A Modified Genetic Algorithm for Multi-Objective Optimization on Running Curve of Automatic Train Operation System Using Penalty Function Method

  • Yanchu Liang
  • Hao Liu
  • Cunyuan QianEmail author
  • Guanlei Wang


The running curve optimization of Automatic Train Operation system usually takes into account running time, energy consumption and passenger comfort. In this paper, in order to provide more comprehensive optimization and accurate reference of running curve for Automatic Train Operation system, we adopted the multi-objective optimization strategy of genetic algorithm to optimize from five aspects: speeding (safety), parking accuracy, punctuality, energy consumption and comfort. In order to increase the convergence speed of genetic algorithm to the optimal solutions, we propose a modified genetic algorithm, which the penalty function method is added into the fitness objective function. The modified genetic algorithm optimization program is written by M language in MATLAB, and combined with a graphical user interface tool to design the optimization system. Its validity is verified by comparison between the tests based on three different interstation of Shanghai Metro Line 11. The results show that it is effective and practicability to use the designed system to optimize the running curve of Automatic Train Operation system.


Automatic train operation (ATO) Modified genetic algorithm (MGA) Multi-objective optimization Running curve Urban rail transit 



This work is supported by the National “Twelfth Five-Year” Pillar program for Science & Technology – the Interoperability Comprehensive Evaluation Integrative Platform and Demonstration for Urban Rail Transit (No.2015BAG19B02).


  1. 1.
    Dong, H.R., Ning, B., Gai, B.G., Hou, Z.S.: Automatic train control system development and simulation for high-speed railways. IEEE Circuits Syst. Mag. 10(2), 6–18 (2010)CrossRefGoogle Scholar
  2. 2.
    Zheng, W., Xu, H.Z.: Modeling and safety analysis of maglev train over-speed protection based on stochastic petri nets. J. China Railway Soc. 31(4), 59–64 (2009)Google Scholar
  3. 3.
    Olsson, N.O.E., Haugland, H.: Influencing factors on train punctuality-results from some Norwegian studies. Transp. Policy. 11(4), 387–397 (2004)CrossRefGoogle Scholar
  4. 4.
    Chen, D., Tang, T., Gao, C., Mu, R.: Research on the error estimation models and online learning algorithm for Train Station parking in urban rail transit. China Railway Sci. 31(6), 122–127 (2010) (in Chinese)Google Scholar
  5. 5.
    Miyatake, M., Ko, H.: Optimization of train speed profile for minimum energy consumption. IEEJ Trans. Electr. Electron. Eng. 5(3), 263–269 (2010)CrossRefGoogle Scholar
  6. 6.
    Karakasis, K., Skarlatos, D., Zakinthinos, T.: A factorial analysis for the determination of an optimal train speed with a desired ride comfort. Appl. Acoust. 66(10), 1121–1134 (2005)CrossRefGoogle Scholar
  7. 7.
    Chang, C.S., Du, D.: Improved optimization method using genetic algorithm for mass transit signalling block-layout design. IEE Proc. - Electric Appl. 145(3), 266–272 (1998)CrossRefGoogle Scholar
  8. 8.
    Ho, T.K., Yeung, T.H.: Railway junction conflict resolution by genetic algorithm. Electron. Lett. 36(8), 771–772 (2000)CrossRefGoogle Scholar
  9. 9.
    Wang, K.K., Ho, T.K.: Dynamic coast control of train movement with genetic algorithm. Int. J. Syst. Sci. 35(13–14), 835–846 (2004)CrossRefGoogle Scholar
  10. 10.
    Domínguez, M., Fernández-Cardador, A., Cucala, A.P., Gonsalves, T., Fernández, A.: Muti objective particle swarm optimization algorithm for the design of efficient ATO speed profiles in metro lines. Eng. Appl. Artif. Intell. 29(3), 43–53 (2014)CrossRefGoogle Scholar
  11. 11.
    Su, S., Tang, T., Li, X., Gao, Z.Y.: Optimization of multitrain operations in a Subway system. IEEE Trans. Intell. Transport. Syst. 15(2), 673–683 (2014)CrossRefGoogle Scholar
  12. 12.
    Ac¿kbas, S., Soylemez, M.T.: Coasting point optimization for mass rail transit lines using artificial neural networks and genetic algorithms. IET Electr. Power Appl. 2(3), 172–182 (2008)CrossRefGoogle Scholar
  13. 13.
    Yang, X., Ning, B., Tang, T.: A two-objective timetable optimization model in Subway Systems. IEEE Trans. Intell. Transp. Syst. 15(5), 1913–1921 (2014)CrossRefGoogle Scholar
  14. 14.
    Yin, J., Chen, D., Tang, T., Zhu, L., Zhu, W.: Balise arrangement optimization for train station parking via expert knowledge and genetic algorithm. Appl. Math. Model. 40(19–20), 8513–8529 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Chang, C.S., Sim, S.S.: Optimising train movements through coast control using genetic algorithms. IEE Proc. - Electric Power Appl. 144(1), 65–73 (1997)CrossRefGoogle Scholar
  16. 16.
    Li, J.Q.: Analysis of the Train’s traction energy consumption of shanghai metro line 11. Mechatronics. 19(6), 32–35 (2013) (in Chinese)Google Scholar
  17. 17.
    Holland, J.: Adaptation in Natural and Artificial Systems, University of Michigan Press, p. 1975. USA, Ann Arbor, MI (1975)Google Scholar
  18. 18.
    Arora, R.K.: Optimization Algorithm and Applications, p. 2015. CRC Press, Hoboken, NJ (2015)CrossRefGoogle Scholar
  19. 19.
    Taboaada, H.A., Espiritu, J.F., Coit, D.W.: MOMS-GA: a multi-objective multi-state genetic algorithm for system reliability optimization design problems. IEEE Trans. Reliab. 57(1), 182–191 (2008)CrossRefGoogle Scholar
  20. 20.
    Kuri-Morales, A.F., Gutiérrez-García, J.: Penalty Function Methods for Constrained Optimization with Genetic Algorithms: A Statistical Analysis. In: Coello Coello, C.A., de Albornoz, A., Sucar, L.E., Battistutti, O.C. (eds.) MICAI 2002: Advances in Artificial Intelligence. MICAI 2002. Lecture Notes in Computer Science, vol 2313. Springer, Berlin (2002)Google Scholar
  21. 21.
    Y. J. Lei, S. W. Zhang (2014) MATLAB genetic algorithm toolbox and its application. Xidian University Press, 2014 (in Chinese)Google Scholar
  22. 22.
    Kumar, R.: Blending Roulette Wheel Selectin & Rank Selection in genetic algorithms. Int. J. Machine Learn. Comput. 2(4), 365–370 (2012)CrossRefGoogle Scholar
  23. 23.
    Syswerda, G.: Simulated crossover in genetic algorithm. Found. Genet. Algorithms. 2, 239–255 (1993)Google Scholar
  24. 24.
    Kaya, M.: The effects of two new crossover operators on genetic algorithm performance. Appl. Soft Comput. 11(1), 881–890 (2011)CrossRefGoogle Scholar
  25. 25.
    Chen, Y., Qian, C.Y., Xi, X.D.: Traction energy consumption test and analysis for shanghai metro AC 16 electromotive train. Urban Mass Transit. 19(9), 34–38 (2016) (in Chinese)Google Scholar
  26. 26.
    Xu, K., Wu, L., Yang, F.F.: Automatic train operation system in urban rail transit based on PSO-ICS algorithm optimization. J. Railway Sci. Eng. 14(12), 2704–2711 (2017) (in Chinese)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018
corrected publication June/2018

Authors and Affiliations

  • Yanchu Liang
    • 1
  • Hao Liu
    • 1
  • Cunyuan Qian
    • 1
    Email author
  • Guanlei Wang
    • 1
  1. 1.Department of Electrical Traction & Control, Institute of Rail TransitTongji UniversityShanghaiChina

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