References

• 1. 1)
     • 19. Shi, Y., Eberhart, R.C.: ‘Empirical study of particle swarm optimization’. Proc. of the Congress on Evolutionary Computation, 1999, pp. 1945–1950.
  2. 2)
     • 8. Gong, C., Zhang, S., Zhang, F., et al: ‘An integrated energy-efficient operation methodology for metro systems based on a real case of Shanghai metro line one’, Energies, 2014, 7, (11), pp. 7305–7329.
  3. 3)
     • 6. Kim, K.M., Oh, S., Han, M.: ‘A mathematical approach for reducing the maximum traction energy: the case of Korean MRT trains’, Lect. Notes Eng. Comput. Sci., 2010, 2182, (1), pp. 2169–2173.
  4. 4)
     • 10. Yang, X., Chen, A., Li, X., et al: ‘An energy-efficient scheduling approach to improve the utilization of regenerative energy for metro systems’, Transp. Res. C, Emerg. Technol., 2015, 57, pp. 13–29.
  5. 5)
     • 7. Chen, E., Yang, X., Ding, Y.: ‘An energy-efficient adjustment approach in subway systems’. IEEE 17th Int. Conf. on Intelligent Transportation Systems (ITSC), 2014, 2014, pp. 2774–2779.
  6. 6)
     • 5. Chen, J.-F., Lin, R.-L., Liu, Y.-C.: ‘Optimization of an MRT train schedule reducing maximum traction power by using genetic algorithms’, IEEE Trans. Power Syst., 2005, 20, (3), pp. 1366–1372.
  7. 7)
     • 4. Lee, C.H., Lu, C.J.: ‘Assessment of grounding schemes on rail potential and stray currents in a DC transit system’, IEEE Trans. Power Deliv., 2006, 21, (4), pp. 1941–1947.
  8. 8)
     • 15. Kennedy, J., William, M.S.: ‘Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator’, www.aic.nrl.navy.mil/∼spears/papers/wcci98.ps.gz.
  9. 9)
     • 20. Shi, Y., Eberhart, R.: ‘A modified particle swarm optimizer’. IEEE Int. Conf. on Evolutionary Computation, 1998, pp. 69–73.
  10. 10)
      • 11. Abido, M.A.: ‘Optimal design of power-system stabilizers using particle swarm optimization’, IEEE Trans. Energy Convers., 2002, 17, (3), pp. 406–413.
  11. 11)
      • 3. Charalambous, C.A., Cotton, I., Aylott, P.: ‘A simulation tool to predict the impact of soil topologies on coupling between a light rail system and buried third-party infrastructure’, IEEE Trans. Veh. Technol., 2008, 57, (3), pp. 1404–1416.
  12. 12)
      • 17. Clerc, M., Kennedy, J.: ‘The particle swarm: explosion, stability and convergence in a multi-dimensional complex space’, IEEE Trans. Evol. Comput., 2010, 6, (1), pp. 58–73.
  13. 13)
      • 12. Robinson, J., Rahmat-Samii, Y.: ‘Particle swarm optimization in electromagnetics’, IEEE Trans. Antennas Propag., 2004, 52, (2), pp. 397–407.
  14. 14)
      • 13. Keynedy, J., Eberhart, R.C.: ‘Particle swarm optimization’. IEEE Int. Conf. on Neural Nerworks, 1995, pp. 1942–1948.
  15. 15)
      • 9. Yang, X., Li, X., Gao, Z., et al: ‘A cooperative scheduling model for timetable optimization in subway systems’, IEEE Trans. Intell. Transp. Syst., 2013, 14, (1), pp. 438–447.
  16. 16)
      • 2. Tzeng, Y., Lee, C.: ‘Analysis of rail potential and stray currents in a direct-current transit system’, IEEE Trans. Power Deliv., 2010, 25, (3), pp. 1516–1525.
  17. 17)
      • 18. Kennedy, J., Barnhart, R.: ‘Particle swarm optimization’. Proc. of the IEEE Int. Conf. on Neural Networks, 1995, pp. 1942–1948.
  18. 18)
      • 1. Liu, Y.C., Chen, J.F.: ‘Control scheme for reducing rail potential and stray current in MRT systems’, IEE Proc., Electr. Power Appl., 2005, 152, (3), pp. 612–618.
  19. 19)
      • 14. Keynedy, J., Eberhart, R.C.: ‘A new optimizer using particle swarm theory’. 6th Int. Symp. on Micromachine and Human Science, 1995, pp. 39–43.
  20. 20)
      • 16. Parsopoulos, K.E., Vrahatis, M.N.: ‘On the computation of all global minimizes through particle swarm optimization’, IEEE Trans. Evol. Comput., 2004, 8, (3), pp. 211–233.