Neurocomputing 169 (2015) 383–391
Contents lists available at ScienceDirect
Neurocomputing
journal homepage: www.elsevier.com/locate/neucom
Multi-objective operation optimization for electric multiple unit-based
on speed restriction mutation
Hui Yang a,b, Hongen Liu a,b,n, Yating Fu a,b
a
b
School of Electrical and Electronic Engineering, East China Jiaotong University, Nanchang 330013, Jiangxi, China
Key Laboratory of Advanced Control and Optimization of Jiangxi Province, Nanchang 330013, Jiangxi, China
art ic l e i nf o
a b s t r a c t
Article history:
Received 27 January 2014
Received in revised form
24 August 2014
Accepted 24 August 2014
Available online 2 May 2015
The electric multiple unit (EMU) is a complex system running in dynamic environments. Satisfaction on
real-time manual operation strategy of the EMU with respect to the multi-objective operation demands,
including security, punctuality, accurate train parking, energy saving and ride comfort, depends on the
drivers' experience and a given V–S curve (velocity versus position curve). To improve the operation
strategy, a multi-objective optimization model of EMU operation is developed on the basis of dynamic
analysis and speed restriction mutation. Using a modified particle swarm optimization algorithm, a
Pareto optimal solution set is obtained by the online optimization of the EMU's operation strategy.
Finally, according to the preference order ranking, an optimal operation strategy is sorted out from the
Pareto set which satisfies the multi-objective requirements in real time. Experimental results on the field
data of CRH380AL (China's railway high-speed EMU type-380AL) demonstrate the effectiveness of the
proposed approach.
& 2015 Elsevier B.V. All rights reserved.
Keywords:
Electric multiple unit
Speed restriction mutation
Operation strategy
Online optimization
Multi-objective particle swarm
optimization algorithm
1. Introduction
The Electric Multiple Unit (EMU) provides passenger transport
services in a complex and dynamic running environment. Since the
services should simultaneously satisfy the multi-objective requirements of security, punctuality, accurate train parking, energy saving
and ride comfort, how to optimize the EMU operation strategy is a
multi-objective optimization problem (MOP). The objective of the
MOP is to obtain satisfying operation strategies which can meet the
multi-objective requirements from numerous operational approaches
[1,2]. On the other hand, stochastic and paroxysmal changes in the
environment, such as natural hazards or equipment failure of the
railroads, lead to speed restriction mutation (SRM). Obviously, SRM
causes many difficulties in solving the MOP of the EMU operation
[3,4]. Moreover, the intense interaction effects among the EMUs
caused by their high-density tracking arouse a higher requirement
for the real-time performance of EMU operation. Further, as the
automatic EMU operation has been a development tendency, it is
critical that the operation strategies are totally reliable [5,6]. Consequently, the operation strategies of EMU not only should meet the
multi-objective requirements, but also have real-time effectiveness.
n
Corresponding author at: School of Electrical and Electronic Engineering, East
China Jiaotong University, Nanchang 330013, Jiangxi, China.
E-mail addresses: [email protected] (H. Yang), [email protected] (H. Liu),
[email protected] (Y. Fu).
http://dx.doi.org/10.1016/j.neucom.2014.08.097
0925-2312/& 2015 Elsevier B.V. All rights reserved.
In previous optimization research on EMU operation, energy
consumption and punctuality were primarily considered as the
optimization indexes. However, the requirements of accurate train
parking and ride comfort, which are closely related with the security
and quality of the transport services, were largely ignored. Furthermore, most of the previous studies were carried out offline. Aiming to
address the optimization problem of EMU operation, an optimization
model based on the optimization index of energy consumption was
built in [7,15], while the other indexes are handled as constraints.
However, they ignored the multi-objective requirements of the
problem. A multi-objective model was established in [1], which
considered the optimization indexes of energy saving, punctuality
and accurate train parking after which a hybrid particle swarm
optimization algorithm (PSO) was employed to optimize the operation
strategies. Unfortunately, they adopted the weighted sum method to
aggregate these optimization indexes into a single index, which
sacrifices the balance and flexibility of optimization results. A multiobjective optimization model based on the indexes of punctuality,
accurate train parking, energy saving and ride comfort was established
in [8]. A modified differential evolution algorithm was adopted to
solve the MOP of EMU operation in an off-line optimal way, so as to
obtain the Pareto optimal solutions. However, there was no guarantee
of the validity of their results in a dynamic environment.
It is well know that the multi-objective PSO (MOPSO) can
efficiently obtain a Pareto solution set of the MOP, as well as be
suitable for solving the MOP of EMU operation [9]. Considering the
challenge of multi-objective planning of urban land-use, the MOPSO
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H. Yang et al. / Neurocomputing 169 (2015) 383–391
algorithm was adopted to optimize the arrangement of urban land
uses in [10], and a Pareto set of land-use arrangements were
obtained. Although their experimental results met the multiobjective requirements well, the efficiency of the MOPSO algorithm
was lower as a result of the growing population. Fortunately, this
problem can usually be solved by using reference points or
preference information to guide the particles to a certain region
of the Pareto Front [11,12]. For instance, the important relationship
between objectives was used as preference information about the
MOPSO algorithm in [12], and the effectiveness of the method was
improved greatly.
In this paper, a multi-objective online optimization model is
established, which based on the indexes of security, punctuality,
accurate train parking, energy saving and ride comfort. Subsequently, the multi-objective online optimization of the EMU
operation is realized by a modified MOPSO algorithm, which based
on real-time data on the running process of EMU. Finally, based on
the principle of balance and the preference order ranking, the
optimal strategy is sorted out from the Pareto set.
The remainder of this paper is organized as follows: Section 2
briefly describes the dynamic analysis of the EMU. The multiobjective online optimization model and method of EMU operation are given in Sections 3 and 4, respectively. The experimental
results and discussions are provided in Section 5. Finally, conclusions and future work are given in Section 6.
2. Dynamic model of the EMU running process
Fig. 1 describes the force acting on EMUs during the running
process.
Based on the force analysis in Fig. 1, the dynamic model of the
EMU's running process is established, as shown in the following
equation [13]:
8
C ¼ uw
>
>
>
>
< w ¼ w0 þ wj
ð1Þ
w0 ¼ a þ byþ cy2
>
>
>
>
: wj ¼ wi þ wr þ ws
where C is the resultant force, u is the controlling force, and u 4 0
refers to traction (Ft) while u o 0 refers to braking force (Fb); w is the
running resistance, which is composed of the basic resistance w0
and the additional resistance wj. Moreover, wj mainly includes ramp
resistance wi, curve resistance wr and tunnel resistance ws; a, b, c
are the drag coefficients [14].
Based on Eq. (1), the dynamics of EMU can be defined as
follows:
8
dt 1
>
>
¼
<
dl
v
ð2Þ
dv
>
>
:v
¼ uðc; vÞ wðl; vÞ
dl
where l A ½0; L0 is the location of EMU, L0 is the station spacing, t is
the running time of EMU; v A ½0; VðlÞÞ is the running speed of EMU,
V(l) is the automatic train protection speed restriction (SR) at the
location l. c A f1; 0; 1g is the operation state of EMU, and “1, 0,
Running direction
wj w0
w
u
Fig. 1. Force analysis of the EMU's running process.
1” refers to the operation state of traction, coasting and braking,
respectively; uðc; vÞ and wðl; vÞ are the same as Eq. (1).
3. Multi-objective online optimization model for EMU
operation
As mentioned above, the optimization of the EMU operation is a
MOP, which should simultaneously meet the multi-objective requirements in a dynamic running environment. Therefore, a multipleobjective online optimization model (MOOM) is built to provide a
quantitative basis for the study.
3.1. Optimization indexes of EMU operation
Accordingly, the optimization indexes for the MOP of the EMU
operation, which include safety allowance, punctuality, energy
consumption, accurate train parking and ride comfort, are detailed
in Sections 3.1.1–3.1.5.
3.1.1. Safety allowance index
The safety allowance of the EMU running process is usually
evaluated by the difference between the speed of the EMU and the
SR [7,15]. Since the SR changes with changes in the running
environment, the SR data are obtained from the driver machine
interface (DMI) of the EMU in each sampling period dt. In this way,
the calculation model of the safety allowance is established in real
time, which is defined as follows:
fv ¼
1
VðlÞ v
ð3Þ
where V(l) and v are the same as Eq. (2), fv is the safety allowance
index for the operation strategy. Obviously, the smaller the fv is,
the safer the running process of EMU becomes.
3.1.2. Punctuality index
The services provided by the EMU are strictly limited by the
train timetable [7,15]. Accordingly, the difference between T (the
actual inter-station running times of the EMU) and T0 (the given
time in the timetable) is taken as the punctuality index, which is
defined as follows:
T¼
N
X
dt;
N ¼ 1; 2; …; K
ð4Þ
1
f t ¼ T T0
ð5Þ
where dt is the sampling period and k is iterations during the
optimization process. The smaller the ft is, the more punctual the
services be.
3.1.3. Energy consumption index
The calculation of the energy consumed in traction is a basis for
the optimization of the operation strategy. The energy consumption is closely related to the conditions of railway line, the EMU's
traction characteristics and operation strategies and so on. Thus, in
the case that the traction characteristics and line conditions are
fixed, the objective of energy saving could be realized by optimizing the operation strategy. However, since the running EMU is a
complex nonlinear system, it is difficult to directly calculate the
energy consumed in traction of its running process. Consequently,
the running process of the EMU is divided into numerous linear
intervals. The traction energy of each interval and the whole
section is shown in the following equations, respectively
[16,17,22]:
Ei ¼ FðvÞ dSðv; dtÞ
ð6Þ
H. Yang et al. / Neurocomputing 169 (2015) 383–391
Z
fe ¼
T
Ei dt
ð7Þ
0
where Ei is the energy consumed in traction in each dS (the
running distance during dt), fe is the total energy consumption, T
and dt are the same as Eq. (5).
The applicability and simplicity of the algorithm makes it more
appropriate for solving lots of engineering optimization problems.
By exchanging information between individuals and group
3.1.4. Accurate train parking index
The difference between X (the actual running distances of EMU
during T) and L0 (the stations' spacing) is defined as the index of
train parking accuracy, as shown in the following:
X ¼ xðTÞ;
X oL0
f d ¼ X L0
4.1. MOPSO algorithm for EMU operation
ð9Þ
PSO is a parallel heuristic random search intelligent optimization method [20]. The algorithm updates particles' velocity and
position through the exchange of information between individuals
and group. Meanwhile, particles save the pBest (best place that
particles have experienced) and the gBest (best place that group
has experienced) during the searching process. The search
mechanism is defined as follows [21,16,17,22]:
8
! !
!
!
>
>
vi ðt þ 1Þ ¼ ωnvi ðtÞ þc1nr1nðxbestðtÞ xi ðtÞ Þ
>
>
>
>
! !
<
þ c2nr2nðgbestðtÞ xi ðtÞ Þ
ð13Þ
>
ω ¼ ωmax ðωmax ωmin Þnt=T max
>
>
>
>
!
! !
>
: x
¼ xi ðtÞ þ vi ðt þ 1Þ
i ðt þ 1Þ
3.1.5. Ride comfort index
Generally, the ride comfort index fc is defined by the change
rate of EMU's velocity (namely the longitudinal impact force), as
shown in the following equation:
dv
ð10Þ
f c ¼ ; f c A ½0; Amax dt
where dv=dt is the change rate of acceleration, which signifies the
comfort condition of the passengers; Amax is the maximum impact
force in which body feels comfortable, and it is usually set as
Amax ¼ 1 m=s2 [18].
3.2. Modeling of the multi-objective online optimization
Based on the optimization indexes in Section 3.1, the MOOM is
established as follows [1,8,12]:
8
dt
1
>
>
¼
>
>
>
dx
v
>
>
< vð0Þ ¼ vðL0 Þ ¼ 0
dv
>
>
>
¼ uðc; vÞ wðl; vÞ
v
>
>
>
> dx
:
v o VðlÞ; l o L0 ; csi A S
without a mutation and crossover operator, the algorithm
satisfies the diversity and efficiency requirements for the online
optimization of the EMU operation quite well.
The efficiency of the algorithm could be further improved by
importing reference information while the initial population
becomes large.
ð8Þ
where fd is the accuracy of EMU parking, and the parking accuracy
should be shorter than 0.0008 km [18].
min y ¼ fðSÞ ¼ ðf v ðcsi Þ; f t ðcsi Þ; f d ðcsi Þ; f e ðcsi Þ; f c ðcsi ÞÞ
385
ð11Þ
ð12Þ
where fðSÞ is the fitness function of the MOOM, and Eq. (12) is
the constraints of the model, csi is the operation strategies which
are composed of ci (operation state of the EMU) and si (corresponding distance that ci continues), S is the search space, and
f v ðcsi Þ; f t ðcsi Þ; f d ðcsi Þ; f e ðcsi Þ; f c ðcsi Þ are the optimization indexes.
To realize the online optimization of the EMU operation, we
obtain l, V(l) and other information about the EMU from the DMI
in real time. Thus, the fitness function and constraints of the
MOOM will change with the change of l in real time.
4. Multi-objective online optimization method for EMU
operation
Recently, MOP has become a research hotspot of the intelligent
optimization. Many artificial intelligence optimization algorithms
and computational intelligence methods, such as genetic algorithm, neural network computing and MOPSO, were introduced to
solve the MOP [19].
The MOPSO is especially suitable for solving the MOP of the
EMU operation. In this paper, the MOPSO algorithm is selected due
to the following advantages:
where vi(t) and xi(t) are the velocity and position of a particle i at
the iterations t, and c1, c2 are the acceleration constants, r1, r2 are
the uniformly distributed random numbers in [0,1], w is the
dynamic weight, Tmax is the maximum iterations.
As a minimization problem with n objective functions (as
shown in Eq. (13), n ¼5), it judges that the solution x1 dominates
solution x2 (namely x1 g x2 ) while their relationships are denoted
as Eq. (14). On the contrary, if x1 is better than x2 in one or more
objectives while x2 is better than x1 for the others, then they are
non-dominated. Furthermore, x1 is the Pareto optimal if x1:x1 g x0 ,
where x1 A S; x0 A S, S is the search space and x0 is the rest of S. All of
the Pareto solutions make up the Pareto solution set:
(
8 i A f1; 2; …; mg; f i ðx1 Þ r f i ðx2 Þ
ð14Þ
( iA f1; 2; …; mg; f j ðx1 Þ o f j ðx2 Þ
where m and fi, fj are the dimensionality and the objective
functions of particles, respectively.
Subsequently, to improve the efficiency of the MOPSO for the
EMU operation, the importance relationship between the objectives
is taken as the preference information of the algorithm [11]. Then,
based on Eqs. (11)–(14), the filtering rule α for Pareto set of the EMU
operation strategies is defined as Eq. (15). In addition, it is observed
from the experimental process that the preference order rankings for
the cases of running states of the EMU are defined as Eqs. (16)–(18):
α ¼ β&ff v ðiÞ r f SR g&ff v ðiÞ r f v ðjÞ&f t ðiÞ rf t ðjÞ
&f d ðiÞ r f d ðjÞ&f e ðiÞ rf e ðjÞ&f c ðiÞ r f c ðjÞg
ð15Þ
β1 ¼ α&ff v ðiÞ o f v ðjÞ&f t ðiÞ o f t ðjÞ&
f d ðiÞ o f d ðjÞ J f e ðiÞ o f e ðjÞ J f c ðiÞ o f c ðjÞg
ð16Þ
β2 ¼ α&ff v ðiÞ o f v ðjÞ&f t ðiÞ o f t ðjÞ&
f d ðiÞ o f d ðjÞ&f e ðiÞ o f e ðjÞ J f c ðiÞ o f c ðjÞg
ð17Þ
β2 ¼ α&ff v ðiÞ o f v ðjÞ&f d ðiÞ o f d ðjÞ&
f e ðiÞ o f e ðjÞ J f t ðiÞ o f t ðjÞ J f c ðiÞ o f c ðjÞg
ð18Þ
where β is the preference information, and β1 ; β2 ; β 3 are the
preference order rankings for the cases of long delay, short delay
and no delay, respectively.
386
H. Yang et al. / Neurocomputing 169 (2015) 383–391
Accordingly, the pseudo code of MOPSO for the EMU operation
is described as
as follows:
8
csi ¼ ½ci ; si >
>
>
>
< ci A f1; 0; 1g;
Algorithm 1. Pseudo code of MOPSO for the EMU operation.
si A ½0; L0 ;
>
>
>
>
: L0 ¼ P si
1:
2:
3:
4:
5:
6:
Initialize the particles and parameters
Define the pbest and gbest of the population
while iter o MaxIT
for Each Particle
Update the velocity and position of particles
Calculate the fitness function value of the MOOM for the
EMU operation in Eq. (11)
7: Obtain the Pareto optimal solutions based on the filtering
rules in Eqs. (15)–(18)
8: Update the pbest
9: end for
10: Update the gbest and external archive size
11: iterþ þ
12: end while
13: Obtain the Pareto set of EMU operation strategies.
where iter and MaxIT refers to the current iterations and the
maximum iterations, respectively.
i ¼ 1; 2; …; k
i ¼ 1; 2; …; k
ð19Þ
where ci, si and L0 are the same as Eq. (12).
4.2.2. Multi-objective online optimization process of EMU operation
Based on Algorithm 1 and the initial operation strategies
described in Eq. (19), the multi-objective online optimization for
the EMU operation is carried out, the specific steps are shown in
Fig. 3. In this study, we use the weighted sum method to rank the
solution set, that is,
(
f ¼ ω1 f v þ ω2 f t þ ω3 f d þ ω4 f e þ ω5 f c
ð20Þ
ω1 þ ω2 þ ω3 þ ω4 þ ω5 ¼ 1
where ω1 ω5 are the weight coefficients determined by the
preference order ranking.
In Fig. 3, the current operation state is composed of the cases of
traction (T), coasting (C) and braking (B). Then the operation
strategies are adjusted as follows: (1) in the operation state of
T : -C-EB-C-T; (2) in the operation state of C : -EB-C-T;
(3) in the operation state of B : -B-C-T. EB is the operation
state of emergency braking.
4.2. Multi-objective online optimization of EMU operation strategy
Generally, the main difficulty in MOP is how to efficiently obtain
the global best solution from the population, as the multiple
objectives (very often conflicting and incommensurable) should be
optimized simultaneously [16,17,22,23]. For instance, although the
objective of energy saving can be realized by extending EMU's
coasting time, it meanwhile increases the running time, which affects
the punctuality index. Furthermore, concerning the multipleobjective optimization of the EMU operation, the optimal solution
for some optimization indexes may be poor for the others in some
cases. Consequently, on the premise of balancing multiple objectives,
although there is a set of Pareto optimal solutions which prefer some
certain optimization indexes, there are no absolutely optimal solutions to the MOP of the EMU operation [11].
In this paper, the initial EMU operation strategies are generated
according to the actual data obtained from field investigation and
research. After this, based on the MOOM in Section 3.2, Algorithm
1 and the initial operation strategies, the multi-objective optimization of the EMU operation is conducted online. Meanwhile, the
useful information on the EMU running process is obtained in real
time, which is used as the preference information of Algorithm 1,
so as to improve the algorithm efficiency.
4.2.1. Generating the initial EMU operation strategies
It is generally know that the operation state of the EMU is
closely related to the running conditions, which mainly include
line characteristics and traction power supply. The line characteristics include line profile, curve and tunnel, as shown in Fig. 2.
Moreover, since the electrified railway network is powered by a
phase splitting supply, it has to establish a neutral section between
the adjacent power supply sections to prevent phase fault,
enabling the EMU to coast through the neutral section [24].
According to the analysis above, the traction calculation is
conducted to generate the initial operation strategies of the EMU
5. Experimental results
In this section, the experimental results are presented to verify
the effectiveness of the proposed method. Firstly, the CRH380AL
service on the Beijing-Shanghai High-speed Railway Line is taken
as the experimental object. Then, the experiments are conducted based on the field data obtained from the EMU running
process. Table 1 shows the basic characteristic parameters of the
CRH380AL. Fig. 4 presents a detailed overview of the BeijingShanghai High-speed Railway Line, whose station spacing from
“Taian” to “Xuzhou East” is 227.78 km [25], where v0 is the initial
speed when the emergency braking happens.
The given time in train timetable is from 10:05:40 to 10:56:51,
which is 3071 s in total. The position error of train parking is
generally required within 0.0008 km, while the running time error
is within 120 s [7,15].
5.1. Field operation strategy
Fig. 5 presents the actual V–S Curve (VSC: velocity versus
position curve) of the EMU running process from “Taian” to
“Xuzhou East”, which is collected in real world. The actual
operation strategy of the process is cs1 in Table 3, whose index
values are a1 in Table 2.
From Fig. 5 and Table 2, it is observed that there is an
inconstant fluctuation of the VSC which results with an increase
in energy consumption, as well as a reduction in ride comfort.
In addition, the velocity of the EMU is almost over the SR in some
places, which may cause safety problems. For instance, in the
local enlarging graphs of Fig. 5, the EMU runs at a speed of
60 70 km/h, which is almost over the SR. This may lead to
damage to the railway turnout or train derailment, etc. Furthermore, f t ¼ 282 s seriously exceeds the permitted scope of train
delays ( 7120 s), while f e ¼ 6966:37 kW h is too high.
H. Yang et al. / Neurocomputing 169 (2015) 383–391
387
Railway
profile
Neutral
section
Curve
Tunnel
Mileage
Fig. 2. The line characteristics of “Taian-Xuzhou East” section.
Begin
Generate the initial operation strategies as shown in
Eq. (19) based on the actual running conditions
Establish the MOOM in Section 3.2 and optimize the
operation strategies above while obtaining the SR and
position data of EMU in real time
Has any SRM been
detected?
Regenerate the initial operation strategies based
on the current operation state
Optimize the operation strategies online
Obtain the Pareto solution set of EMU operation
strategies using Algorithm 1
Sort the optimal operation strategy out from above
solution set by the weighted sum method in Eq. (20)
Fig. 4. The Beijing-Shanghai High-speed Railway Line.
End
Taian−Xuzhou East
Fig. 3. Flow chart of the multi-objective online optimization for EMU operation.
SRC
AVSC
350
Table 1
The basic characteristic parameters of CRH380AL.
Parameter value section
Full weight
Maximum running speed
Maximum traction power
Braking deceleration
Braking distance
890 t
350 km/h
21 560 kW
ab ¼ 0:519 m=s2 ðv0 Z 250 km=hÞ
sb r 3:8 km ðv0 r 300 km=hÞ
5.2. Multi-objective optimization of EMU operation
According to the analysis in Section 5.1, it is concluded that there
is much scope for the optimization of field operation strategies.
Therefore, the multi-objective offline optimization is conducted for
the EMU's operation strategies, which is similar to that in [8,9], so as
to identify the disadvantages of the offline method. Then, the
operation strategies are optimized with the method of multiobjective online optimization. Finally, the effectiveness of the
proposed method is verified via a comparison of the offline and
online optimization results, as well as the field data.
speed (km/h)
Parameter name
300
250
80
200
75
150
70
100
65
60
690
50
0
500
550
692
600
694
650
700
rail mileage (km)
Fig. 5. Actual V–S curve of the EMU running process (SRC: speed restriction curve,
AVSC: actual V–S curve).
Being limited by the given running time in train timetable, the
VSC of the EMU running process generally is close to the SRC.
However, it is unavoidable that the EMU encounters occasional
388
H. Yang et al. / Neurocomputing 169 (2015) 383–391
emergencies in the complex and dynamic running environment.
These emergencies, such as equipment failure, natural hazards and
interaction effects between EMUs, result in the sudden fall of SRC
(namely the SRM), as shown in Fig. 7 [26].
Therefore, to verify the efficiency and effectiveness of the
proposed method based on the field data, it assumes that there
is a SRM section from 593 km to 598 km, where the SRC suddenly
Table 2
Index values of the operation strategies.
i
j
fv
ft (s)
fd (km)
f e ðkW hÞ
fc
a
1
3.2615
228
0.000263
6966.37
0.41632
b
2
3
4
2.1195
1.4192
1.9191
32
24
27
0.000179
0.000319
0.000239
6611.53
6621.45
6633.65
0.31514
0.31521
0.31537
c
5
6
7
8
9
3.4522
2.3901
1.4953
4.7784
2.5041
29
11
25
27
18
0.000638
0.000253
0.000483
0.000124
0.000228
6619.28
6625.43
6631.72
6637.74
6645.79
0.31561
0.31542
0.31537
0.31581
0.31541
d
10
11
12
13
14
15
1.2784
1.4953
1.5919
2.0522
2.6021
2.5903
37
35
95
21
86
27
0.000824
0.000483
0.000179
0.000238
0.000128
0.000256
6637.74
6631.72
6609.45
6614.28
6639.99
6620.43
0.31742
0.31562
0.31586
0.31635
0.31646
0.31565
e
16
17
18
19
20
21
22
2.6403
5.8509
1.7919
5.4522
1.5953
7.7849
2.4031
27
38
45
43
79
47
98
0.000276
0.000116
0.000159
0.000838
0.000453
0.000624
0.000131
6620.83
6629.30
6601.45
6614.28
6621.72
6636.74
6632.99
0.31575
0.31549
0.31537
0.31542
0.31581
0.31561
0.31541
falls from 315 km/h to 285 km/h. The results of offline and online
optimization are presented in Sections 5.2.1 and 5.2.2, respectively.
5.2.1. Multi-objective offline optimization of EMU operation
In this section, the optimization experiments for the EMU
operation are carried out with a multi-objective offline optimization method by reference to [8,9]. The experimental results are
shown as Figs. 6(a), 7(e), the b in Table 2 and the cs2 in Table 3.
As shown as the local enlarging graphs of Fig. 7(e), the VSC
failed to react to the sudden SRM as emergencies result in the
failure of the operation strategy cs2 obtained from offline optimization experiments. Obviously, it is difficult for the offline optimization method to meet the requirements of MOP in this paper,
which proposes the need for an online optimization approach.
5.2.2. Multi-objective online optimization of EMU operation
The online experiments are carried out and the experimental
results are compared to the offline optimization results and field
data. In the experiments, whenever there is a SRM, the EMU
operation strategies are quickly adjusted from the current operation state to the braking state or emergency braking state. As a
result, the punctuality and energy consumption of the EMU
running processes are seriously affected, while train parking
accuracy and ride comfort are also affected to some extent.
Furthermore, the punctuality index is closely associated with the
other four indexes. Therefore, according to the delay degree of the
EMU's running state obtained from the real-time data, the priority
rankings of these indexes are set as the preference information of
Algorithm 1. The experimental results and discussions based on
the following three cases are shown in (1), (2) and (3) as follows:
in the table, a is the index values of the field operation strategy; b, c,
d, e are index values of the Pareto solution sets corresponding to the
Pareto solution
Pareto solution
6635
6650
6640
6625
fe(kw.h)
fe(kw.h)
6630
6620
6630
6620
6615
6610
6610
3
35
fd(k
m)
6
30
2.5
−4
x 10
−4
x 10
25
2
1.5
20
15
30
km
ft(s)
25
4
fd(
)
20
2
0
15
10
Pareto solution
6640
6640
6630
6630
fe(kw.h)
fe(kw.h)
Pareto solution
6620
6610
6600
1
0.75
x 10
6620
6610
6600
1
−3
ft(s)
0.75
100
80
0.5
fd(
km
)
60
0.25
40
0
20
ft(s)
x 10
100
80
0.5
−3
fd(
km
)
60
0.25
40
0
20
ft(s)
Fig. 6. Distribution of the Pareto sets obtained from multi-objective optimization. (a) Offline optimization, (b) in the case of long delay, (c) in the case of short delay and (d) in
the case of no delay.
H. Yang et al. / Neurocomputing 169 (2015) 383–391
389
400
SRC
AVSC
VSC
350
300
SRC
VSC
350
300
250
250
320
200
320
200
310
300
150
310
300
150
290
100
290
100
280
270
585
50
0
500
590
595
550
600
600
605
0
650
SRC
VSC
350
280
270
585
50
500
590
550
595
600
600
605
650
700
SRC
VSC
350
300
300
250
250
320
320
200
200
310
310
300
150
300
150
290
290
100
100
280
270
585
50
0
500
590
595
550
600
600
280
270
585
50
605
650
700
0
500
550
590
595
600
600
605
650
700
Fig. 7. V–S curves of EMU running process. (e) Offline optimization, (f) in the case of long delay, (g) in the case of short delay and (h) in the case of no delay.
Table 3
Operation strategies of the EMU.
cs1
cs2
cs3
cs4
cs5
c1
s1
c2
s2
c3
s3
c4
s4
c5
s5
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
/
/
/
/
/
/
1.1
1.3
25.4
2.7
26.1
2.5
27.4
2.7
25.4
3.6
23.3
4.7
23.4
5.6
25.4
5.5
14.8
4.7
1.7
0.26
0.22
/
/
/
/
/
/
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
/
/
/
/
/
/
/
/
1.1
1.3
25.2
2.3
25
3.1
27.8
3
25.2
4.5
22.8
4.4
22.7
6.6
26.4
5.4
14.5
6.2
0.28
/
/
/
/
/
/
/
/
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
/
/
1.1
1.3
25.2
2.2
25
2.2
0.8
0.9
26.2
3.5
23.2
7.5
8.14
0.12
2.01
0.13
11.2
4.1
23.7
5.2
27.7
5.4
14.3
6.46
0.22
/
/
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1.1
1.3
25.1
2.1
25.4
4.2
26.6
2.4
25.1
1.2
1.2
3
8.55
0.22
2.23
0.1
11.1
4.2
22.5
6.7
1.2
1
24.3
5.4
14.4
5.7
1.38
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
/
/
/
/
1.1
1.3
25.1
2.3
25.2
3.6
27.5
3.3
26.3
3.2
8.35
0.3
2.1
0.25
10.8
5.6
22.9
7.7
24.2
5.2
14.5
5.5
1.48
/
/
/
/
figures (a), (b), (c), (d) in Fig. 6, respectively. i-ordinal number of
the Pareto solution sets, j-ordinal number of operation strategies,
fv-security, ft(s)-punctuality, fd(km)-train parking accuracy, f e ðkW hÞ
energy consumption, fc-ride comfort.
(1) Long delay: In the case of long delay, the proposed method gives
priority to the optimization indexes of f v ; f t ; f d while also considering
the indexes of fe and fc, so as to improve the security (including the
indexes of f v ; f d ) and punctuality of the EMU running process as far as
possible. The index values of the Pareto solution set obtained from the
multi-objective online optimization are the c in Table 2. Then, based
on the principle of balance, the optimal operation strategy for this case
is obtained from the Pareto set, which is shown as the cs3 in Table 3,
whose index values are the c6 in Table 2.
As indicated by the VSC in Fig. 7(f) and the cs3 in Table 3, in order
to improve the punctuality index in this case, the optimal operation
strategy keeps the EMU running at a higher speed while decreasing
the coasting distance when the EMU encounters a SRM. Moreover,
the local enlarging graphs of Fig. 7(f) show the operation state
switch from braking to coasting when the speed becomes much
lower than the SR, and then back again when the speed is almost
over the SR. As a result, comparing the optimization indexes in c to
that of b and a in Table 2, it is observed that ft of the optimal
strategy is much better than the other strategies, while f v ; f d ; f c are
also not bad. Unfortunately, fe of the optimal operation strategy is
not yet satisfactory, which due to the traction distance being longer.
(2) Short delay: To improve the security, punctuality and efficiency
of the running process in the case of short delay, the proposed
method gives priority to the indexes of f v ; f t ; f e ; f d . Subsequently,
index values of the Pareto solution set of this case are the d in
390
H. Yang et al. / Neurocomputing 169 (2015) 383–391
Table 2. In addition, the optimal operation strategy in this case is the
cs4 in Table 3, whose index values are the d13 in Table 2.
The VSC in Fig. 7(g) and the cs4 in Table 3 show that, on the
premise of security, the optimal operation strategy balances ft and
fe by controlling the coasting distance appropriately. Since it is
limited by the given time T0, the running speed of the EMU does
not drop too much in the case of short delay. Moreover, a
comparison of these index values indicates that the optimal
operation strategy has kept the EMU running process more secure,
punctual and efficient.
(3) No delay: Since the EMU runs at the state of no delay, the
proposed method gives priority to the optimization indexes of f v ; f e ; f d ,
so as to ensure that the running process of EMU is secure and efficient.
Accordingly, the index values of the Pareto solutions set in this case are
the e in Table 2 and the corresponding optimal operation strategy is the
cs5 in Table 3, whose index values are the e18 in Table 2.
Based on the comparisons between the AVSC in Fig. 5 and the VSC
in Fig. 7(e), it can be concluded that there is a large scope for the
optimization of the efficiency of the EMU running process in this case.
For instance, comparing figures (h) to (f) and (g) in Fig. 7, it is observed
that the optimal operation strategy keeps the coasting distance as long
as possible while giving attention to ft. As a result, most of the
optimization indexes of the optimal operation strategy (the e18 in
Table 2) are better than that of field data (the a1 in Table 2).
Additionally, the fc of the operation strategies obtained from
the multi-objective optimization are within [0.3, 0.4], which
satisfy the comfort condition well (within 71 m/s2 [18]). Most
of the index values fd of the optimal operation strategies are better
than that of the field operation strategy. Furthermore, the operation strategies of EMU corresponding to the AVSC/VSC in Figs. 5–7
are shown in Table 3.
Finally, through the experiments above, the optimal operation
strategies have been obtained, which corresponding to the current
running state of the EMU. Based on these operation strategies, the
services provided by the EMU could be more secure, punctual, accurate,
energy efficient and comfortable. In the table, cs1 is the actual operation
strategy; cs2 cs5 are the optimal operation strategies obtained from
the multi-objective optimization experiments, which correspond to the
VSC in Fig. 7(e)–(h), respectively. ci A f1; 0; 1g is the EMU operation
state of traction, coasting and braking, respectively; si (km) is the
distance that ci keeps, and/means none.
6. Conclusions
In this paper, based on the SRM and field data, a multi-objective
online optimization method has been presented for improving the
EMU operation. Under assumption that there is a stochastic SRM
railway section, we considered three different EMU running states:
long delay, short delay and no delay. Some offline and online
optimization experiments were conducted by using the field data
in real world. The comparisons of these experimental results
showed that the optimal strategies meet the multi-objective
requirements for the EMU operation in real time.
It has been aware that the running process of EMU is too complex
to exactly compute the proposed optimization indexes. Thus, we plan
to improve the accuracy of the multi-objective model in our further
studies. Moreover, the convergence of the MOPSO algorithm will be
further improved to meet the real-time requirement.
Acknowledgment
The authors acknowledge the financial supports from the
National Natural Science Foundation of China (61164013, 51174091,
61364013, U1334211), and the key program of China Ministry of
Railway (2011Z00-2D).
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Hui Yang received his M.S. and Ph.D. degrees from
Northeastern University, Shenyang, China, in 1988 and
2004, respectively. He is a Professor in the School of
Electrical and Electronic Engineering of East China
Jiaotong University, Nanchang, China. His current
research interests are intelligent transportation system
control, complex system modeling, control and optimization, process industry integrated automation technology and applications.
H. Yang et al. / Neurocomputing 169 (2015) 383–391
Hongen Liu received his B.S. degree from the School of
Electrical and Electronic Engineering of East China
Jiaotong University, Nanchang, China, in 2012. He is
currently working toward the M.S. degree with the
Control Science and Engineering, East China Jiaotong
University. His current research interests are high
speed EMU optimal operation and control, complex
system modeling, control and optimization.
391
Yating Fu received her B.S. degree from the School of
Electrical and Electronic Engineering of East China
Jiaotong University, Nanchang, China, in 2011. She is
currently working toward the M.S. degree with the
Traffic Information Engineering and Control, East China
Jiaotong University. Her current research interests are
high speed EMU optimal operation and control, complex system modeling, control and optimization.