Li, X., Ralescu, D., Tang, T. (2011). FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION
MODEL AND ALGORITHM. Iranian Journal of Fuzzy Systems, 8(4), 77-91. doi: 10.22111/ijfs.2011.309

Xiang Li; Dan Ralescu; Tao Tang. "FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION
MODEL AND ALGORITHM". Iranian Journal of Fuzzy Systems, 8, 4, 2011, 77-91. doi: 10.22111/ijfs.2011.309

Li, X., Ralescu, D., Tang, T. (2011). 'FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION
MODEL AND ALGORITHM', Iranian Journal of Fuzzy Systems, 8(4), pp. 77-91. doi: 10.22111/ijfs.2011.309

Li, X., Ralescu, D., Tang, T. FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION
MODEL AND ALGORITHM. Iranian Journal of Fuzzy Systems, 2011; 8(4): 77-91. doi: 10.22111/ijfs.2011.309

FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION
MODEL AND ALGORITHM

^{1}State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao-
tong University, Beijing 100044, China

^{2}Department of Mathematical Sciences, University of Cincinnati, Cincin-
nati, Ohio 45221, USA

Abstract

Train energy saving problem investigates how to control train's
velocity such that the quantity of energy consumption is minimized and some
system constraints are satis ed. On the assumption that the train's weights
on different links are estimated by fuzzy variables when making the train
scheduling strategy, we study the fuzzy train energy saving problem. First, we
propose a fuzzy energy consumption minimization model, which minimizes the
average value and entropy of the fuzzy energy consumption under the maximal
allowable velocity constraint and traversing time constraint. Furthermore, we
analyze the properties of the optimal solution, and then design an iterative
algorithm based on the Karush-Kuhn-Tucker conditions. Finally, we illustrate
a numerical example to show the effectiveness of the proposed model and
algorithm.

[1] Y. Bai, B. Mao, F. Zhou, Y. Ding and C. Dong,Energy-ecient driving strategy for freight trains based on power consumption analysis, Journal of Transportation Systems Engineering and Information Technology,9(3) (2009), 43-50.

[2] E. Castillo, I. Gallego, J. M. Urena and J. M. Coronado,Timetabling optimization of a single railway track line with sensitivity analysis, Top, 17(2) (2009), 256-287.

[3] C. S. Chang and S. Sim,Optimising train movements through coast control using genetic algorithms, IEE Proceedings-Electric Power Applications, 144(1) (1997), 65-73.

[4] S. Eati and H. Roohparvar,The minimization of the fuel costs in the train transportation,Applied Mathematics and Computation,175 (2006), 1415-1431.

[5] K. Ghoseiri, F. Szidarovszky and M. J. Asgharpour,Amulti-objective train scheduling model and solution, Transportation Research Part B, 38 (2004), 927-952.

[6] P. Howlett,The optimal control of a train, Annals of Operations Research, 98 (2000), 65-87.

[7] P. Howlett, P. Pudney and X. Vu,Local energy minimization in optimal train control, Au-tomatica,45(11)(2009), 2692-2698.

[8] K. B. Khan and X. S. Zhou,Stochastic optimization model and solution algorithm for ro-bust double-track train-timetabling problem, IEEE Transactions on Intelligent Transportation Systems,11(1)(2010), 81-89.

[9] E. Khmelnitsky,On an optimal control problem of train operation, IEEE Transactions on Automatic Control,45(7) (2000), 1257-1266.

[10] D. R. Kraay, P. T. Harker and B. Chen,Optimal pacing of trains in freight railroads: model formulation and solution, Operations Research, 39 (1991), 82-99.

[11] X. Li and B. Liu,A sucient and necessary condition for credibility measure, Internationa Journal of Uncertainty, Fuzziness & Knowledge-Based Systems,14(5) (2006), 527-535.

[12] P. Li and B. Liu,Entropy of credibility distributions for fuzzy variables, IEEE Transactions on Fuzzy Systems,16(1) (2008), 123-129.

[13] B. Liu and Y. Liu,Expected value of fuzzy variable and fuzzy expected value models, IEEETransactions on Fuzzy Systems,10(4) (2002), 445-450.

[14] R. Liu and I. M. Golovitcher,Energy-ecient operation of rail vehicles, Transportation Research Part A,37(2003), 917-932.

[15] M. Miyatake and H. Ko,Optimization of train speed pro le for minimum energy consumption,IEEJ Transactions on Electrical and Electronic Engineering,5 (2010), 263-269.

[16] L. Yang, K. P. Li and Z. Y. Gao,Train timetable problem on a single-line railway with fuzzy passenger demand, IEEE Transactions on Fuzzy Systems, 17(3)(2009), 617-629.

[17] L. Yang, Z. Y. Gao and K. P. Li,Passenger train scheduling on a single-track or partially double-track railway with stochastic information, Engineering Optimization, 42(11) (2010),1003-1022.