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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 46, 2015 

A publication of 

 
The Italian Association 

of Chemical Engineering  
Online at www.aidic.it/cet 

Guest Editors: Peiyu Ren, Yancang Li, Huiping Song 
Copyright © 2015, AIDIC Servizi S.r.l., 
ISBN 978-88-95608-37-2; ISSN 2283-9216 

Research on the Middle-Distance Running Achievement 
Prediction for College Students Based on LSSVMGAS 

Xiaobing Yang, Suqiong Feng* 

Sichuan Agricultural University 
fengtingting0828@163.com 

By the combination of the computer technology and the physical training, we can better predict the training 
achievement. Then we can make the targeted training for the college students. Therefore, the combination of 
the physical training for the college students and the computer technology has become a trend. Middle -
distance running is one of the most important standards for the physical training of the college students. 
Improving the middle-distance running performance not only improves the physical quality of the college 
students, but also improves the perseverance of the college students. In this paper, we combine the LSSVM 
method with the GAS method and propose the improved LSSVMGAS method. In the experimental part, we 
use the LSSVMGAS method to predict achievement of the middle-distance running for the college students 
and achieve the better results. 

1. Introduction 

In June 30, 2015, health and family planning commission issues a report. The report shows that the average 
height of adult male and female is 167.1cm and 155.8cm in China. It is lower than the average level of Japan. 
In this report, we can see that the physical quality of Chinese people is not optimistic. In National Standar d for 
Sports Training, the middle-distance running is easy to be neglected of the college students. To middle -
distance running not only enhances the physical quality for the college students, but also hones the character 
and will. Qiuhe Huang, Lanyong Wei and Haifeng Huo (2014) researched the college teachers’ teaching 
ability.  
Tang Chifei (2008) studied the running train for the college students. The author thought that the running train 
for the college students must be in accordance with their own growth and make the most effective use of their 
energy. Chi Hua (2013) et al. researched the college students’ running pain sensation scale. According to the 
item analysis, reliability and validity, the sensation scale could better reflect the degree and level o f the feeling 
pain of running for the college students. Guan Qingli and Wang Haiyuan (2010) proposed that the long-
distance running should take the physical education and the extra-curricular activities as the carrier. And it 
needed the participation of the teachers and the students. Zhao Fangye (2013) thought that the college 
physical education must adapt to the physical conditions of the contemporary college students. We should 
make the reform from the education philosophy, curriculum structure, teaching management link and the 
assessment indicator. In addition, Lin Zhenglan (2013), Pang Rong (2011) also studied the question. 
Support vector machine (SVM) was a data mining method based on the statistical learning theory. Tao Lin  
(2015) et al. studies the SVM Least squares support vector machine (LSSVM) was a new support vector 
machine. The operation speed of the LSSVM was faster than other support vector machines. Therefore, it had 
the wide application. Now, the LSSVM had many applications in the industrial chemical by Mohammad 
Mesbah et al. (2015), Hossein, Safari et al. (2014) Hamidreza Yarveicy et al. (2014), energy by Xing Yan and 
Nurul A (2013) and weather by Yi Zhang et al.. Gravitational search algorithm (GSA) was an intelligent 
optimization algorithm which was proposed in 2009. The thought of GSA algorithm was derived from Newton’s 
law of gravity. It guided the optimization search according to the group intelligence which generated by the 
gravity among the particles. The gravitational search concept was simple, easy to achieve and needed to 
adjust a few parameters. Now, Oliveria, Zikang Su, Beatriz Gonzalez and other people (2015) studied the 
gravitational search algorithm.  

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1546069

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Yang X.B., Feng S.Q., 2015, Research on the middle-distance running achievement prediction for college students 
based on lssvmgas, Chemical Engineering Transactions, 46, 409-414  DOI:10.3303/CET1546069  

409



In this paper, we combine the LSSVM with GAS and propose an improved LSSVMGAS method. Then, we use 
the method to predict the middle-distance running performance for the college students and achieve the good 
results. The structure of this paper is as follows. The first part is the introduction. In this part, we present the 
research status of the related content. The second part introduces the LSSVM. The third part is the basic 
principle of GSA. In the fourth part, we combine the LSSVM with GSA method and pro pose the improved 
LSSVMGAS method. The fifth part is the numerical analysis and the last part is the conclusion.  

2. The LSSVM method 

We suppose the training data set is ( , ), 1, 2, ,i ix y i N . ix  and iy  are the input vector and the corresponding 
output respectively. The input space dR  is mapped into a feature space Z though the nonlinear function 

( )
i

x . 
The linear function of the feature space defines as follows. 

( , ) ( )
T

y f x x b         (1) 
,Z b R   

According to the principle of the risk minimization, we can get the objective function 
2

,
1

1
min

2 2

. . ( )

0

1, 2, ,

N
T

i

i

T

i i i
s t y x b

i N

 


  

  







  







    (2) 

  is the penalty factor, i  is an error variable to indicate an error between the true output value of the sample 
i  and its estimated value. 
We can construct the corresponding Lagrange function: 

2

1 1

1 1
( , , , ) ( )

2 2

N N
T T

i i i i i i

i i

L b x b y          
 

             (3) 

Where i  is the Lagrange multiplier. 

3. Basic principle of GSA 

The gravitational search algorithm is a kind of group intelligence optimization algorithm which is proposed by 
Esmat professor. The magnitude of the gravitational force is proportional to the mass of the two particles. And 
it is inversely proportional to the distance of the two particles. 

1 2

2

M M
F G

R
     (4) 

The gravitational force
ij

F between the particle that the quality is i and the particle that the quality is j is 

expressed by the following function. 

2

aj pi

ij

M M
F G

R


     (5) 

ij

i

ii

F
a

M
     (6) 

aj
M  is the active gravitational mass of the particle j . piM  is the passive gravitational mass of the particle i . 

ii
M  is the inertia mass of the particle i . 

In the search space of D  dimension, we assume that there are N  particles. We define the location of the i   

particle as 
1

( , , , , )
d n

i i i i
X x x x  and 1, 2, ,i N . Where, N  is the population quantity. 

d

i
x  is the location of the  

i  particle in d  dimension. Now, we assume that the gravity and the mass of the particle are determined by  
the target function value of the search space. We calculate the inertia mass of the particle according to the  
formula (7) and (8). and we get the normalized mass according to the formula (9). 

, 1, 2, ,
ai pi ii i

M M M M i N        (7) 

( ) ( )
( )

( ) ( )

i

i

fit t worst t
m t

best t worst t





    (8) 

410



1

( )
( )

( )

i

i N

j

j

m t
M t

m t






    (9) 

Where, ( )
t

fit t  is the fitness degree value of the i  particle at t  time. 
Then, we can calculate the gravity of each particle in each dimension according to the following formula. The 
gravity of the i  particle and the j  particle in d  dimension is, 

( ) ( )
( ) ( ( ) ( ))

( )ij
i jd d d

j i

ij

M t M t
F G t x t x t

R t 


 


               (10) 

( )
d

j
x t  represents the location of the j  particle in d  dimension. ( )dix t  represents the location of the i  particle 

in d  dimension.   is a very small constant which is to prevent the denominator is zero.  
In the gravitational search algorithm, in order to increase the random properties of the algorithm, we think that 
the force of the particle i  is equal to the sum of other particles. The value is defined as follows. 

1,

( ) ( )
N

d d

i j ij

j j i

F t rand F t
 

                 (11) 

Where, 
j

rand  is a random number which belongs to [0,1] . 

According to Newton’s second theorem, the acceleration of the particle i  in d  dimension at t  time is defined 
as follows. 

( )
( )

( )

d

d i

i

i

F t
a t

M t
                (12) 

Where, ( )
i

M t  is the inertia mass of the particle i  at t  time. 
We update the speed and the location according to the following formula.  

( 1) ( ) ( )
d d d

i i i i
v t rand v t a t                   (13) 

( 1) ( ) ( 1)
d d d

i i i
x t x t x t                   (14) 

We assume that the number of the particles is Nbest . And the Nbest  changes with the time. Therefore, 
Nbest  decreases from the initial 0N . In the initial time, the particles have forces. As the time goes on, some 
particles that the masses are bigger begin to force other particles that the masses are sm aller. To the end, 
there is only particle forcing other particles. Therefore, the formula can be changed as follows. 

,

( ) ( )
N

d d

i j ij

j Kbest j i

F t rand F t
 

                 (15) 

Where, Kbest  is the set of the particles that the inertia masses are bigger.  

4. LSSVMGSA 

This paper establishes the predicted model of LSSVM and GSA. Firstly, we improve the GSA algorithm. In 
addition, GSA will optimize the parameter of the LSSVM model. The linear combination of the intermediate 
nodes is the output and each intermediate node corresponding to a support vector. 

In GSA algorithm, the expected particle is guided by the resultant. And it moves to the particle that the quality 
is heavy. At the same time, during the moving of the expected particle, it is also influenced by other particles. 
Therefore, when we calculate the resultant, there may be some deviations. Therefore, we introduce the 
correction factor to modify the resultant force in the algorithm.  

( ) ( )x M i M j                 (16) 

2

( ) 2

0

x C
y x

k x x C




 
  

                (17) 

1
cos( ( ))k y x     

Where,   is the correction factor that the force needs to add. 1k  and 2k  are the adjustable parameters. And 

they can be adjusted according to the different locations. C  is a coefficient which is related to the 2k . 
1

2

2

k
C




                (18) 

( )y x  is a function. And the new formula is as follows. 

411



1 2

1, 1,

( ) ( ) cos( ( ( ) ( ) )) ( )
N N

d d d

i ij ij

j j i j j i

F t F t k k M i M j F t
   

                       (19) 

The fitness function is defined as: 
2

1

1
( )

N

i p

i

fitness y y
N 

                 (20) 

N  is the number of the training samples.
i

y  is the true value, 
p

y  is the fitted value. 

The flow chart of LSSVMGAS is as follows.  
Start

The initial model 

parameter 

Select the type of kernel 

parameter 

Build LSSVM model

Initialize the particle 

swarm

Calculate the fitness 

function

Update gravitation constant, 

the optimal particle , the worst 

particle and the Inertial  mass

Calculate the correction 

factor

Calculate the resultant force 

and update acceleration

Update the location and 

speed of the particle swarm

Stopping 

criteria 
NY

Obtain the optimal 

parameter combination 

Build the optimal 

LSSVM model 

Output the predictive value

End

New input

 

Figure 1: Flow chart of LSSVMGAS 

5. Numerical analysis 

In the numerical experiment, we predict the long-distance running performance for the college students. We 
choose 4 college students to run and predict their performances. There are two male college students and two 
female college students. The male college students run 1000 meters and the female college students run 800 
meters. Firstly, we collect data of 30 groups’ long-distance running. The first 20 groups are as the training sets 
and the last 10 groups are as the predicted sets. The data of the training sets is as follows. 

Table 1: The data of the training set 

No Male1 Male2 Female1 Female2 
1 224 210 214 225 
2 226 209 218 226 
3 218 203 211 217 
4 226 208 208 220 
5 230 205 205 221 
6 217 214 210 214 
7 214 212 213 218 
8 210 210 211 219 
9 215 208 216 225 

10 223 213 213 227 
11 225 211 218 225 
12 228 214 223 224 
13 219 207 220 221 
14 220 194 213 218 
15 223 205 211 217 
16 216 203 206 219 
17 224 206 214 223 
18 225 218 215 224 
19 233 220 218 221 
20 228 216 220 227 

412



Then, we predict the performance. The predicted performance and the actual performance are as follows.  

Table 2: The actual values and the predicted values 

No 
Male1 Male2 Female1 Female2 

Actual 
values 

Predicted 
values 

Actual 
values 

Predicted 
values 

Actual 
values 

Predicted 
values 

Actual 
values 

Predicted 
values 

21 225 227 215 213 217 219 224 223 
22 223 224 217 215 213 215 224 224 
23 220 220 208 210 214 214 221 223 
24 218 220 210 211 216 215 218 220 
25 221 218 213 211 218 217 220 221 
26 224 222 214 214 217 215 218 219 
27 223 224 212 213 213 214 223 222 
28 225 224 208 209 211 212 226 225 
29 224 223 207 209 208 210 227 226 
30 224 224 210 211 207 208 225 224 

We compare the actual performance with the predicted performance. The results are as follows.  

 

Figure 2: The experiment results of male1          Figure 3: The experiment results of male2 

Figure 4: The experiment results of female1         Figure 5: The experiment results of female2 

From the above figure, we can see that the predicted value which is obtained by the LSSVMGAS method is 
very close to the actual values. The two curves of each training set are very similar. From the experiment, we 
can know that the LSSVMGAS method achieves the good results. The experiment shows that the 
LSSVMGAS method is feasible and effective.  

7. Conclusions 

The middle-distance running is popular by the teachers and the students. And the majorly of teachers pay 
more and more attention to the middle-distance running with the computer technology. In this paper, we 
propose the LSSVMGAS method to predict the middle-distance running performance and the targeted 
training. The main work of this paper is as follows. Firstly, we introduce the research status of the related 
content. Secondly, we introduce the LSSVM method and GAS method. Thirdly, we combine the LSSVM 
method with the GAS method and propose the improved LSSVMGAS method. Fourthly, we use the 
LSSVMGAS method to predict the middle-distance running performance for the college students. And it 
achieves the good experimental results. The content of this part has some reference value for the research of 
the LSSVM and the physical quality of the college students. 

413



Acknowledgment 

This research is supported by Undergraduate Theses Incubation Program of Sichuan Agricultural University. 

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