Computational Intelligence - November 2013 - 46

Table 2 Scenario 1: Mission setting.

530
saTelliTe
number

iniTial sTaTe
(x d , y d , z d , xo d , yo d , zo d )

Final sTaTe
(x d , y d , z d , xo d , yo d , zo d )

1

(-233.01, 499.90, -403.59,
0.2479, 0.4622, 0.4294)

(-533.01, 701.55, -923.20,
0.3479,1.0573, 0.6026)

(332.97, 153.62, 576.72,
0.0762, -0.6605, 0.1319)

(570.29, 572.40, 987.78,
0.2839, -1.1312, 0.4916)

(-99.97, -653.52, -173.16,
-0.3241, 0.1983, -0.5613)

(-37.31, -1273.96, -64.62,
-0.6318, 0.0740, -1.0942)

3

Initial Orbit
Reference Satellite
Initial Formation
Desired Orbit
Desired Formation

1500
1000
z/m

500

510
500
490

CLBSO-DB
CLBSO-RGC
CLBSO-RS
BSO
PSO

480
470
460

10 20 30 40 50 60 70 80 90 100
Iteration

Figure 9 Convergence behaviors of CLBSO-DB, CLBSO-RGC, CLBSO-RS, BSO and PSO averaged over 10 Monte Carlo simulations in
Scenario 1.

Table 3 Scenario 1: Average performance of different
algorithms in 10 runs.

0
-500
-1000

algoriThm

1000

0
10
00
20
00

00

10

00

-1500

20

Efficiency

2

520

0
-1000

y/m

x/m
Initial Orbit
Reference Satellite
Initial Formation
Desired Orbit
Desired Formation

(a)
1500

clbso

indicaTor

clbso-db

clbso-rgc clbso-rs bso

Pso

CPU (s)

10.83

10.89

10.96

11.41

4.26

COnveRGenCe 46
SPeeD

68

70

85

90

COSt

1.8842

1.8841

1.8871 1.9389

1.8845

Table 4 Scenario 1: Optimal impulses for each satellite.

1000

oPTimal imPulse

z/m

500
0
-500

saTelliTe
number

imPulse oPTimal imPulse
number Dv = [u x, u y , u z], (m/s)

imPlemenTing Time t, (s)

1

1

(0.1570, 0.0001, 0.2666)

1200

2

(-0.1574, -0.0001, -0.2779) 4479

1

(-0.1570, -0.0001, -0.2658) 2249

2

(0.1575, 0.0001, 0.2789)

5541

1

(-0.2234, 0.0331, -0.4025)

273

2

(-0.0747, -0.0331, -0.1450) 6335

2

-1000
3

-1500
-1500 -1000 -500

0
y/m

500

1000 1500

paper, three different strategies of selecting x r1 and x r2
are investigated:

(b)
Figure 8 Reconfiguration mission 1 for three satellites. (a) 3-dimension. (b) 2-dimension.

search characteristic capture and thus enhance the optimization
performance.
In this section, we propose a closed-loop strategy based BSO
(CLBSO), which generates new individuals by making use of
feedback information and gains a better tradeoff between exploration and exploitation during the search process. Specifically, a
new individual y i is generated by adding innovative information
to an old individual x i according to
y ij = x ij + (x rj1 - x rj2) $ random (t),
j
r1

(16)
j
r2

where j is the dimension index, and x and x are two
selected individuals to generate feedback information. In this

46

IEEE ComputatIonal IntEllIgEnCE magazInE | noVEmBER 2013

1) Difference with the Best
The CLBSO algorithm using this updating strategy is called
closed-loop brain storm optimization using difference with the
best (CLBSO-DB), where x r1 is chosen as the best individual
in the current population and x r2 is identical with x i . This
mechanism is inspired by the updating rule of PSO, which
mimics the natural phenomenon that each bird updates its
position towards the one with the global best position.
2) Random Selection
In this strategy, x r1j and x r2j are two distinct individuals randomly selected from the current population. The resulting
algorithm is called closed-loop brain storm optimization using
random selection (CLBSO-RS).



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