Brief description of SMA
1 Approach food
To model the approaching behavior of slime mould as a mathematical equation, the following rule is
proposed to imitate the contraction mode:
𝑋
(
𝑡
+
1
)
=
𝑋
𝑏
(
𝑡
)
+
𝑣𝑏
∙
𝑊
∙
𝑋
𝐴
(
𝑡
)
―
𝑋
𝐵
(
𝑡
)
, 𝑟
<
𝑝
𝑣𝑐
∙
𝑋
(
𝑡
)
, 𝑟
≥
𝑝
(1)
where
𝑣𝑏
is a parameter with a range of
[
―
𝑎,𝑎
]
,
𝑣𝑐
decreases linearly from one to zero.
𝑡
represents the current iteration,
𝑋
𝑏
represents the individual location with the highest odor
concentration currently found,
𝑋
represents the location of slime mould,
𝑋
𝐴
and
𝑋
𝐵
represent two
individuals randomly selected from the swarm,
𝑊
represents the weight of slime mould.
The formula of
𝑝
is as follows:
𝑝
=
tanh
|
𝑆
(
𝑖
)
―
𝐷𝐹
|
(2)
where
𝑖
∈
1,2,…,𝑛
,
𝑆
(
𝑖
)
represents the fitness of
𝑋
,
𝐷𝐹
represents the best fitness obtained in all
iterations.
The formula of
𝑣𝑏
is as follows:
𝑣𝑏
=
[
―
𝑎,𝑎]
(3)
𝑎
=
arctanh
(
―
𝑡
max
_𝑡
+
1)
(4)
The formula of
𝑊
is listed as follows:
𝑊(𝑆𝑚𝑒𝑙𝑙𝐼𝑛𝑑𝑒𝑥(𝑖))
=
1
+
𝑟
∙
𝑙𝑜𝑔
𝑏𝐹
―
𝑆
(
𝑖
)
𝑏𝐹
―
𝑤𝐹
+
1
,𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛
1
―
𝑟
∙
𝑙𝑜𝑔
𝑏𝐹
―
𝑆
(
𝑖
)
𝑏𝐹
―
𝑤𝐹
+
1
,
𝑜𝑡ℎ𝑒𝑟𝑠
(5)
𝑆𝑚𝑒𝑙𝑙𝐼𝑛𝑑𝑒𝑥
=
𝑠𝑜𝑟𝑡(𝑆)
(6)
where
𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛
indicates that
𝑆
(
𝑖
)
ranks first half of the population ，
𝑟
denotes the random
value in the interval of
[
0,1
]
，
𝑏𝐹
denotes the optimal fitness obtained in the current iterative
process,
𝑤𝐹
denotes the worst fitness value obtained in the iterative process currently,
𝑆𝑚𝑒𝑙𝑙𝐼𝑛𝑑𝑒𝑥
denotes the sequence of fitness values sorted(ascends in the minimum value problem).
2 Wrap food
The mathematical formula for updating the location of slime mould is as follows:
𝑋
∗
=
𝑟𝑎𝑛𝑑
∙
(
𝑈𝐵
―
𝐿𝐵
)
+
𝐿𝐵,𝑟𝑎𝑛𝑑
<
𝑧
𝑋
𝑏
(
𝑡
)
+
𝑣𝑏
∙
𝑊
∙
𝑋
𝐴
(
𝑡
)
―
𝑋
𝐵
(
𝑡
)
,𝑟
<
𝑝
𝑣𝑐
∙
𝑋
(
𝑡
)
, 𝑟
≥
𝑝
(7)
where
𝐿𝐵
and
𝑈𝐵
denote the lower and upper boundaries of the search range,
𝑟𝑎𝑛𝑑
and
𝑟
denote
the random value in [0,1].
