A novel \(\hbox {CACO}_{\mathrm{R}}\)-SVR multi-objective optimization approach and its application in aerodynamic shape optimization of high-speed train

  • Ye Zhang
  • Guo Wei Yang
  • Di Long Guo
  • Zhen Xu Sun
  • Da Wei Chen
Methodologies and Application


A chaos ant colony optimization algorithm for continuous domain is proposed based on chaos optimization theory and ant colony optimization algorithm. The searching abilities of optimization algorithms with different coding methods are compared, and the results indicate that the proposed algorithm has better performance than genetic algorithm and particle swarm optimization algorithm. Based on the non-dominated sorting concept and niching method, a multi-objective chaos ant colony optimization algorithm is also constructed and numerical results show that the improved algorithm performs well at solving multi-objective optimization problems. An optimal support vector regression model based on radial basis kernel function is developed for the small sample size and nonlinear characteristics of streamlined head optimization. On the basis of the above work, a multi-objective optimization design for the aerodynamic head shape of high-speed train is developed using a modified vehicle modeling function parametric approach. The optimization results demonstrate that the new optimization design method has exceptional searching abilities and high prediction accuracy. After optimization, the aerodynamic drag of the simplified train with three carriages is reduced by 10.52% and the aerodynamic lift of the tail car is reduced by 35.70%. The optimization approach proposed in the present paper is simple yet efficient and sheds light on the engineering design of aerodynamic shape of high-speed trains.


Chaos ant colony optimization Support vector machine Multi-objective optimization Vehicle modeling function High-speed trains 



This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (class B) (Grant No. XDB22020000) and National Key Research & Development Projects (Grant No. 2017YFB0202800), and the Computing Facility for Computational Mechanics Institute of Mechanics at the Chinese Academy of Sciences is also gratefully acknowledged.

Compliance with ethical standards

Conflict of interest

Authors ZHANG Ye, YANG GuoWei, GUO DiLong, SUN ZhenXu, and CHEN DaWei declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CRRC Qingdao Sifang Co., LTDQingdaoChina
  2. 2.Institute of MechanicsChinese Academy of SciencesBeijingChina
  3. 3.School of Engineering SciencesUniversity of Chinese Academy of SciencesBeijingChina

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