Optimal shape design of an autonomous underwater vehicle based on multi-objective particle swarm optimization

  • Qirong TangEmail author
  • Yinghao Li
  • Zhenqiang Deng
  • Di Chen
  • Ruiqin Guo
  • Hai Huang


Optimization of autonomous underwater vehicle’s shape is usually a multi-objective optimization problem, which is essential for autonomous underwater navigation and manipulation. To overcome the inefficiency of computational fluid dynamics software during the optimization process and the limitations of traditional single-objective optimization, a novel strategy combining genetic expression programming and crowding distance based multi-objective particle swarm algorithm is presented. Its central idea is as follows, several underwater vehicle shapes are analysed to obtain their water resistances and determine the best underwater robot shape. Shape factor of the bow and shape factor of the stern are employed as design variables, and sample points are selected by the optimal latin hypercube design. Then gene expression programming method is used to establish the surrogate model of resistance and surrounded volume. After that, the surrogate model based on the gene expression programming method is compared with that based on the surface respond method. The results show the superiority of the GEP method. Then the resistance and surrounded volume are set as two optimized variables and Pareto optimal solutions are obtained by using multi-objective particle swarm algorithm. Finally, the optimization results are compared with the hydrodynamic calculations, which shows the method proposed in the paper can greatly reduce the cost of computation and improve the efficiency of optimal shape design for underwater vehicle.


Autonomous underwater vehicle Shape optimization Gene expression programming Multi-objective particle swarm optimization 



This work is supported by the Projects of National Natural Science Foundation of China (No. 61603277, 61873192, 51579053), the Key Pre-Research Project of the 13th-Five-Year-Plan on Common Technology (No. 41412050101), the SAST Project (No. 2016017). Meanwhile, this work is also partially supported by the Fundamental Research Funds for the Central Universities, and the Youth 1000 program project. It is also partially sponsored by the Key Basic Research Project of Shanghai Science and Technology Innovation Plan (No. 15JC1403300), as well as the project supported by China Academy of Space Technology. All these supports are highly appreciated.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratory of Robotics and Multibody System, School of Mechanical EngineeringTongji UniversityShanghaiPeople’s Republic of China
  2. 2.National Key Laboratory of Science and Technology on Underwater VehicleHarbin Engineering UniversityHarbinPeople’s Republic of China

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