Application of PPC Model Based on RAGA in Real Estate Investment Decision-Making

doi:10.4236/eng.2009.12012

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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

Email: [email protected], telasi@163.com, liyancang@163.com

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 *

{(,)|

ij i



1, 2...,;1, 2...,}nj p, *(, )

ij is the jth indexed value of

section , and ,

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

(,)( )

(, )() ()

ij xj

xi j

jx j





For the smaller and better indicators

max

max min

() (,)

(, )() ()

jxij

xi j

jx j



 (1)

Here: max ()

j, min()

j—the jth maximum and mini-

mum indicators’ values; (, )

ij—indicators normalized

eigenvalue sequences.

3.2. Structure Projection Target Function ()Qa

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

()(). (,)

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



(3)

Here:

S—Projection value standard deviation;

D—Projection value of the local density of . ()zi



()( )

zi Ez

Szn









(4)

((,)).((,)

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

max 2

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



, 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

S. J. ZHOU ET AL.

108

() .

axQ aSD



(6)

Constraints:

..()1

sta 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

()( ) (,)

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

(,)( )

(, )() ()

ij xj

xi j

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

orith

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.

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

() (,)

(, )() ()

jxij

xi j

jx j





For example, the failure rate of investment of A is

normalized by the following formula:

0.0350.0330.2000

0.0350.025

x





The normalized matrix can be obtained:

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

5. Conclusions

And then substituting *

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



mutation probability ,

0.8

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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