Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1779–1792 | Cite as

Multi-objective optimization of the aerodynamic shape of a long-range guided rocket

  • Cao Runduo
  • Zhang Xiaobing


The parameter values associated with the optimal aerodynamic shape of a long-range guided rocket (LGR) are different from those of an unguided rocket because the shapes and design objectives are different. Here we establish a multi-objective optimization model of the aerodynamic shape of an LGR for the purpose. Moreover, a rapid aerodynamic calculation method is used, which is much more efficient than wind-tunnel tests or computational fluid dynamics (CFD). Previously, the aerodynamic shape of an unguided rocket would be optimized by identifying one parameter as a single objective and regarding the others as constraints. Here, we use version II of the non-dominated sorting genetic algorithm (NSGA-II) and the real-coding genetic algorithm (RGA) to solve this multi-objective optimization problem (MOP). The results obtained by the two algorithms show an improved lift/drag ratio of the LGR with optimal aerodynamic shape, better maneuverability, and acceptable stability. Furthermore, the optimum and original schemes are calculated using CFD, and the pressure contours show that the results are qualitatively correct. This method can be used to design the optimal aerodynamic shape of this type of rocket.


NSGA-II Multi-objective optimization Long-range guided rockets Aerodynamic shape design 



Lift-force coefficient


Drag-force coefficient


Pitching-moment coefficient


Total length of rocket


Length of nose


Length of tailfin root


Length of tailfin tip


Sweepback of tailfin’s leading edge


Sweepback of tailfin’s trailing edge


Position of tailfin


Position of pressure center


Mach number


Reynolds number


Angle of attack


Length of body (calibers)


Length of tail


Length of canard root


Length of canard tip


Sweepback of canard’s leading edge


Sweepback of canard’s trailing edge


Position of canard


Position of gravity center



This work is supported by the National Natural Science Foundation of China (Grant No. 11502114), China Postdoctoral Science Foundation funded project (Grant No. 2015 M581797),the Natural Science Foundation of Jiangsu Province (Grant No. BK20131348) and Key Laboratory Foundation of the People’s Republic of China (Grant No. 9140C300206120C30110).


  1. An H, Chen S, Huang H (2015) Laminate stacking sequence optimization with strength constraints using two-level approximations and adaptive genetic algorithm. Struct Multidiscip Optim 51(4):1–16MathSciNetCrossRefGoogle Scholar
  2. Anderson MB (1995) The potential of genetic algorithms for subsonic wing design, AIAA Paper 95-3925, Aircraft Engineering, Technology, and Operations Congress, Meeting Paper Archive.
  3. Anderson MB, Gebert GA (1996) Using Pareto genetic algorithms for preliminary subsonic wing design, AIAA Meeting Papers on Disc, 1996, pp.363–371
  4. Anderson MB (2000) Missile Aerodynamic Shape Optimization Using Genetic Algorithms. J Spacecr Rocket 37(5):663–669CrossRefGoogle Scholar
  5. Arrieta AJ, Striz AG (2005) Optimal design of aircraft structures with damage tolerance requirements. Struct Multidiscip Optim 30(2):155–163CrossRefGoogle Scholar
  6. Auman LM, Kreeger RE (1998) Aerodynamic characteristics of a canard-controlled missile with a free-spinning tail. AIAA Paper 98–410, 36th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings.
  7. Bramlette M, Cusic R (1989) A comparative evaluation of search methods applied to the parametric design of aircraft. In: Schaffer JD (ed) Proceedings of the Third International Conference on Genetic Algorithms. Morgan Kaufmann, San MateoGoogle Scholar
  8. Deb K (2001) Multi-objective optimization using evolutionary algorithms. John Wiley & Sons Ltd., Singapore (ISBN 9814-12-685-3) zbMATHGoogle Scholar
  9. Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. International Conference on Parallel Problem Solving From Nature 1917:849–858Google Scholar
  10. Fazeley HR, Taei H, Naseh H et al (2016) A multi-objective, multidisciplinary design optimization methodology for the conceptual design of a spacecraft bi-propellant propulsion system. Struct Multidiscip Optim 53:145–160MathSciNetCrossRefGoogle Scholar
  11. Gage P, Kroo I (1993) A role of genetic algorithms in a preliminary design environment. AIAA Paper 93-3933Google Scholar
  12. Holland JH (1992) Adaptation in natural and artificial systems. MIT, CambridgeGoogle Scholar
  13. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471MathSciNetCrossRefzbMATHGoogle Scholar
  14. Kaufmann M, Dan Z, Wennhage P (2009) Integrated cost/weight optimization of aircraft structures. Struct Multidiscip Optim 41(2):325–334CrossRefGoogle Scholar
  15. Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufmann, San FranciscoGoogle Scholar
  16. Kroo I, Altus S (1994) Multidisciplinary optimization methods for aircraft preliminary design. AIAA Paper 94-4325, 5th Symposium on Multidisciplinary Analysis and Optimization, Multidisciplinary Analysis Optimization Conferences.
  17. Lamar M, Richard EK (1998) Aerodynamic characteristics of a canard-controlled missile with a free-spinning tail[C]. AIAA Paper 98–410Google Scholar
  18. Li KJ, Zhang XB (2011) Multi-objective optimization of interior ballistic performance using NSGA II. Propellants, Explosives, Pyrotechnics 36(3):282–290CrossRefGoogle Scholar
  19. Li KJ, Zhang XB (2012) Using NSGA-II and TOPSIS Methods for Interior Ballistic Optimization Based on One-Dimensional Two-Phase Flow Model[J]. Propellants, Explos, Pyrotech 37(4):468–475CrossRefGoogle Scholar
  20. Liu X, Cheng G, Yan J et al (2012) Singular optimum topology of skeletal structures with frequency constraints by AGGA. Struct Multidiscip Optim 45(3):451–466CrossRefGoogle Scholar
  21. Masoud E, Mohammad RF, Jafar R (2011) Multidisciplinary design of a small satellite launch vehicle using particle swarm optimization. Struct Multidiscip Optim 44:773–784CrossRefGoogle Scholar
  22. Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32:269–289CrossRefGoogle Scholar
  23. Menter FR, Rumsey LC (1994) Assessment of two-equation turbulence models for transonic flows. AIAA Paper, 94-2343, , Fluid Dynamics Conference.
  24. Mohammad SS, Mohammad TD (2016) A practical method for aerodynamic investigation of WIG. Aircraft Engineering and Aerospace Technology 88(1):73–81CrossRefGoogle Scholar
  25. Neufeld D, Behdinan K, Chung J (2010) Aircraft wing box optimization considering uncertainty in surrogate models. Struct Multidiscip Optim 42(5):745–753CrossRefGoogle Scholar
  26. Oyama A, Obayashi S, Nakamura T (2001) Real-Coded Adaptive Range Genetic Algorithm Applied to Transonic Wing Optimization. Appl Soft Comput 1(3):179–187CrossRefGoogle Scholar
  27. Sharatchandra MC, Sen M, Gad-el-Hak M (1998) New Approach to Constrained Shape Optimization Using Genetic Algorithms. AIAA J 36(1):35–42CrossRefzbMATHGoogle Scholar
  28. Shi JG, Wang ZY (2006) Aerodynamic Design and Analysis of Canard Rudder for Gliding Extended Range Projectile. Journal of Ballistics 18(4):33–37MathSciNetGoogle Scholar
  29. Shi JG, Wang ZY (2009) Aerodynamic Shape Optimum Design Method for Guided Projectile Equipped with Canard. Journal of Nanjing University of Science and Technology 33(5):555–559Google Scholar
  30. Sleesongsom S, Bureerat S, Tai K (2013) Aircraft morphing wing design by using partial topology optimization. Struct Multidiscip Optim 48(6):1109–1128MathSciNetCrossRefGoogle Scholar
  31. Wu JF (2009) The Aerodynamic Configuration Design of Stability and Control of Canard Configuration Guided Rocket. Master Thesis, Nanjing University of Science and Technology, NanjingGoogle Scholar
  32. Young RY (2010) An aerodynamic shape optimization study to maximize the range of a guided missile. AIAA Paper 10-4240, 28th AIAA Applied Aerodynamics Conference.
  33. Yu W, Zhang X (2010) Aerodynamic Analysis of Projectile in Gun System Firing Process. J Appl Mech 77(5):051406CrossRefGoogle Scholar
  34. Zhang GQ, Yu SCM, Schlüter J (2016) Aerodynamic Characteristics of a Wrap-around Fin Rocket. Aircraft Engineering and Aerospace Technology 88(1):82–96CrossRefGoogle Scholar
  35. Zhou CS, Ju YT (2014) Theory of Rocket Projectile Design. Beijing Institute of Technology Press, BeijingGoogle Scholar
  36. Zhou G, Ma ZD, Cheng A et al (2015) Design optimization of a runflat structure based on multi-objective genetic algorithm. Struct Multidiscip Optim 51:1363–1371CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Energy and Power EngineeringNanjing University of Science and TechnologyNanjingChina

Personalised recommendations