OPTIMIZATION CONTROL OF E-BUSINESS INCOME BASING
ON INTERVAL GENETIC ALGORITHM OF
MULTI-OBJECTIVE
Qin Liao and Zhonghua Tang
School of Mathematical Science, South China University of Technology
Guangzhou, Guangdong 510640, P. R. China
Keywords: Interval Genetic Algorithm, Optimal Control, E-Business Income.
Abstract: In order to control the E-Business income, the relationship between 9 influencing factors and 3 controlling
objectives is built by neural network. Then an interval genetic algorithm of multi-objective (IGAMO) is
proposed to obtain the satisfactory interval solution instead of a single point solution provided by traditional
algorithm. The IGAMO is constructed with 2-step genetic algorithm to find expending intervals satisfying
the multiple income objectives, thus we gain the control conditions for influencing factors to make the
income indexes fall in the anticipant intervals. The optimal control of E-Business income is proved to be
feasible according to the analysis of the data collected from example e-Business enterprises of Guangzhou.
1 INTRODUCTION
E-Business control problem is a hot theme of
researches in recent year (Pham, 2004; Lui et al.,
2002). In our former work, an evaluation-factor
system and an evaluation method are proposed
according to the survey of the operation mode of
E-Business of Guangzhou (Liu et al., 2005).The
research outcome also bring out a valuable question:
Can the relationship model between the influencing
factors and income of E-Business be established,
with which the E-Business income can be
manipulated effectively by controlling the
influencing factors? Many researches are focusing
on predicting the income in future by the given
values of influencing factors. However, works on
setting the influencing factors at certain levels in
order to control the E-Business income are rare.
Suppose there are t indexes reflecting the situation of
E-Business income denoted as Y
i
(i=1,2,…,t). For
Y
i-min
≤Y
i
≤Y
i-max
, how to determine the interval (c
j
,d
j
)
of the influencing factor x
j
(j=1,2,…,n)? That is to
solve the optimal control problem of influencing
factor
x
j
under the multiple conditions in (1).
Y
i-min
≤Y
i
≤Y
i-max
, Y=( Y
1
, Y
2
, … ,Y
t
)
(1)
Since it is difficult to solve these global optimization
problems with multiple objectives and variables by
traditional methods, this paper takes advantage of
interval genetic algorithm to solve them.
The rest of the paper is organized as follow:
Section 2 presents the IGAMO; Section 3 apply
the IGAMO to solve the optimal control of
E-Business income basing on data of enterprises
in Guangzhou. Section 4 concludes the paper.
2 INTERVAL GENETIC
ALGORITHM OF
MULTI-OBJECTIVE
Traditional genetic algorithm is to find the best
individual
(0) (0) (0) (0)
12
(, , )
n
XXXX= "
which is called the
satisfactory solution. In fact, it is too demanding to
fix factors at certain values in real control problem.
Therefore, a more practical way is to search for a
series of optimal intervals of influencing factors
x
j
to
satisfy (1).
IGAMO is a two-step genetic algorithm aiming at
figuring out the optimal intervals: the first step
genetic algorithm is to find out the satisfactory
200
Liao Q. and Tang Z. (2007).
OPTIMIZATION CONTROL OF E-BUSINESS INCOME BASING ON INTERVAL GENETIC ALGORITHM OF MULTI-OBJECTIVE.
In Proceedings of the Third International Conference on Web Information Systems and Technologies - Society, e-Business and e-Government /
e-Learning, pages 200-203
DOI: 10.5220/0001264502000203
Copyright
c
 SciTePress

solution while the second step is to determine the
optimal control intervals basing on the satisfactory
intervals expanded from the satisfactory solution.
The relationship of dependent variables Y=( Y
1
,
Y
2
, … ,Y
t
) and the influencing factors x
j
, x
j
,…,x
j
is
shown as follow:
12
11
(, , , ) ( ( ) )
Mn
ii n iq qjjqi
qj
YFxx x f Vf wx r θ
==
== −−
∑∑
"
,
min maxiii
YYY
−−
≤≤
,
j
jj
axb≤≤
,
1, 2, ,it
=
"
,
1, 2 , ,jn= "
(2)
where F
i
is a BP Neural Network model, V
iq
are the
connection weight of output and hidden neurons
while w
qj
of hidden and input neurons, θ
q
, r
i
are
thresholds and
f
is sigmoid function.
2.1 Obtaining the Optimal Solution
For every j
(1,2,,)jn= "
, randomly generate N genes
()k
j
x
(1,2,,)kN= "
, respectively from
[,]
j
j
ab
,thus the
k
th
individual is denoted as
() () () ()
12
{, ,,}
kkk k
n
X
xx x= "
,
then the population with N individuals is
(1) (2) ( )
{, ,, }
N
SXX X= "
and the dependent variables of
()k
X
in S is
() () ()
12
(,,,)
kk k
t
YY Y"
.The midpoint is
presented as
min max
2
ii
imid
YY
Y
−−
−
+
=
and the fitness
function is defined as:
()
() 2
1
1
1
() sgn()
()
t
k
ii
t
k
i
iimid
i
FX D
YY
β
α
=
−
=
=+
−+
∑
∑
(3)
where
,0
i
α
β >
and
midi
k
i
ii
i
YY
YY
D
−
−−
−−
−
=
)(
minmax
2
,
,0
sgn( )
0, 0
ii
i
i
DD
D
D
>
⎧
=
⎨
>
⎩
(4)
Parameters
,
i
α
β
guarantee the existence of
individuals that satisfy (1).
The first step of genetic algorithm is to search for
and obtain the optimal individual
(0) (0) (0)
012
(,,, )
n
Xxx x= "
touching or closest to
12
(, ,,)
mid mid t mid
YY Y
−− −
"
.
2.2 Generating Optimal Intervals
Having found out the optimal individual
(0) (0) (0)
012
(,,,)
n
Xxx x= "
, to determine the intervals for
factors
x
j
, let
() ()
1
1
max{ } min{ }
kk
jj j
kN
kN
Cx x
≤≤
≤≤
=−
,where
()k
j
x
are genes from the individuals marked in the first
step. Generate the positive real number
j
ε
(0) (0)
min{ , , 2}
jjjjjj
bxx aC ε =− −
，
1, 2, ,jn= "
(5)
So the satisfactory solution is expanded from single
points
x
j
to centre fixed intervals
(0) (0)
(, )
j
jj j
xx
ε
ε −+
, M
new individuals
() () () ()
12
(,,,)
kkk k
n
Xxx x= "
are randomly
generated from intervals
(0) (0)
(, )
jjjj
xx
ε
ε −+
,
1, 2 , ,k
M
= "
.
Then
S’ is the new population possessing M+1
individuals
(0) (1) ( )
,,,
M
XX X"
. The fitness function
is defined as (3).
The second step genetic algorithm is carried out with
these M+1 individuals. After a certain times of
evolutions through the defined crossover operator
and mutation operator, we gain individuals whose
fitness is no less than that of X
0
.
All the individuals that satisfy all
()
max min
2
k
ii
iimid
YY
YY
−−
−
−
−<
(1,2,,)it
=
"
are sorted by the
fitness value in descending order and the top w
individuals are chosen.
Suppose the j
th
gene of the w individuals are ranked
from small to big as
12
,,,
w
jj j
x
xx
 
"
, so the corresponding
interval of the j
th
gene is
1
[, ]
w
jj
x
x

,
1, 2 , ,
j
n= "
.
2.3 Statistical Test
To calculate the probability of the output Y=( Y
1
,
Y
2
, … ,Y
t
) of the combination of values randomly
selected from the n intervals
1
[, ]
w
j
j
x
x

obtained in
the second step, which are supposed to satisfy that
Y
i-min
≤Y
i
≤Y
i-max
, this paper hold a random test with H
test samples. Select
x
j
from intervals
1
[, ]
w
jj
x
x

to
form individuals
() () () ()
12
{, ,, }
kkk k
n
X
xx x= "
(1,2,,)kH= "
,
calculate
(1) ( 2 ) ( )
{, ,, }
H
YY Y"
with
(1) (2) ( )
{, ,, }
H
XX X"
,
compared with the anticipant intervals of dependent
variables and count the quantity of
() () () ()
12
(,,,)
j
jj j
t
YYY Y= "
which satisfy
()
mi n ma x
j
iii
YYY
−−
≤≤
, then the frequency of individuals’
output bounded in the anticipant intervals is obtained
to describe the probability that the outputs of the
OPTIMIZATION CONTROL OF E-BUSINESS INCOME BASING ON INTERVAL GENETIC ALGORITHM OF
MULTI-OBJECTIVE
201

combination of x
j
derived from
1
[, ]
w
jj
x
x

are in the
anticipant intervals.
By the process mentioned above, we have the
optimal intervals for multiple variables
x
j
and the
control probability with Y
i-min
≤Y
i
≤Y
i-max
.
3 OPTIMIZATION CONTROL OF
E-BUSINESS INCOME
3.1 e-Business Income and the
Influencing Factors
Basing on the evaluation-factor system established in
(Liu et al., 2005), the circumstance of E-Business
income is evaluated by three indexes: Profit growth
rate (
Y
1
), Turnover rate (Y
2
), Sales profit rate (Y
3
)
while the influencing factors are concluded as
follow: Customer resources (
x
1
), Customer service
(
x
2
), Delivery system (x
3
), Online transaction system
(
x
4
), Construction of software & hardware (x
5
),
Combination of inner and outer information
management (
x
6
), Network technique & service (x
7
),
Marketing for internet (
x
8
), Training (x
9
). 20 groups
of data collected from example E-Business
enterprises of Guangzhou are showed in Table 1.
The values of these factors are scores in interval [0,
5] determined by E-Business experts. The three
indexes of E-Business income are produced by the
data collected during the investigations of a number
of enterprises. The value of turnover rate should be
real number in the interval [0, 1] while the other two
in the interval [0, +∞].
3.2 Interval Optimization Control
Model of e-Business Income
According to (1), let n=9, t=3, M=12. The BP neural
network model of three income indexes and 9
influencing factors is built up by learning samples
and tested by test samples. Table 2 shows the
parameters.
Table 1: Income and influencing factors of e-Business.
x
1
x
2
x
3
x
4
x
5
x
6
x
7
x
8
x
9
Y
1
Y
2
Y
3
4.5 5.0 3.8 4.9 4.7 4.1 4.9 4.5 3.2 11.90 40.47 13.46
2.6 4.6 4.1 3.6 4.7 4.6 4.7 4.9 2.4 10.56 68.23 14.04
3.7 2.6 3.2 4.0 4.5 4.9 1.9 3.8 1.8 6.61 35.39 8.208
4.4 4.6 3.2 3.9 4.5 4.7 1.7 2.8 1.4 9.44 28.84 9.204
4.9 4.8 2.9 3.8 4.5 4.9 1.6 4.0 4.2 4.26 38.59 8.052
4.6 3.0 2.9 2.6 5.0 1.2 1.7 2.6 3.7 9.42 24.91 7.135
4.6 2.5 2.3 3.7 4.8 4.7 2.2 3.4 4.4 8.66 24.17 9.028
4.6 2.8 2.7 3.7 4.9 4.0 1.9 1.6 3.6 4.36 35.91 7.266
4.5 4.7 1.6 4.2 4.7 4.8 2.4 3.5 3.9 5.27 42.97 7.549
4.5 4.7 3.2 3.9 4.6 5.0 1.1 1.6 4.2 8.81 16.77 9.141
4.5 2.1 2.9 3.6 5.0 4.9 2.3 2.9 2.0 7.65 37.34 8.509
4.4 3.8 2.7 3.4 5.0 2.6 3.7 3.9 2.7 5.04 39.54 8.280
4.4 3.2 1.8 3.7 4.5 0.8 4.6 4.7 4.8 8.86 38.64 9.462
3.5 3.9 3.6 4.0 4.5 1.9 4.3 4.0 4.0 9.37 24.36 6.565
0.6 4.8 3.4 4.3 4.5 1.1 4.1 4.7 4.7 7.02 18.65 7.809
2.8 3.6 3.8 4.3 4.8 2.8 3.6 4.5 2.5 9.80 20.31 7.882
3.8 2.2 3.6 3.2 4.3 3.6 2.9 2.0 3.5 1.81 13.31 6.939
3.1 4.9 2.9 3.8 2.7 3.8 0.8 2.1 2.8 1.99 23.86 5.810
4.6 1.7 2.0 3.8 3.5 4.8 1.8 2.0 1.4 4.18 8.26 6.119
1.8 3.0 1.7 3.1 4.9 3.4 3.8 4.3 2.4 4..51 17.27 6.521
Table 2: Parameters of BP NN evaluation model of
income.
Input
neurons
Hidden
neurons
Output
neurons
Training
times
Total
error
Total test
error
9 12 3 20000 0.01 0.017
The anticipant range of these income indexes-Profit
growth rate (
Y
1
), Turnover rate (Y
2
) and Return on
investment (
Y
3
)) are shown in Table 3.
Table 3: Anticipant range of indexes of E-Business
income.
Indexes Y
1
Y
2
Y
3
Anticipant range 7%-9% 25%-35% 9%-11%
First, the midpoints of anticipant ranges are
computed according to Table 3 shown below:
Y
1-mid
=0.08, Y
2-mid
=0.30, Y
3-mid
=0.10
With the definition of fitness function in (3), the
first-step genetic algorithm is carried out and the
optimal individual
(0) (0) (0)
012 9
( , , , ) (4.4382,4.8610,Xxx x=="
3.5106,2.6649,4.5582,2.7313,3.2844,3.7715,2.2959)
, where
WEBIST 2007 - International Conference on Web Information Systems and Technologies
202

the size of the population N=100; the selection rule
is fitness-proportionate selection, the crossover rule
is one-point crossover and the mutation rule is
uniform mutation; the probability of crossover
P
c
=0.5 while that of mutation P
m
=0.1, α=0.4,β
1
=0.45,
β
2
=0.51, β
3
=0.38, times of evolution are 10000.
Generate
ε
j
according to (4) to construct intervals
(0) (0)
(, )
j
jj j
xx
ε
ε −+
, which can be viewed in Table 4.
In order to find out the optimal intervals of
x
j
, the
second step is carried out: 500 individuals
(1) ( 2) (500)
{, ,, }XX X"
are generated randomly with their
gene
()k
j
x
selected from
(0) (0)
(, )
j
jj j
xx
ε
ε −+
. The
fitness function is still defined by (3).When
P
c
=0.5 ,P
m
=0.05, evolution times are 5000. It turned
out that there are totally 491 individuals satisfying:
() () ()
11 22 33
0.01, 0.05, 0.01
kk k
mid mid mid
YY YY YY
−−−
−< −< −<
Let w=300, choose the top w individuals and the
interval of the j
th
gene, noted as
1 300
[, ]
jj
x
x

, generated
from these individuals are shown in Table 5.
Table 4: Intervals of influencing factors in the first-step.
Factor
x
1
x
2
x
3
x
4
x
5
x
6
x
7
x
8
x
9
(0)
jj
x
ε
−
4.05 4.73 2.82 2.41 4.16 1.83 2.81 3.16 1.55
(0)
j
j
x
ε
+
4.82 4.99 4.19 2.91 4.95 3.63 3.75 4.37 3.03
Table 5: Final intervals of influencing factors.
Factor
x
1
x
2
x
3
x
4
x
5
x
6
x
7
x
8
x
9
1
j
x

4.31 4.73 3.36 2.59 4.46 2.47 3.05 3.57 2.22
300
j
x

4.45 4.93 3.61 2.82 4.78 2.96 3.44 3.84 2.41
5000 test samples are generated in the corresponding
intervals. Compare the outputs
Y
i
with the anticipant
ranges. We conclude that the probability that the
outputs fall in the anticipant ranges is about 99.5%,
which means as long as the influencing factors are
held at the levels between those shown in Table 5,
the E-Business income could be controlled under the
expectation shown in Table 3 effectively.
4 CONCLUSIONS
The interval genetic algorithm of multi-objective can
effectively solve the optimization control problems
with multiple objectives and variables, which can
hardly be solved by traditional methods. Enterprises
can control the E-Business income and profit
effectively by taking the process control of the
influencing factors. Not only does the result of this
paper provide a feasible way to realize the anticipant
income of E-Business but also can be promoted to
the optimal control problems in other domains.
REFERENCES
Liao Q. ， Gu H. M., Hao Z. F. (2005). Fuzzy
Comprehensive Evaluation of E-Commerce and
Process Improvement. Lecture Notes in Computer
Science No. 3828, pp. 366-374.
Li K.,Guo M.Y., Li L.(2004). Switching cost, market
effects and the pricing model of e-Commerce. Proc.
IEEE Int. Conf. Serv. Comput. SCC, pp. 403-408.
Pham, Trung T. (2004). Quantitative approach to using
E-commerce data to monitor and control the
performance of a supply chain.
Proc. IEEE Int. Conf.
e_technology e-Commerce e-Service EEE, pp.
157-162.
Liu Z. Squillante M.S. Wolf J.L. (2002). Optimal
control of resource allocation in e-business
environments with strict quality-of-service
performance guarantees. Decision and Control,
Proceedings of the 41st IEEE Conf., pp.4431- 4439.
Liao Q., Li J., Hao Z. F., Li X. W. (2005). Optimized
Fuzzy Evaluation Model on Security Risk of
Underground network, Asia Pacific Symposium on
Safety , pp. 129-135.
Li Y. Q. & Liao Q. (2004). Influence Factors and
Mathematical Modeling of the Security of
Underground Gas Conduit Network. Journal of South
China of University of Technology
（ Natural Science
Edition
） , Vol. 32, pp. 89-93.
OPTIMIZATION CONTROL OF E-BUSINESS INCOME BASING ON INTERVAL GENETIC ALGORITHM OF
MULTI-OBJECTIVE
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