IEEE
Proof
4 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 00, NO. 00, 2008
Similarly, c
qj
points to a parameter set stored in a compo-213
nent database C. If there are S
c
j
choices for c
qj
, there are S
c
j
214
parameter sets in C (i.e., c
qj
∈ [1, S
c
j
]). The structure of C215
is (5) as shown at the bottom of the this page, where c
j
vn
is216
the value of the nth choice for c
qj
,c
j
pn
is the pheromone of217
the choice c
j
vn
, and c
j
tol
is the tolerance of the jth component.218
The variables c
j
v1
,c
j
v2
...,c
j
vk
..., and c
j
vS
c
j
∈ [C
j
min
,C
j
max
]are219
generated throughout the algorithm, as will be described in220
Section III, C
j
min
and C
j
max
are the lower and upper limits of221
the search space for the jth component.222
B. Fitness Function223
Each ant has a fitness value [i.e., Φ
q
in (1)] showing the degree224
of attainment on the optimization objectives. The multiobjective225
functions used in [22] for optimizing PCS and FN are adopted.226
Their definitions are described as follows.227
1) Fitness Function for Optimizing PCS: The fitness func-228
tion for evaluating the ants for optimizing PCS is based on the229
following considerations, including:230
1) the steady-state error of the output voltage v
o
within the231
required input voltage range v
in
∈ [V
in,min
,V
in,max
] and232
output load range R
L
∈ [R
L,min
,R
L,max
];233
2) the operation constraints on circuit components, such as234
the maximum voltage and current stresses, ripple voltage,235
and ripple current;236
3) the steady-state ripple voltage on v
o
;237
4) the intrinsic factors associated with the components, such238
as the total cost, physical size, etc.239
Each of the aforementioned objectives is mathematically de-240
scribed by an objective function. The formula of each objective241
function i s given in [22]. Φ
q
is the total sum of three compo-242
nents, including Φ
q
−1
, Φ
q
0
, and Φ
q
+1
. Φ
q
−1
is the fitness value of243
ant q when the component values are all reduced by the corre-244
sponding tolerance stored in the last columns in (4) and (5). Φ
q
0
245
is the fitness value of ant q when the components are in their 246
corresponding nominal values. Φ
q
+1
is the fitness value of ant q 247
when the component values are increased by the corresponding 248
tolerance stored in the last columns of (4) and (5). Thus 249
Φ
q
=
Φ
q
−1
+Φ
q
0
+Φ
q
+1
3
. (6)
2) Fitness Function for Optimizing FN: The fitness function
250
for optimizing FN is based on the following considerations: 251
1) the steady-state error of v
o
within the required input volt- 252
age range v
in
∈ [V
in,min
,V
in,max
] and output load range 253
R
L
∈ [R
L,min
,R
L,max
]; 254
2) the maximum overshoot and undershoot, and the settling 255
time of v
o
during the startup; 256
3) the steady-state ripple voltage on v
o
; 257
4) the dynamic behaviors as in 2) during the input voltage 258
and output load disturbances. 259
Again, the objective functions of these objectives are defined 260
in [22], and the tolerances of the components will be taken into 261
calculations as in (6). 262
III. OPTIMIZATION PROCEDURES 263
With the help of the flowchart in Fig. 3, the optimization 264
procedures consist of eight steps. 265
Step 1—Initialization: The values of d
i
vm
(for i = 266
1, 2,...,M and m =1, 2,...,S
d
i
) in (4), and the tolerances 267
d
i
tol
in (4) and c
j
tol
in (5) are initialized with the available 268
values provided by the manufacturers, and that of c
j
vn
(for 269
j =1, 2,...,N and n =1, 2,...,S
c
j
) in (5) are initialized 270
evenly over the search space and the number of choices as- 271
signed (i.e., S
c
j
). Thus 272
c
j
vn
=(n − 1)
(C
j
max
− C
j
min
)
S
c
j
+ C
j
min
. (7)
D =
{d
1
v1
,d
1
p1
}, {d
1
v2
,d
1
p2
}, ··· {d
1
vm
,d
1
pm
}, ··· {d
1
vS
d
1
,d
1
pS
d
1
},d
1
tol
{d
2
v1
,d
2
p1
}, {d
2
v2
,d
2
p2
},
.
.
. {d
2
vm
,d
2
pm
}, ··· {d
2
vS
d
2
,d
2
pS
d
2
},d
2
tol
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
{d
i
v1
,d
i
p1
}, {d
i
v2
,d
i
p2
}, ··· {d
i
vm
,d
i
pm
}, ··· {d
i
vS
d
i
,d
i
pS
d
i
},d
i
tol
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
{d
M
v1
,d
M
p1
}, {d
M
v2
,d
M
p2
}, ··· {d
M
vm
,d
M
pm
}, ··· {d
M
vS
d
M
,d
M
pS
d
M
},d
M
tol
(4)
C =
{c
1
v1
,c
1
p1
}, {c
1
v2
,c
1
p2
}, ··· {c
1
vn
,c
1
pn
}, ··· {c
1
vS
c
1
,c
1
pS
c
1
},c
1
tol
{c
2
v1
,c
2
p1
}, {c
2
v2
,c
2
p2
},
.
.
. {c
2
vn
,c
2
pn
}, ··· {c
2
vS
c
2
,c
2
pS
c
2
},c
2
tol
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
{c
j
v1
,c
j
p1
}, {c
j
v2
,c
j
p2
}, ··· {c
j
vn
,c
j
pn
}, ··· {c
j
vS
c
j
,c
j
pS
c
j
},c
j
tol
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
{c
N
v1
,c
N
p1
}, {c
N
v2
,c
N
p2
}, ··· {c
N
vn
,c
N
pn
}, ··· {c
N
vS
c
N
,c
N
pS
c
N
},c
N
tol
(5)
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