A Research Based On Adaptive Genetic Algorithm Optimal Embattling Method

Ye-yang Panl, Jin-jie Yaol

iNational key laboratory, North university of China

Tai Yuan, China

Abstract- In the high-speed flight target positioning, the base algorithm has the problems such as premature and slow

stations' locations influence the target localization accuracy convergence speed[5-7],this paper uses the method of adaptive

directly. As the traditional base station layout positioning precision adjusting crossover probability and mutation probability to

is not high, this paper proposes an optimal layout base station improve the searching speed and precision of genetic

scheme which is based on adaptive genetic algorithm. The paper algorithm.At the same time, the paper will propose adaptive

introduces the GA from the selection, crossover and mutation genetic algorithm which is applied to the base station layout,to

operations, with the geometrical factor --GDOP as fitness function, get the optimal positioning base station layout scheme.

and realizes the ground stations optimal layout. The simulation

results show that the scheme can optimize the base stations'

locations, and improve the positioning precision of high speed

targets.

Keywords-Ground base station; TDOA; Adaptive genetic

algorithm; Cloth station optimization

I. INTRODUCTION

In the time difference of arrival(TDOA) positioning,the

target positioning accuracy is closely related to the base station

layout [ 1]. At present,the base station layout mainly have some

kinds like star cloth station [2],rhombus station[3],inverted

triangle station[4].The star station is placing two positioning

base stations in flight direction, the other two positioning base

stations are on both sides of the placement area;rhombus

station is placing two positioning base stations respectively in

the start and the end of the process, the other two positioning

base stations in flight are on both sides of the area;inverted

triangle station is placing a positioning base station at the

target,the other three positioning base stations are placed at the

end of flying area. The three kinds of base station layout

schemes are simple,but the accuracy is not high and often not

the optimal layout scheme. The researchers propose optimized

layout scheme based on genetic algorithm. While genetic

978-1·4799-4860-4/14/$31.00 copyright 2014 IEEE ICIS 2014, June 4·6,2014, Taiyuan, China

II. GENETIC ALGORITHM

Genetic algorithm (GA) was founded by lHolland

professor in the university of Michigan in 1975. The algorithm

is based on natural selection and natural genetics, imitating

biological evolution and genetic regularity, using the

operations such as reproduction, crossover and mutation, to

select the superior and eliminate the inferior, and finally fmd

the optimal solution or approximate optimal solution. As a

natural evolutionary optimization method, genetic algorithm

has a strong global search ability, simply and generally.

However, there are some problems with the standard genetic

algorithm: the early evolutionary premature convergence; the

late middle evolutionary individuals are less competitive and

evolving more slowly; in the evolutionary population,

individual can't be guaranteed the optimal one; non-uniform to

find the optimal solution in the search space.

III. OPTIMAL EMBATTLING ALGORITHM BASED ON

ADAPTIVE GENETIC ALGORITHM

In this algorithm, the calculate process includes:

parameter determination, parameter coding, initialization,

fitness, selection, crossover and mutation, etc., as is shown in

fig. 1 :

Fig.l. Process of adaptive genetic algorithm

A. Parameter Determination

In the adaptive genetic algorithm,the parameters include

population size,variable scope, number of iterations,

reproduction probabilitY,crossover probability and mutation

probability, etc.

B. Parameter Coding

Because genetic algorithm can't deal with the parameters

in actual problems directly, the parameters must be coded, that

is turn the actual problem parameters into the genetic space

composed of chromosomes gene according to certain

structures. In the genetic algorithm, the typical encoding of

parameters are binary coding and real coding. The principle of

binary coding is simple and versatile, but the accuracy is not

high, the target scalability is not strong, and the length of the

code is limited. While real coding reflects the parameters

directly with a representation of a real number, convenience

and intuitive, and the accuracy is high, but need to design

special genetic operations. Because the target position

coordinates are real numbers, the real number encoding is

used.

C. Initialization

In the base station layout, there are four stations, and each

of them is 3d coordinate, that is to say, if we want to achieve

optimum base station layout, we should determine 12 variables.

If the population number is 20,the initialization of population

size of genetic algorithm is 20 X 12 matrix.

D. Fitness

Fitness is a measure to evaluate whether the population is

good or bad, to determine the basis of individual species is to

be breed or to be eliminated. The genetic algorithm uses the

fitness function of the individuals to evolve. To determine the

population fitness function is very important. The optimal

layout of goal is to make higher positioning accuracy. In

conclusion, the population fitness function can be represented

as follow:

Fitness = -,-i=--,-I __ _ N

N is the number of test points of the flying track.

E. Choose

In this base station layout optimization scheme, the

operation is to select excellent individuals from the population,

and guarantee the quality of the population. Its basic idea is: in

the area of [O,Sum/ M], we generate a random number which

is defined as a pointer p, individual species set pointers in

equal distance as[p,p+l,p+2, ... ,p+M-1l,according to its status

in populations in random traversal sampling (SUS). When

performing selection operation, the probability of individuals

to be selected can be expressed as follow:

F(x;) = !(x;) If(x;) i=1 (2)

F(Xi) is the probability of Xi to be selected , f(Xi) is the fitness

function value of Xi.

F. Crossover

Crossover operation is to combine the group fitness

information of individuals, increase the diversity of the species,

and obtain better individual species. It makes two parents Xl

and X2 of the population to cross, after crossover operation

the children are as follows :

{X; : rxi +(I-r)X2 X2-rX2+(1-r)X1 (3)

r is the crossover probability among [0, 1). When the crossover

probability r is a constant, that is uniform crossover, the same

parents individuals cross can only get same children which is

not conducive to improve the population diversity. Different

crossover probability will also effect crossover operation.

When the crossover probability changes in non-uniform cross,

can increase the population diversity, improve the global

search ability of population.

In the adaptive genetic algorithm which is proposed in

this paper, when the population fitness tend to be same, Pc

increase; when the population fitness relative disperse, Pc

decrease. According to this, the adaptive crossover probability

can be expressed as follow :

{p (F;max -F;mJr -fav)

cmax .{' .{' � = Jmax-Javg

�max

j?favg j <fal'g (4)

Pmax is maximum crossover probability, Pernin is minimum

crossover probability, favg is the population average fitness, f is

the fitness of the parameters, fmax is the maximum population

fitness.

G. Mutation

Mutation is to keep the diversity of population, to

enhance the search ability of algorithm. At the beginning of

genetic algorithm, the population diversity is rich. In order to

speed up the algorithm, the mutation probability is small. With

the ongoing of iterative process, the individuals become closer

to each other, the population diversity turn weak, the mutation

probability should be large enough to maintain the diversity of

the population. Similarly, the generation populations' mutation

probability should be change according to the individual

fitness. According to the relationship among the mutation

I .. I 4000 - --J __ L __ 1 __ L __ 1 __ 1- __ 1 __ -1 __ I __

I I I I I I I I I I I I I I I I I I 3000 --1 --1--1 --1--1- - T --1- - T -- 1--

2000 - -1--I- --1 - - +- --1- - +- --1- - + -- 1--

� 1000 - � -- � --:-- f- -

-1000 _ � __ L __ 1 __ L __ 1 __ 1.- __ 1 __ � __ I __ I I I I I I I I I

-2000 - ---, - - r --1 - - r --1- - T --1- - T -- 1--.. -3000 0'-------='0.-=-2 ----"0.4:---:'-0.6:--0":0.8:---'-, - ':'::.2-----"L.4-----,,'::- .6-----c''::-.8-----'

Xlm x 104

Fig.2. The optimal station layout scheme

probability, the evolution algebra and individual fitness values,

the adaptive mutation probability P rn can be designed as

follow :

Pnunam is maximum mutation probability, usually take O.l;Pnunin

is the minimum mutation probability, usually take O.OOI;frnax is

the biggest population fitness; favg is the average fitness; f is the

fitness of the parameters.

IV. RESULT

In the simulation, locating is in the

space: {XE [O,30000],YE [-5000,5000],ZE [O,20]}, TDOA base

stations' number is 4, population size M is 20, variable

dimension is 12, minimum crossover probability is OA,the

biggest crossover probability is 0.9,the minimum mutation

probability is O.OOI,the biggest mutation probability is

O.l,maximum iteration is 300.After the iteration, the optimal

layout plan is shown in fig.2.The values of GDOP average

change along with the number of iteration as is shown in fig.3.

251,--�-�--�-�-�---.

2DI

'liD IiIneM

-'-'-'- GA - AGA

·'�-�"�-�_=--�'"=--3m�-�2=''��''' number of iterations

Fig. 3. GDOP relationship along with the change of the

number of iterations

TABLE!. AGA ALGORITHM ARE USED TO GET THE BASE STATION LAYOUT POSlTlON

coordinate value

X/km

Y Ikm

Z/km

Base station [

0.8589

-2.7365

0.0072

Base station II

7.2341

4.2996

0.0016

Base station III

12.5003

1.2109

0.0034

Base station IV

19.8705

1.7939

0.0161

We can see from the diagram, in this optimization layout

scheme, the base station positions which are shown in TABLE

I, are irregular quadrilateral distribution, and the average of

GDOP is 15.98, and positioning accuracy is higher. Compared

with genetic algorithm (GA), AGA also has a faster

convergence speed, and overcomes the weakness of genetic

algorithm. However, the optimal station layout positions which

were gotten from adaptive genetic algorithm are applied to

calculate Latin America - ROM lower CRLB. In this case, the

CRLB is 13500.6, which is far from the traditional layout. To

satisfy the CRLB and GDOP at the same time, the adaptive

genetic algorithm can realize the base station layout

optimization effectively.

v. CONCLUSION

To satisfy the requirements of high speed target base

station layout, this paper proposes an optimal layout method

which is based on adaptive genetic algorithm. The simulation

result shows that the scheme can get the optimal layout scheme

while the precision index GDOP and CRLB are optimal. It can

be widely applied to the base station target positioning and

tracking test, etc.

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