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An improved multi-objective optimization algorithm with mixed variables for automobile engine hood lightweight design

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Abstract

Engine hood is one of the important parts of the vehicles, which has influences on the lightweight, structural safety, pedestrian protection, and aesthetics. The optimization design of engine hood is a high-dimensional, multi-objective, and mixed-variable optimization problem. In order to reduce the physical test investment in the development and improve the efficiency of optimization, this article proposes a data-driven method for optimal hood design. A newly proposed single-objective optimization algorithm is improved by several strategies for multi-objective constrained problem with mixed variables. Then the hood is optimized through the specially designed machine learning model. Finally, both the hood's weight and pedestrian injury are reduced while maintaining structural stiffness and frequency in the desired range. The comparative study and final hood optimization results prove the effectiveness of the proposed method.

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References

  1. Z. Zhao et al., Data mining application on crash simulation data of occupant restraint system, Expert Systems With Applications, 37 (8) (2010) 5788–5794.

    Article  Google Scholar 

  2. F. Pan et al., Metamodel-based lightweight design of B-pillar with TWB structure via support vector regression, Computers & Structures, 88 (1) (2010) 36–44.

    Article  Google Scholar 

  3. A. Fotouhi and M. Montazerigh, Tehran driving cycle development using the k-means clustering method, Scientia Iranica, 20 (2) (2013) 286–293.

    Google Scholar 

  4. P. Baraldi et al., Hierarchical k-nearest neighbours classification and binary differential evolution for fault diagnostics of automotive bearings operating under variable conditions, Engineering Applications of Artificial Intelligence, 56 (11) (2016) 1–13.

    Article  Google Scholar 

  5. Z. Liu et al., Lightweight design of automotive composite bumper system using modified particle swarm optimizer, Composite Structures, 140 (2016) 630–643.

    Article  Google Scholar 

  6. P. Du et al., A novel hybrid model for short-term wind power forecasting, Applied Soft Computing, 80 (2019) 93–106.

    Article  Google Scholar 

  7. M. R. Bonyadi and Z. Michalewicz, Particle swarm optimization for single objective continuous space problems: a review, Evolutionary Computation, 25 (1) (2017) 1–54.

    Article  Google Scholar 

  8. R. D. Aldabbagh et al., Algorithmic design issues in adaptive differential evolution schemes: review and taxonomy, Swarm and Evolutionary Computation, 43 (2018) 284–311.

    Article  Google Scholar 

  9. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc., Boston (1989).

    MATH  Google Scholar 

  10. R. Storn and K. Price, Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11 (4) (1997) 341–359.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. A. Formato, Central force optimization: a new metaheuristic with applications in applied electromagnetics, Progress In Electromagnetics Research, 77 (2007) 425–491.

    Article  Google Scholar 

  12. E. Rashedi, H. Nezamabadi-Pour and S. Saryazdi, GSA: a gravitational search algorithm, Information Sciences, 179 (13) (2009) 2232–2248.

    Article  MATH  Google Scholar 

  13. Z. W. Geem, J. H. Kim and Loganathan, A new heuristic optimization algorithm: harmony search, Simulation, 76 (2) (2001) 60–68.

    Article  Google Scholar 

  14. D. Karaboga and B. Basturk, A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm, J. Glob. Optim., 39 (3) (2007) 459–471.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Mirjalili, Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems, Neural Computing and Applications, 27 (4) (2016) 1053–1073.

    Article  MathSciNet  Google Scholar 

  16. S. Mirjalili, S. M. Mirjalili and A. Lewis, Grey wolf optimizer, Advances in Engineering Software, 69 (2014) 46–61.

    Article  Google Scholar 

  17. J. Kennedy and R. Eberhart, Particle swarm optimization, IEEE Proceedings of ICNN’95 — International Conference on Neural Networks (2002).

    Google Scholar 

  18. E. Cuevas et al., A swarm optimization algorithm inspired in the behavior of the social-spider, Expert Systems with Applications, 40 (16) (2013) 6374–6384.

    Article  Google Scholar 

  19. X. Liang et al., An adaptive particle swarm optimization method based on clustering, Pattern Analysis and Applications, 18 (1) (2015) 431–448.

    Google Scholar 

  20. M. Taherkhani and R. Safabakhsh, A novel stability-based adaptive inertia weight for particle swarm optimization, Applied Soft Computing, 38 (2016) 281–295.

    Article  Google Scholar 

  21. Y. B. Shin and E. Kita, Search performance improvement of particle swarm optimization by second best particle information, Applied Mathematics and Computation, 246 (2014) 346–354.

    Article  MathSciNet  MATH  Google Scholar 

  22. B. Jiang and N. Wang, Cooperative bare-bone particle swarm optimization for data clustering, Soft Computing, 18 (6) (2014) 1079–1091.

    Article  Google Scholar 

  23. M. Yang et al., Differential evolution with auto-enhanced population diversity, IEEE Transactions on Cybernetics, 45 (2) (2014) 302–315.

    Article  Google Scholar 

  24. N. Lyn et al., Population topologies for particle swarm optimization and differential evolution, Swarm and Evolutionary Computation, 39 (2018) 24–35.

    Article  Google Scholar 

  25. S. Bureerat and S. Sleesongsom, Constraint handling technique for four-bar linkage path generation using self-adaptive teaching—learning-based optimization with a diversity archive, Engineering Optimization, 1 (2020) 1–18.

    Google Scholar 

  26. Z. Liu, H. Li and P. Zhu, Diversity enhanced particle swarm optimization algorithm and its application in vehicle lightweight design, Journal of Mechanical Science & Technology, 33 (2) (2019) 695–709.

    Article  Google Scholar 

  27. S. S. Fan and E. Zahara, A hybrid simplex search and particle swarm optimization for unconstrained optimization, European Journal of Operational Research, 181 (2) (2007) 527–548.

    Article  MathSciNet  MATH  Google Scholar 

  28. I. B. Aydilek, A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems, Applied Soft Computing, 66 (2018) 232–249.

    Article  Google Scholar 

  29. Z. H. Zhou, Y. Yu and C. Qian, Evolutionary Learning: Advances in Theories and Algorithms, Springer (2019) 3–10.

    Book  MATH  Google Scholar 

  30. D. A. Van Veldhuizen and G. B. Lamont, Multiobjective evolutionary algorithms: analyzing the state-of-the-art, Evolutionary Computation, 8 (2) (2014) 125–147.

    Article  Google Scholar 

  31. D. Liu, K. C. Tan, C. K. Goh and W. K. Ho, A multiobjective memetic algorithm based on particle swarm optimization, IEEE Transactions on System, Man, and Cybernetics, Part B (Cybernetics), 37 (1) (2007) 42–50.

    Article  Google Scholar 

  32. G. E. P. Box, W. G. Hunter and J. S. Hunter, Statistics for Experimenters, John Wiley & Sons, New Jersey (1978).

    MATH  Google Scholar 

  33. I. M. Sobol, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, 55 (1) (2001) 271–280.

    Article  MathSciNet  MATH  Google Scholar 

  34. J. Kennedy, Bare bones particle swarms, IEEE Swarm Intelligence Symposium (2003) 80–87.

    Google Scholar 

  35. M. Mahdavi, M. Fesanghary and E. Damangir, An improved harmony search algorithm for solving optimization problems, Applied Mathematics & Computation, 188 (2) (2007) 1567–1579.

    Article  MathSciNet  MATH  Google Scholar 

  36. J. Zhang, JADE: adaptive differential evolution with optional external archive, IEEE Transactions on Evolutionary Computation, 13 (5) (2009) 945–958.

  37. P. Kaelo and M. M. Ali, Integrated crossover rules in real coded genetic algorithms, European Journal of Operational Research, 176 (1) (2007) 60–76.

    Article  MathSciNet  MATH  Google Scholar 

  38. R. V. Rao, V. J. Savsani and D. P. Vakharia, Teaching— learning-based optimization: a novel method for constrained mechanical design optimization problems, Computer Aided Design, 43 (3) (2011) 303–315.

    Article  Google Scholar 

  39. Ş. Gulcu and H. Kodaz, A novel parallel multi-swarm algorithm based on comprehensive learning particle swarm optimization, Engineering Applications of Artificial Intelligence, 45 (2015) 33–45.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (#51705312, #11772191).

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Correspondence to Ping Zhu.

Additional information

Han Li is a Ph.D. candidate at School of Mechanical Engineering, Shanghai Jiao Tong University, P. R. China. His research interests include missing data imputation, applications of industrial data, and heuristic optimization and evolutionary learning.

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Li, H., Liu, Z. & Zhu, P. An improved multi-objective optimization algorithm with mixed variables for automobile engine hood lightweight design. J Mech Sci Technol 35, 2073–2082 (2021). https://doi.org/10.1007/s12206-021-0423-5

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  • DOI: https://doi.org/10.1007/s12206-021-0423-5

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