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counter=0
max_fitness=maximum of possible fitness in an arbitrary problem setting
level= max_fitness
Repeat
counter=counter+1
step = exp( -1*counter)*max_fitness
each particle i
Update particle position x
i
According to one of the three below equations
For each particle i
compute situation according to equation 3, 6 and 9
a=make_decide(Automata
i
, situation)
if(a=0)
l
i
g
+
elseif(a=1)
v
(
t
1
=
w
v
(
t
)
+
w
(
x
(
t
)
−
x
(
t
))
+
w
(
x
(
t
)
−
x
(
t
))
i
1
i
2
i
3
i
l
i
+
elseif(a=2)
v
(
t
1
=
r
v
(
t
)
+
r
(
x
(
t
)
−
x
(
t
))
i
1
i
2
i
v
i
(
t
+
1
=
random
Endif
End for
x
i
'=x
i
+v
i
if(f(x
i
')> f(x
i
))
punish(Automata
i
,situation,a)
else
reward(Automata
i
,situation,a))
End if
if(f(x
i
')<level)
x
i
=x
i
'
End if
if(f(xi')<f(xg))
x
g
=x
i
'
End if
if(f(x
i
')<f(x
l
i
)
x
l
i
=x
i
End if
level=level+step
Until termination criterion reached
Fig. 1.
Pseudo code of the proposed algorithm
4 Experimental Study
Branke [4] introduced a dynamic benchmark problem, called moving peaks
benchmark (MPB) problem. In this problem, there are some peaks in a multi-
dimensional space, where the height, width and position of each peak change during
the environment change. This function is widely used as a benchmark for dynamic
environments in literature [12] and [17].
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