Separated Adverse Pressure Gradient Flows,” AIAA J., 30(8). pp. 2066–2072. [CrossRef]
Yang, B., 2001, “A New Blade Design Scheme for Reversible Axial Flow Fan & Research on the Combined Cascades,” Ph.D. dissertation, Shanghai Jiaotong University, Shanghai, China.


Grahic Jump Location
Fig. 1

Flow chart of PSO–PG

Grahic Jump Location
Fig. 2

Griewank function: (a) xi ∈ [-600,600], (b) xi ∈ [-50,50], and (c) xi ∈ [-5,5]

Grahic Jump Location
Fig. 3

Simulation experiments results: (a) tests of dependence on inertia weight, (b) tests of dependence on maximum flying velocity, (c) tests of dependence on positive constants, and (d) tests of dependence on particle size

Grahic Jump Location
Fig. 4

Geometry comparison: dashed line—NACA 63012 and solid line—optimized

Grahic Jump Location
Fig. 5

Single airfoil performance (cal., Re = 3.25 × 105)

Grahic Jump Location
Fig. 6

Velocity contours: (a) α = 2.5 deg, NACA 63012; (b) α = 2.5 deg, the optimized; (c) α = 12.5 deg, NACA 63012; and (d) α = 12.5 deg, the optimized

Grahic Jump Location
Fig. 7

Experimental rig: 1—centrifugal fan, 2—regulator, 3—test cascade, 4—angle scale, A—measure point for volume rate, B—measure point at inlet, C—measure point at outlet

Grahic Jump Location
Fig. 8

Cascade performance (exp., Re = 3.25 × 105)

Grahic Jump Location
Fig. 9

Pressure distribution: (a) cascade (α=5.32), single airfoil (α=5) and (b) cascade (α=12.67), single airfoil (α=12.5)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In