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Step4.3: according to equation (5), compute gain of pure strategy of task t i in
the coalitions.
Step4.4: according to equation (7) and mixed strategy x i , compute expected
gain of task t i .
Step4.5: update busy time and energy of each coalition according to equation
(8) and equation (9);
Step4.6: compare expected gain of task t i and all pure gain, then update the
value of fitness according to equation (10);
Step4.7: if t i is the last task, then end; else i plus 1 and go to step4.2 .
Step5: determine whether need to update the local optimal solution or the global op-
timal solution;
Step6: The number of iterations plus 1;
Step7: Judge whether the number of iterations reaches the upper limit ite max . If
ite=ite max , then return X gBest , else go to Step2.
During the process of computing, we need to handle the three parameters of the
utility function (execute time, transmission energy consumption and residual energy).
In this paper, the value mapped to the interval [0, 0.5] by using sigmoid function, as
shown in equation (16) and equation (17):
1
fx
()
=−
+
1
(17)
e
x
1
+
1
fx
()
=
0.5
(18)
e
x
1
+
1
nt
=−
+
1
(19)
i
nt
nt
i
min
nt
nt
1
+
e
max
min
1
cos
t
=−
+
1
(20)
ij
cos
t
cos
t
ij
min
cos
t
cos
t
1
+
e
max
min
1
e
=−
+
1
(21)
i
ee
i
min
e
e
1
+
e
max
min
4
Simulation and Results
Our simulation study is conducted for a WSN of n nodes that are placed uniformly in a
rectangular region of 200 by 200 meters, and 10% of the nodes are elected as the
leader. The requirements of the subtask are distributed in the range of the interval (2,
6]. In the same situation, the greater the value is, the longer the time of executing this
task is. This value also reflects the difficulty of the task processing. The ability of
executing task is distributed in the range of the interval (15, 25], the greater the value
is, the stronger the ability is. The energy consumption is distributed in the range of the
 
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