# Group Search Optimizer for the Mobile Location Management Problem

Authors: Dan Wang; Congcong Xiong; Wei Huang
Journal: The Scientific World Journal
 (2014)

---

## Abstract

We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach.


---

## Body

## 1. Introduction

Mobile location management becomes more and more important with the rapid growing mobile network in recent years. Lots of novel applications for data transfer based on fax, voice, and many other mobile services need to be taken into account for making the next generation of mobile network, which supports a basic global personal communication network. To support such applications, mobility management has to be considered when designing infrastructure for wireless mobile networks [1–4].Reporting cells scheme is conventionally a kind of location management strategies for implementing effective location management [5]. In this case, the minimization of location management cost is considered to decide the reporting cells configuration and finding the optimal set of the reporting cells can be regarded as an optimization problem. However, it is the fact that such an optimization problem has been proven an NP-complete problem [6]. To address this problem, many optimization approaches have been proposed in the past decades. Pioneering work by Taheri and Zomaya [7, 8], Demestichas et al. [9], and Yuen and Wong [10] has studied the mobile location management problem using different evolutionary optimization approaches. In a nutshell, evolutionary algorithms have proven to be very useful for optimizing such problems.Recently, group search optimizer (GSO) [11] inspired by animal behavior is proposed as a new evolutionary algorithm, and it obtains effective competitive performance when solving some optimization problems [12, 13]. However, such animal behavior-inspired algorithm is essentially stochastic search techniques like many other evolutionary algorithms. Such random mechanism leads to premature convergence problem due to purely random resampling or selections of individuals from a given population, which may lead to revisiting nonproductive regions of the search space [12]. This drawback sometimes limits the application of GSO when dealing with online problems or real-time constraints.In this paper, we propose a diversity-guided group search optimizer (DGSO) to deal with the location management in mobile computing. In the design of DGSO, diversity guidance is used to prevent the fact that the reducing diversity takes place too early. With the use of diversity guidance, selection operator keeps the diversity of population. Moreover, the proposed DGSO is employed to optimization of the set of the reporting cells in the mobile location management problem.


## 2. Mobile Location Management Problem

In cellular network systems, the mobile location management problem consists of two basic operations, namely, location update and location inquiry. The location update corresponds to the notification of current location, performed by mobile terminals when they change their location in the network, while the location inquiry is the operation of determining the location of the mobile terminal, which is executed by the network when it tries to direct an incoming call to the user [5].As to mobile location management problem, here we consider minimizing the location management cost, which includes location update operation and location paging operation.The location update cost (LUC) corresponds to the cost of user which performs an update when it moves from the current location area into another location area. If we consider a typical GSM network as shown in Figure1, it is easy to see the total number of users that enter in the white location area. The location update cost can be calculated as the following expression:
(1)NLUC=2013+296+306+524+352+784+659+203+68+98+1024+698+452+365+685+124+235+241=9127.Figure 1
Entering flow of users and call arrival.The location paging operation cost is caused by the network when it tries to locate a user’s mobile terminal, during the location inquiry, and normally the number of paging transactions is directly related to the number of incoming calls [7]. Figure 2 shows an example of incoming calls to the white location area. The paging cost can be obtained as follows:
(2)NP=968+365+765+1025+787+287+635=4832.Figure 2
Entering flow of users for an instant locafiguretion area.Generally, the total cost of location areas is computed by using the following formula [7]:
(3)Cost=β×NLUC+NP.The cost of a location update is normally considered to be 10 times greater than the cost of paging; that is,β=10 [1, 14–16]. With the combination of location update cost (1) and location paging costs (2), the total cost by (3) can be calculated as follows:
(4)Cost=10×9127+4832=96102.In the reporting cells scheme the location updates only are preformed when a mobile user enters in a reporting cell and the vicinity factor of each cell must be considered [1]. In this case, the genetic formula given by (3) must be readjusted and it is formulated as [15]
(5)Cost=β×∑i∈SNLUC(i)+∑i=0NNP(i)×V(i),
where N is the number of location updates related to the reporting cell i, S represents the subset of reporting cells, Np is the number of incoming calls of cell i, N is the number of cells that compound the mobile network configuration, and V is the vicinity factor attributed for cell i.


## 3. Group Search Optimizer Algorithm

Like the swarm intelligence evolutionary algorithms, GSO is also a population-based optimization algorithm. The population is called agroup and each individual in the population is called amember[17, 18].


### 3.1. Main Operators in GSO

The GSO algorithm that is based on the producer-scrounger (PS) model has three basic operators. The main operators in GSO algorithm are as follows.


#### 3.1.1. Initialization

For convenience, the related symbols are summarized as follows [19]: in a n-dimension search space, the ith member at the kth iteration has a current position Xik∈Rn; a head angle φik=(φi1k,…,φi(n-1)k)∈Rn-1, and a search direction of the ith member which is a unit vector Dik(φik)=(di1k,…,dink)∈Rn; the unit vector can be calculated as [20]
(6)di1k=∏q=1n-1cos⁡⁡(φiqk)dijk=sin⁡(φi(j-1)k)∏q=jn-1cos⁡⁡(φiqk)(j=2,…,n-1)dink=sin⁡(φi(n-1)k),
where the Xik, φik, and dik are randomly generated for the initialization of group.For simplifying the algorithm computational capability, we assume that there is only one producer (here we select the best member as the producer) at each iteration for calculating the group member’s fitness value.


#### 3.1.2. Producing

When the only producer is selected, it scans the environment for searching the resource. In the GSO algorithm [18], the scanning field was characterized by the maximum pursuit angle θmax⁡ and the maximum pursuit distance lmax⁡. The kth iteration of the Xp behaves as follows.First, the producer will randomly scan three points for getting the best point [21]: at zero degree, the point represents as follows:
(7)Xz=Xpk+r1lmax⁡Dpk(φk).In the right hand side hypercube, the point is expressed as follows:(8)Xr=Xpk+r1lmax⁡Dpk(φk+r2θmax⁡2).In the left hand hypercube, the point represents as follows:(9)xl=Xpk+r1lmax⁡Dpk(φk-r2θmax⁡2),
where r1 is the normally distributed random number and r2 is the distributed random sequence in the range between 0 and 1.Second, the producer will find the best point by calculating the fitness value. If the producer cannot find the better resource than the current position, the current position is considered the best point; otherwise, the current point will be changed, and the new angle is generated by using the following formula:(10)φk+1=φk+r2αmax⁡,
where αmax⁡ denotes the maximum turning angle.Assuming that it could not find the better resource than the current position after theath iterations, we have the angle:
(11)φk+a=φk.


#### 3.1.3. Scrounging

Randomly select 80% from the rest of members to perform scrounging.


#### 3.1.4. Dispersion

In the disperse operator, we use the random walks [22–24] for searching the distributed resources. At the kth iteration, it generates a random head angle φi using (5); it chooses a random distance
(12)li=a·r1lmax⁡
and the new point is
(13)Xik+1=Xik+liDik(φk+1).


### 3.2. Diversity-Guided GSO

Like the most of population-based algorithms, the initializationgroup (population) and the searching operators are started withrandom guesses due to the lack of a priori information. To alleviate this problem, diversity guidance is explored here for increasing the diversity of initialization group and the generation jumping embedded in the GSO algorithm. Here the variable “diversity” of group (population) [25] is calculated as follows:
(14)diversity=1|S|•|L|•∑i=1|S|∑j=1N(pij-p-j)2,
where S is the group (population), |S| is the size of group, |L| is the length of longest the diagonal in the search space, N is the dimension of the problem, pij is the jth value of the ith individual, and p-j is the jth value of the average point p-; it has also stressed that the diversity measure is independent of group size, the dimensionality of the problem, and the search range in each dimension. For convenience, in this paper w1, w2 are set as 0.33 and 0.66, respectively. The procedure of diversity-guided operator is realized as follows.Case I.
If diversity is less than dLow, setlmax⁡=w1*lmax⁡.Case II.
If diversity is greater than dHigh, do nothing(lmax⁡=lmax⁡).Case III.
If diversity is greater than or equal to dLow, and diversity is less than dHigh, setlmax⁡=w2*lmax⁡.Herelmax⁡ is defined in formula (2), (3), and (4); dLow, dHigh, w1, and w2 are given numbers.Furthermore, the procedure of DGSO can be outlined as shown in Algorithm1.Algorithm 1:Procedure of diversity-guided GSO (DGSO).
/* Diversity-Guided GSO (DGSO) */
(1)BEGIN
(2) Initialization (Generate uniformly distributed random population);
(3) While the termination condition isn’t satisfied
(4)Diversity-Guided Operator;
(5)Producing;
Scrounging;
Dispersion;
(6)  End While
(7)END


## 3.1. Main Operators in GSO

The GSO algorithm that is based on the producer-scrounger (PS) model has three basic operators. The main operators in GSO algorithm are as follows.


### 3.1.1. Initialization

For convenience, the related symbols are summarized as follows [19]: in a n-dimension search space, the ith member at the kth iteration has a current position Xik∈Rn; a head angle φik=(φi1k,…,φi(n-1)k)∈Rn-1, and a search direction of the ith member which is a unit vector Dik(φik)=(di1k,…,dink)∈Rn; the unit vector can be calculated as [20]
(6)di1k=∏q=1n-1cos⁡⁡(φiqk)dijk=sin⁡(φi(j-1)k)∏q=jn-1cos⁡⁡(φiqk)(j=2,…,n-1)dink=sin⁡(φi(n-1)k),
where the Xik, φik, and dik are randomly generated for the initialization of group.For simplifying the algorithm computational capability, we assume that there is only one producer (here we select the best member as the producer) at each iteration for calculating the group member’s fitness value.


### 3.1.2. Producing

When the only producer is selected, it scans the environment for searching the resource. In the GSO algorithm [18], the scanning field was characterized by the maximum pursuit angle θmax⁡ and the maximum pursuit distance lmax⁡. The kth iteration of the Xp behaves as follows.First, the producer will randomly scan three points for getting the best point [21]: at zero degree, the point represents as follows:
(7)Xz=Xpk+r1lmax⁡Dpk(φk).In the right hand side hypercube, the point is expressed as follows:(8)Xr=Xpk+r1lmax⁡Dpk(φk+r2θmax⁡2).In the left hand hypercube, the point represents as follows:(9)xl=Xpk+r1lmax⁡Dpk(φk-r2θmax⁡2),
where r1 is the normally distributed random number and r2 is the distributed random sequence in the range between 0 and 1.Second, the producer will find the best point by calculating the fitness value. If the producer cannot find the better resource than the current position, the current position is considered the best point; otherwise, the current point will be changed, and the new angle is generated by using the following formula:(10)φk+1=φk+r2αmax⁡,
where αmax⁡ denotes the maximum turning angle.Assuming that it could not find the better resource than the current position after theath iterations, we have the angle:
(11)φk+a=φk.


### 3.1.3. Scrounging

Randomly select 80% from the rest of members to perform scrounging.


### 3.1.4. Dispersion

In the disperse operator, we use the random walks [22–24] for searching the distributed resources. At the kth iteration, it generates a random head angle φi using (5); it chooses a random distance
(12)li=a·r1lmax⁡
and the new point is
(13)Xik+1=Xik+liDik(φk+1).


## 3.1.1. Initialization

For convenience, the related symbols are summarized as follows [19]: in a n-dimension search space, the ith member at the kth iteration has a current position Xik∈Rn; a head angle φik=(φi1k,…,φi(n-1)k)∈Rn-1, and a search direction of the ith member which is a unit vector Dik(φik)=(di1k,…,dink)∈Rn; the unit vector can be calculated as [20]
(6)di1k=∏q=1n-1cos⁡⁡(φiqk)dijk=sin⁡(φi(j-1)k)∏q=jn-1cos⁡⁡(φiqk)(j=2,…,n-1)dink=sin⁡(φi(n-1)k),
where the Xik, φik, and dik are randomly generated for the initialization of group.For simplifying the algorithm computational capability, we assume that there is only one producer (here we select the best member as the producer) at each iteration for calculating the group member’s fitness value.


## 3.1.2. Producing

When the only producer is selected, it scans the environment for searching the resource. In the GSO algorithm [18], the scanning field was characterized by the maximum pursuit angle θmax⁡ and the maximum pursuit distance lmax⁡. The kth iteration of the Xp behaves as follows.First, the producer will randomly scan three points for getting the best point [21]: at zero degree, the point represents as follows:
(7)Xz=Xpk+r1lmax⁡Dpk(φk).In the right hand side hypercube, the point is expressed as follows:(8)Xr=Xpk+r1lmax⁡Dpk(φk+r2θmax⁡2).In the left hand hypercube, the point represents as follows:(9)xl=Xpk+r1lmax⁡Dpk(φk-r2θmax⁡2),
where r1 is the normally distributed random number and r2 is the distributed random sequence in the range between 0 and 1.Second, the producer will find the best point by calculating the fitness value. If the producer cannot find the better resource than the current position, the current position is considered the best point; otherwise, the current point will be changed, and the new angle is generated by using the following formula:(10)φk+1=φk+r2αmax⁡,
where αmax⁡ denotes the maximum turning angle.Assuming that it could not find the better resource than the current position after theath iterations, we have the angle:
(11)φk+a=φk.


## 3.1.3. Scrounging

Randomly select 80% from the rest of members to perform scrounging.


## 3.1.4. Dispersion

In the disperse operator, we use the random walks [22–24] for searching the distributed resources. At the kth iteration, it generates a random head angle φi using (5); it chooses a random distance
(12)li=a·r1lmax⁡
and the new point is
(13)Xik+1=Xik+liDik(φk+1).


## 3.2. Diversity-Guided GSO

Like the most of population-based algorithms, the initializationgroup (population) and the searching operators are started withrandom guesses due to the lack of a priori information. To alleviate this problem, diversity guidance is explored here for increasing the diversity of initialization group and the generation jumping embedded in the GSO algorithm. Here the variable “diversity” of group (population) [25] is calculated as follows:
(14)diversity=1|S|•|L|•∑i=1|S|∑j=1N(pij-p-j)2,
where S is the group (population), |S| is the size of group, |L| is the length of longest the diagonal in the search space, N is the dimension of the problem, pij is the jth value of the ith individual, and p-j is the jth value of the average point p-; it has also stressed that the diversity measure is independent of group size, the dimensionality of the problem, and the search range in each dimension. For convenience, in this paper w1, w2 are set as 0.33 and 0.66, respectively. The procedure of diversity-guided operator is realized as follows.Case I.
If diversity is less than dLow, setlmax⁡=w1*lmax⁡.Case II.
If diversity is greater than dHigh, do nothing(lmax⁡=lmax⁡).Case III.
If diversity is greater than or equal to dLow, and diversity is less than dHigh, setlmax⁡=w2*lmax⁡.Herelmax⁡ is defined in formula (2), (3), and (4); dLow, dHigh, w1, and w2 are given numbers.Furthermore, the procedure of DGSO can be outlined as shown in Algorithm1.Algorithm 1:Procedure of diversity-guided GSO (DGSO).
/* Diversity-Guided GSO (DGSO) */
(1)BEGIN
(2) Initialization (Generate uniformly distributed random population);
(3) While the termination condition isn’t satisfied
(4)Diversity-Guided Operator;
(5)Producing;
Scrounging;
Dispersion;
(6)  End While
(7)END


## 4. Experimental Studies

This section reports the experimental results of the proposed DGSO for solving the location management problem in mobile computing. We compared the performance of DGSO with the performance achieved by some “common” algorithms [8] such as genetic algorithm, tabu search, and the ant colony algorithm, respectively. All algorithms are tested based on three test networks with different sizes, and each algorithm is run 200 times for each test network. Furthermore, to compare with the results reported in the literatures, thecost per call arrival [26] divided the total cost by the total number of call arrivals is used as the fitness (objective value).The parameters of DGSO and GSO are as follows [8]: the initialization of population is generated uniformed at random; the initial head angle is set to be π/4; the maximum pursuit angle θmax⁡ is π/a2, where a is given by Round(n+1) and n is the dimension of solutions; the maximum turning angle is θmax⁡/2.


### 4.1. Test Network with 16 Cells

The first experiment is implemented based on a4×4 size network, whose data set is shown in Table 1 [26]. Here the wmi and wci denote a movement weight and call arrival weight for the cell i, respectively.Table 1
Cells attribute for the4×4 test network.
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
1
518
517
5
1617
642
9
445
251
13
307
25
2
774
573
6
472
951
10
2149
224
14
385
540
3
153
155
7
650
526
11
1658
841
15
1346
695
4
1696
307
8
269
509
12
952
600
16
572
225The algorithm presented earlier is adapted here to solve the problem. Figure3 shows the process of optimization with the successive generations by using the GSO and DGSO, respectively. Table 2 summarizes the comparison results of running the algorithms. It is evident that the proposed DGSO and GSO lead to smaller mean value in comparison with the GA; however, the two GSOs obtain the same results as the AC, TDE, and HCDE. That is, the above five algorithms obtain the optimal solution with reporting cells configuration shown in Figure 4.Table 2
Results for the4×4 network.
Algorithms
Average value
Deviation
Minimum value
Deviation
Maximum value
Deviation
GA [26]
12.253
0.006%
12.252
0.000%
12.373
0.986%
TS [26]
12.252
0.000%
12.252
0.000%
12.252
0.000%
AC [26]
12.252
0.000%
12.252
0.000%
12.252
0.000%
TDE [27]
12.252
0.000%
12.252
0.000%
12.252
0.000%
HCDE [27]
12.252
0.000%
12.252
0.000%
12.252
0.000%
Our methods
GSO
12.252
0.000%
12.252
0.000%
12.252
0.000%
DGSO
12.252
0.000%
12.252
0.000%
12.252
0.000%Figure 3
Performance index in successive generations (4×4 network).Figure 4
4
×
4 test network optimal solution with reporting cells configuration.


### 4.2. Test Network with 36 Cells

For the second experiment, a6×6 size network is utilized, and Table 3 provides the data set [26]. After running the GSOs with 150 generations, we get the comparison of GSO and DGSO shown in Figure 5. It shows that both DGSO and GSO have low cost and rapid convergence. The comparison results of some common algorithms are summarized in Table 4.Table 3
Cells attribute for the6×6 test network.
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
1
1039
714
10
296
221
19
1945
462
28
1342
370
2
1476
120
11
793
856
20
1368
682
29
814
721
3
262
414
12
317
652
21
1850
241
30
747
769
4
442
639
13
507
238
22
1131
700
31
146
17
5
1052
419
14
603
964
23
236
23
32
904
265
6
1902
332
15
1479
789
24
1622
827
33
359
958
7
444
494
16
756
457
25
16
328
34
1729
191
8
1103
810
17
695
708
26
332
255
35
190
551
9
1829
546
18
356
825
27
1203
393
36
1907
467Table 4
Results for the6×6 network.
Algorithms
Average value
Deviation
Minimum value
Deviation
Maximum value
Deviation
GA [26]
11.511
0.343%
11.471
0.000%
12.030
4.867%
TS [26]
11.471
0.000%
11.471
0.000%
11.471
0.000%
AC [26]
11.472
0.007%
11.471
0.000%
11.573
0.883%
TDE [27]
11.471
0.000%
11.471
0.000%
11.471
0.000%
HCDE [27]
11.471
0.000%
11.471
0.000%
11.471
0.000%
Our methods
GSO
11.456
0.853%
11.426
0.000%
11.471
0.289%
DGSO
11.432
0.676%
11.426
0.000%
11.471
0.795%Figure 5
Performance index in successive generations (6×6 network).As shown in Table4, the minimization cost of DGSO is only 11.425, while the best optimal cost reported in previous literatures is 11.471. It appears that the proposed DGSO outperforms several previous algorithms known in the literature. Figure 6 depicts the optimal solution with reporting cells configuration.Figure 6
6
×
6 test network optimal solution with reporting cells configuration.


### 4.3. Test-Network with 64 Cells

The last experiment is carried out on a8×8 size test network, whose data set is given in Table 5 [26]. Figure 7 describes the process of optimization using GSO and DGSO with a size of 100 populations and 150 generations, respectively. It shows that DGSO has less cost and rapid convergence in comparison with GSO. In the 4×4 and 6×6 size test networks, the results of DGSO are the same as the GSO due to the relative small size of test network. With the increase of the size of network, we can safely expect that the DGSO may obtain better performance than the original GSO.Table 5
Cells attribute for the8×8 test network.
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
1
553
968
17
626
184
33
121
952
49
524
345
2
907
745
18
104
787
34
1410
367
50
1400
135
3
515
827
19
1408
319
35
1011
132
51
393
175
4
1965
705
20
1256
25
36
1298
439
52
1272
596
5
1336
902
21
1637
934
37
1634
134
53
1197
677
6
1318
498
22
1950
414
38
1750
153
54
462
283
7
1292
807
23
101
104
39
1948
612
55
548
139
8
1789
62
24
539
881
40
662
216
56
500
307
9
541
331
25
655
694
41
700
878
57
113
272
10
1071
212
26
131
793
42
765
957
58
47
931
11
1759
787
27
1227
955
43
756
363
59
1676
38
12
1416
664
28
450
126
44
436
820
60
1017
896
13
1413
938
29
470
268
45
672
362
61
1307
164
14
1224
719
30
1081
96
46
822
356
62
499
78
15
484
794
31
1714
285
47
1912
637
63
1451
303
16
543
543
32
308
368
48
1402
626
64
1606
578Figure 7
Performance index in successive generations (8×8 network).The cost of the proposed DGSO is also compared with the performance of some other algorithms; refer to Table6. The minimum value of the DGSO and some other algorithms are almost the same; however, it is evident that the performance of the proposed DGSO is better in sense of its maximum value and deviation. Figure 8 describes the optimal solution with reporting cells configuration.Table 6
Results for the8×8 network.
Algorithms
Average value
Deviation
Minimum value
Deviation
Maximum value
Deviation
GA [26]
14.005
1.619%
13.782
0.000%
14.617
6.454%
TS [26]
13.791
0.071%
13.782
0.000%
13.999
1.580%
AC [26]
14.107
2.361%
13.801
0.141%
14.407
4.539%
TDE [27]
13.889
0.776%
13.782
0.000%
14.093
2.256%
HCDE [27]
13.788
0.043%
13.782
0.000%
13.892
0.798%
Our methods
GSO
13.791
0.497%
13.782
0.000%
14.102
2.321%
DGSO
13.780
0.037%
13.782
0.000%
13.883
0.786%Figure 8
8
×
8 test network optimal solution with reporting cells configuration.


## 4.1. Test Network with 16 Cells

The first experiment is implemented based on a4×4 size network, whose data set is shown in Table 1 [26]. Here the wmi and wci denote a movement weight and call arrival weight for the cell i, respectively.Table 1
Cells attribute for the4×4 test network.
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
1
518
517
5
1617
642
9
445
251
13
307
25
2
774
573
6
472
951
10
2149
224
14
385
540
3
153
155
7
650
526
11
1658
841
15
1346
695
4
1696
307
8
269
509
12
952
600
16
572
225The algorithm presented earlier is adapted here to solve the problem. Figure3 shows the process of optimization with the successive generations by using the GSO and DGSO, respectively. Table 2 summarizes the comparison results of running the algorithms. It is evident that the proposed DGSO and GSO lead to smaller mean value in comparison with the GA; however, the two GSOs obtain the same results as the AC, TDE, and HCDE. That is, the above five algorithms obtain the optimal solution with reporting cells configuration shown in Figure 4.Table 2
Results for the4×4 network.
Algorithms
Average value
Deviation
Minimum value
Deviation
Maximum value
Deviation
GA [26]
12.253
0.006%
12.252
0.000%
12.373
0.986%
TS [26]
12.252
0.000%
12.252
0.000%
12.252
0.000%
AC [26]
12.252
0.000%
12.252
0.000%
12.252
0.000%
TDE [27]
12.252
0.000%
12.252
0.000%
12.252
0.000%
HCDE [27]
12.252
0.000%
12.252
0.000%
12.252
0.000%
Our methods
GSO
12.252
0.000%
12.252
0.000%
12.252
0.000%
DGSO
12.252
0.000%
12.252
0.000%
12.252
0.000%Figure 3
Performance index in successive generations (4×4 network).Figure 4
4
×
4 test network optimal solution with reporting cells configuration.


## 4.2. Test Network with 36 Cells

For the second experiment, a6×6 size network is utilized, and Table 3 provides the data set [26]. After running the GSOs with 150 generations, we get the comparison of GSO and DGSO shown in Figure 5. It shows that both DGSO and GSO have low cost and rapid convergence. The comparison results of some common algorithms are summarized in Table 4.Table 3
Cells attribute for the6×6 test network.
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
1
1039
714
10
296
221
19
1945
462
28
1342
370
2
1476
120
11
793
856
20
1368
682
29
814
721
3
262
414
12
317
652
21
1850
241
30
747
769
4
442
639
13
507
238
22
1131
700
31
146
17
5
1052
419
14
603
964
23
236
23
32
904
265
6
1902
332
15
1479
789
24
1622
827
33
359
958
7
444
494
16
756
457
25
16
328
34
1729
191
8
1103
810
17
695
708
26
332
255
35
190
551
9
1829
546
18
356
825
27
1203
393
36
1907
467Table 4
Results for the6×6 network.
Algorithms
Average value
Deviation
Minimum value
Deviation
Maximum value
Deviation
GA [26]
11.511
0.343%
11.471
0.000%
12.030
4.867%
TS [26]
11.471
0.000%
11.471
0.000%
11.471
0.000%
AC [26]
11.472
0.007%
11.471
0.000%
11.573
0.883%
TDE [27]
11.471
0.000%
11.471
0.000%
11.471
0.000%
HCDE [27]
11.471
0.000%
11.471
0.000%
11.471
0.000%
Our methods
GSO
11.456
0.853%
11.426
0.000%
11.471
0.289%
DGSO
11.432
0.676%
11.426
0.000%
11.471
0.795%Figure 5
Performance index in successive generations (6×6 network).As shown in Table4, the minimization cost of DGSO is only 11.425, while the best optimal cost reported in previous literatures is 11.471. It appears that the proposed DGSO outperforms several previous algorithms known in the literature. Figure 6 depicts the optimal solution with reporting cells configuration.Figure 6
6
×
6 test network optimal solution with reporting cells configuration.


## 4.3. Test-Network with 64 Cells

The last experiment is carried out on a8×8 size test network, whose data set is given in Table 5 [26]. Figure 7 describes the process of optimization using GSO and DGSO with a size of 100 populations and 150 generations, respectively. It shows that DGSO has less cost and rapid convergence in comparison with GSO. In the 4×4 and 6×6 size test networks, the results of DGSO are the same as the GSO due to the relative small size of test network. With the increase of the size of network, we can safely expect that the DGSO may obtain better performance than the original GSO.Table 5
Cells attribute for the8×8 test network.
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
Cells
w
m
i
w
c
i
1
553
968
17
626
184
33
121
952
49
524
345
2
907
745
18
104
787
34
1410
367
50
1400
135
3
515
827
19
1408
319
35
1011
132
51
393
175
4
1965
705
20
1256
25
36
1298
439
52
1272
596
5
1336
902
21
1637
934
37
1634
134
53
1197
677
6
1318
498
22
1950
414
38
1750
153
54
462
283
7
1292
807
23
101
104
39
1948
612
55
548
139
8
1789
62
24
539
881
40
662
216
56
500
307
9
541
331
25
655
694
41
700
878
57
113
272
10
1071
212
26
131
793
42
765
957
58
47
931
11
1759
787
27
1227
955
43
756
363
59
1676
38
12
1416
664
28
450
126
44
436
820
60
1017
896
13
1413
938
29
470
268
45
672
362
61
1307
164
14
1224
719
30
1081
96
46
822
356
62
499
78
15
484
794
31
1714
285
47
1912
637
63
1451
303
16
543
543
32
308
368
48
1402
626
64
1606
578Figure 7
Performance index in successive generations (8×8 network).The cost of the proposed DGSO is also compared with the performance of some other algorithms; refer to Table6. The minimum value of the DGSO and some other algorithms are almost the same; however, it is evident that the performance of the proposed DGSO is better in sense of its maximum value and deviation. Figure 8 describes the optimal solution with reporting cells configuration.Table 6
Results for the8×8 network.
Algorithms
Average value
Deviation
Minimum value
Deviation
Maximum value
Deviation
GA [26]
14.005
1.619%
13.782
0.000%
14.617
6.454%
TS [26]
13.791
0.071%
13.782
0.000%
13.999
1.580%
AC [26]
14.107
2.361%
13.801
0.141%
14.407
4.539%
TDE [27]
13.889
0.776%
13.782
0.000%
14.093
2.256%
HCDE [27]
13.788
0.043%
13.782
0.000%
13.892
0.798%
Our methods
GSO
13.791
0.497%
13.782
0.000%
14.102
2.321%
DGSO
13.780
0.037%
13.782
0.000%
13.883
0.786%Figure 8
8
×
8 test network optimal solution with reporting cells configuration.


## 5. Conclusions

This paper presents the DGSO and shows its application to mobile location management problem. Two important aspects are worth highlighting here.(1)
We proposed the design of DGSO with the aid of diversity operator. Experimental results based on8×8 test network demonstrate the contribution of diversity-guided operator.(2)
We employ GSO and DGSO to deal with the mobile location management problem. Experimental results show that DGSO exhibits good performance in the comparison with some other algorithms reported in the literatures.



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*Source: 430705-2014-08-11.xml*