Information Technology Reference
In-Depth Information
c
2
denotes learning factor.
w
denotes Inertia weight, and it is linearly decreasing
weight, and decrease from
w
max
to
w
min
, as shown in equation (13):
ww
ite
−
w
=−×
w
ite
max
min
(14)
max
max
Where
ite
max
denotes maximum number of iterations.
Definition 3.
if mixed Nash equilibrium solution X meets
∀
,
ij
,
, it is called standardized solution.
x
i
j
≥
0
x
i
j
=
1
and
j
If the solution of particles during the iteration of PSO is not the standardized solu-
tion, we should deal it with the method shown in equation (14) and (15):
0
i
j
i
j
x
<
0,
x
>
0
1,
(15)
i
i
x
0
≤≤
x
1
j
j
(16)
xx
i
=
i
x
i
j
j
j
j
3.2
PSO Algorithm Process
Input:
(1)
The size of population K, the maximum number
ite
max
;
(2)
Inertia weight
w
, maximum weight values
w
max
, minimum weight value
w
min
;
(3)
Learning factor
c
1
and
c
2
, the value is 2 in our experiments;
(4)
Initialize set of tasks
T= (t
1
, t2, ···, t
m
)
, set of tasks requirements
REQ= (req
1
, req
2
,
···, req
n
)
, an ability matrix
Bb
×
=
()
ij
, and the energy consumption matrix
l
m
COST= (cost
ij
)
m×l
.
Output:
(1)
the best mixed strategy
X
*
;
(2)
Residual energy of each coalition
RE=(re
1
, re
2
, …, re
l
)
;
(3)
Busy time of coalitions
BUSY= (busy
1
, busy2, ···, busy
l
)
.
Step1:
Initialize the population. Initialize each particle X, each component of the
vector
x
i
is random number between 0-1, then handle
x
i
according to equa-
tion (14) and (15);
Step2:
compute
V
i
(t+1)
of
i
-th particle according to equation (11), then update
X
i
(t+1)
according to equation (12);
Step3:
handle
V
i
(t+1)
according to equation (14) and (15);
Step4:
compute fitness value of
X
i
(t+1)
;
Step4.1:
input mixed strategy matrix
X
, busy time and energy of each coali-
tion, and set of tasks;
Step4.2:
for task
t
i
, compute its executing time and transmission energy con-
sumption in the coalitions;
