Engineering, 2009, 2, 106-110
doi:10.4236/eng.2009.12012 Published Online August 2009 (http://www.SciRP.org/journal/eng/).
Application of PPC Model Based on RAGA in Real Estate
Investment Decision-Making
Shujing ZHOU, Fei WANG, Yancang LI
College of Civil Engineering, Hebei University of Engineering, Handan, China
Received May 17, 2009; revised June 26, 2009; accepted July 5, 2009
Abstract
According to the size of the projector function to evaluate the merits of the program, Projection Pursuit
method is applied to real estate investment decision-making by using the real coding based on Accelerating
Genetic Algorithm (RAGA) to optimize the Projection Pursuit Classification (PPC) process and a wide range
of indicators value was projected linearly. The results are reasonable and verified with an example. At the
same time, the subjective of the target weight can be avoided. It provides decision-makers with comprehen-
sive information on all the indicators of new ideas and new methods
Key words: Real Estate, PPC Model, Investment Decision-Making, Accelerating Genetic Algorithm
1. Introduction
The real estate industry is now one of the major pillar
industries of economic development in the world. Due to
the late start of our country’s real estate economy, in-
vestment decision-making theory is not perfect in the
study—how to program in a multi-selection process, to
avoid the subjective factors on the impact of real estate
investment decision-making so as to achieve the best
overall efficiency of the purpose of the program. At pre-
sent, on the real estate investment decision-making, there
are two commonly used methods. The first mainly is
single-objective decision-making, respectively, in Net
Present Value (NPV), Internal Rate of Return (IRR), Pay-
back Period (Pt), such as a single evaluation index [1].
Although the method is convenient, simple, and easy
to understand, it’s not a comprehensive reflection of the
merits of the project. Another method is multi-objective
decision-making method which includes Analytic Hier-
archy Process (AHP) [2,3] and Fuzzy Comprehensive
Evaluation methods [4]. Calculation of these methods is
more complex, and the determination of weight for
greater subjectivity in the practical application is more
inconvenient and not objective enough. In order to avoid
the weighing of the subjective in computational process,
this paper introduces a Projection Pursuit Classification
model to the real estate investment decision-making to
achieve the dimensionality reduction process of
multi-index high-dimensional data which could evaluate
real estate investment plan in many fields and join the
RAGA suitably for multi-dimensional global optimiza-
tion with the PPC model.
2. Methodology of PP
Projection Pursuit is used to analyze high-dimensional
data, in particular the non-normal nonlinear analysis of
high dimensional data as a statistical method [5-7]. It is
imitated by the experienced workers of data analysis by
Friedman and Tukey (1974) who put forward the whole
spread to the extent and degree of local cohesion com-
bining to make a new index for clustering and classifica-
tion analysis. Projection Pursuit method can overcome
the success of high-dimensional data—“dimension
curse”, which is brought about by serious difficulties. It
is because that its analysis of the data in the low-dimen-
sional subspace conducted for 1 to 3-dimensional projec-
tion space data points is dense enough, and sufficient
data in the projection space can be found in the structure
or characteristics. It can exclude from the interference of
the variables which have nothing to do with the data
structure and characteristics or the relationship between

S. J. ZHOU ET AL.
107
variables is very loose. In addition, the high dimensional
data can be projected into the one-dimensional space by
PP method again after the one-dimensional projection
analysis of the data to compare the different requirements
of one-dimensional projection results so that the best pro-
jection can be find out. Projection Pursuit method is the
same as other non-parametric methods which can be used
to solve some nonlinear problems. Although it is data
based on linear projection, it is used to find a linear pro-
jection of the non-linear structure, and it also can be used
to solve the nonlinear problem to some extent. At present,
the method has been applied in many fields [8–13].
3. The PPC Model Based on RAGA
The PPC model based on RAGA will be applied to spe-
cific real estate investment program of merit-based
evaluation. Firstly, the evaluation index of investment
program (high-dimensional data) is projected to the
one-dimensional subspace, and the Projection Pursuit
Classification model is established with RAGA. Then
after numerous operations to find the best projection di-
rection to calculate the best value, the best program can
be selected based on the best value.
3.1. Normalization of Decision-Making Indictors
Set [14-17]
Indicators for decision-making program set * {(,)|
x
ij i

1, 2...,;1, 2...,}nj p, *(, )
x
ij is the jth indexed value of
section , and , in
p
respectively indicate the number
of decision-making program and the number of indica-
tors. For the elimination of all dimensions and uniform
changes in the scope of the value of the indicators, we
need to conduct it with the normalization:
For the greater and better indicators:
*
min
max min
(,)( )
(, )() ()
x
ij xj
xi j
x
jx j


For the smaller and better indicators
*
max
max min
() (,)
(, )() ()
x
jxij
xi j
x
jx j

 (1)
Here: max ()
x
j, min()
x
j—the jth maximum and mini-
mum indicators’ values; (, )
x
ij—indicators normalized
eigenvalue sequences.
3.2. Structure Projection Target Function ()Qa
Pr ojection Pursuit Method is integrated {x*(i,j)|=1,
2,... }pp-dimensional data into a {(1),(2),..., ()}aaa ap
for the projection of one-dimensional projection of the
direction of the value of ()zi
1
()(). (,)
p
j
zia jxi j

(1,2,...)in (2)
Here: —unit length vector. According to n{()|1,zii

2..., }n, one-dimensional map analysis and evaluation
are spread. Projection indicators in the integrated value,
the value of requirements of the projector is char-
acterized by the spread of local projection point intensive,
as far as possible, preferably into a number of pool points
Mission; and on the whole, the projection points, spread
as far as possible between the mission, the projection
target function can be expressed as:
()zi
() .QaS D
zz

(3)
Here:
z
S—Projection value standard deviation;
z
D—Projection value of the local density of . ()zi

1
2
()( )
1
n
i
zi Ez
Szn




(4)
11
((,)).((,)
nn
ij
RrijuRrijDz  ) (5)
Here: —the average of sequence{(()Ez )|1,2...,zi i

}n; —local density radius of the window. It is the
selected window to be included in the projection of the
average number of points which should not be too few,
so as to avoid moving average deviation too much. With
the increase of , can be determined based on the
pilot, which range from
R
nR
max 2
2
p
rRp
(, )ri j
 ; —the
distance between the samples, (, )()zi z
0
( )ri jj;
—unit step function, the time when , and its
value to 1; when
(ut)t
0t

, the function value is 0.
3.3. Optimize the Projection Index Function
When the index value of the program is given, the pro-
jection target function only follows Projection
direction ’s change to change. Different projection
directions reflect different construction of data charac-
teristics. The best projection direction which is most
greatly possible to expose some kinds of characteristic
structure is the high-dimensional data. We can estimate
the best projection direction through the solution projec-
tion target function maximization question. And the
maximization objective function is:
()Qa
a

S. J. ZHOU ET AL.
108
() .
M
axQ aSD
zz

(6)
Constraints:
2
..()1
1
p
sta j
j


 (7)
It is a complex misalignment optimization question,
which takes {as the optimized vari-
able; it is also difficult to deal with it by the traditional
optimized method. Therefore, this paper, which simulates
biological survival of the fittest with the group informa-
tion mechanism of real-coded genetic algorithm, solves
the high-dimensional global optimization problem.
()|1, 2,...}aj jp
3.4. Program with Classification and Pecking
Order
The best projection direction of by the third step is
give into
1
*
a
()( ) (,)
p
i
zia jxi j
*()zi

, and we can get the
value from a projection of the program point. In the light
of the sequence of value which is from big to
small, the merits of the program can be determined.
*()zi
3.5. Acceleration by Real-Coded Genetic
Algorithm (RAGA) [18]
Standard genetic algorithm (referred to as SGA) usually
uses the binary encoding; the individual genotype which
constitutes the SGA is a string of binary code symbols.
Simple binary encoding is simple, while the genetic ma-
nipulation is done, and it facilitates the realization of
user-friendly schema theorem theoretical analysis of al-
gorithms easily, such as crossover and mutation, but it
does not reflect easily the problem of the structural char-
acteristics for some continuous function optimization
problems, as the optimization efficiency of the standard
genetic algorithm obviously depends on the optimization
of variable size between the initial changes. Study shows
that the operation—crossover operator to operate, the
function of searching excellently in the standard genetic
algorithm selection operator will be weaken with the
increasing of evolutionary optimization iterations gradu-
ally. There are many phenomenons which are in the
practical application most far from the overall advan-
tages of the standard genetic algorithm. It is seeking a
standstill excellent work, and at this time, it is similar to
many individuals and even to repeat. To this end, it is
believed that the initial change is the new range of initial
changes. Returning the standard genetic algorithm gives
rise to accelerate the formation of operation. The range
of outstanding individuals will be gradually reduced,
with the most advantages from the getting closer and
closer, until individual value of the optimal criterion
function is less than a stetted value or the accelerating
frequency is achieved in the process of algorithm. Then
end up the entitle algorithm. The best individual in the
current groups is designated as a result of accelerating
genetic algorithm. This method is the accelerating ge-
netic algorithm which is based on real-coded.
3.6. Programming Diagram
This paper proposed the steps of the model as shown in
Figure 1.
4. Case Studies
In order to verify the effectiveness of the model applied
in the real estate investment decision-making, we se-
lected a real estate company’s six investment programs
to carry on comprehensive evaluation. Table 1 lists seven
original data values in the six programs:
Note: The data are derived from the financial data of a
real estate investment company.
For the greater and better indicators, such as the ex-
pectations of net present value index, the risk of profit
values, expectations of net present value, financial net
present value and economic net present value, the data
were treaded as follows:
*
min
max min
(,)( )
(, )() ()
x
ij xj
xi j
x
jx j


For example, the expectations of net present value in-
dex of program A is normalized by the following for-
mula:
Figure 1. Programming diagram of PPC model based on
RAGA.
RAGA al
g
orith
m
Sort Optimization
Evaluation index system
PPC model
The best projection direc-
tion
The best projection value

S. J. ZHOU ET AL.
109
Table 1. The real estate investment program of the index value.
Program
Expectations
of net pre-
sent value
index
Failure
rate of
investment
The risk
of loss
of value
(million)
The risk of
profit
value(million)
Expectations
of net present
value(million)
Financial net
present
value(million)
Economic net
present
value(million)
A 2.80% 3.30% 0.0910 0.0920 0.0830 0.0850 0.0860
B 2.75% 3.00% 0.0915 0.0910 0.0820 0.0900 0.0860
C 3.67% 2.50% 0.0820 0.0780 0.0850 0.0860 0.0950
D 3.32% 2.70% 0.0800 0.0800 0.0860 0.0900 0.0880
E 3.21% 3.30% 0.0800 0.0800 0.0850 0.0830 0.0880
F 2.70% 3.50% 0.1000 0.0850 0.0840 0.0800 0.0750
And then substituting into Formula (2), the com-
prehensive evaluation values of all programs projection
can be get.
*
a
11
0.0280 0.0270.8969
0.0367 0.027
x 

The smaller and better indicator, such as the failure
rate of investment and the risk of investment losses, the
use of Formula (1) for the next normalized:
*( )(0.9401,1.2352,1.8888,zj1.8888,1.2352,0.1553)
*
max
max min
() (,)
(, )() ()
x
jxij
xi j
x
jx j


For example, the failure rate of investment of A is
normalized by the following formula:
12
0.0350.0330.2000
0.0350.025
x


The normalized matrix can be obtained:
*
X
=
0.8969 0.2000 0.45001.00000.2500 0.5000 0.5500
0.9485 0.5000 0.4250 0.9286 0.00001.00000.5500
0.0000 1.00000.90000.00000.7500 0.6000 1.0000
0.36080.80001.0000 0.14291.00001.0000 0.6500
0.4742 0.20001.00000.1429 0.7500 0.3000 0.6500
1.00000.0000 0.0000 0.5000 0.5000 0.0000 0.0000
















In the light of the sequence of value which is
from big to small, we can get the value of every invest-
ment program. That is the best program of C and D. De-
cision-makers can refer C or D to the decision-making,
but taking into account the failure rate of investment of C
significantly lower than that of D, we can see that C
possess the best investment value. Moreover, we could
further analyze the influenced degree of every indicators
of evaluation to get the results of comprehensive evalua-
tion by the best direction of projection. In the light of
sequence of values which is from big to small, the
order of the contribution rate can be obtained. The se-
quence as follows: the failure rate of investment, the risk
of loss of value, economic net present value, financial net
present value, net present value expectations, the risk of
profit values, expectations of net present value index. So
the results of the application match up to the practice.
This is satisfactory.
*()zi
*
a
5. Conclusions
And then substituting *
X
into Formula (2)-(5 ) in
turn, the projection target function in this case is found,
and then use RAGA to optimize the problem assured
with the Formula (6) and (7). Select the initial parent
population size, crossover probability
400n0.8
c
P

,
mutation probability , 0.8
m
P0.05

, to accelerate
the cycle 20 times, then reach the maximum indicator
function value of 0.4213, the best projection direction:
1) Projection Pursuit Classification model takes the
original data of the program for analysis directly; the
amount of information will not be lost.
2) In PPC model, high dimensional data will be pro-
jected Into the one-dimensional space, which can avoid
the subjective determination of the weight indicator of
unfavorable factors in the traditional methods, and a
comprehensive evaluation of the decision-making pro-
gram has been achieved. The high-dimensional data of
the global optimization problems will be solved by com-
*(0.0232,0.5210,0.4936,0.0495,a
0.2146, 0.4142, 0.5141)

S. J. ZHOU ET AL.
110
bining RAGA with PPC model, which has provided a
solid algorithm guarantee for the expansion and applica-
tion of the PPC model.
3) The application of PPC model based on RAGA in
the real estate investment comprehensive evaluation, not
only reached a comprehensive evaluation of every pro-
gram for the quality sequence, but also reflected the im-
portance of the various evaluation indicators to the over-
all evaluation by optimizing the projection direction. It
also can avoid factitious interference of the experts em-
powering, such as the Analytic Hierarchy Process, fuzzy
comprehensive evaluation methods, which has overcome
successfully the shortcomings of traditional methods. It
provides a new idea and method to the study in the real
estate investment decision-making evaluating.
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