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In-Depth Information

optimization: Chemotaxis, Swarming, Reproduction and Elimination-dispersal. The

variables that used in the formula are explained in following.

j
index for the chemotactic step

k
index for reproduction step

l
index of the elimination-dispersal step

p
dimension of the search space

S
total number of bacteria in the population

:

c
N
the number of chemotactic steps

:

s
N
the swimming length

:

N

the number of reproduction steps

re

N

:

the number of elimination-dispersal events

ed

ed
P
elimination-dispersal probability

:

:

(
iC
the size of step taken in the random location specified by the tumble

Chemotaxis: This simulates the movement of E.coli bacteria through swimming

and tumbling via flagella. Swim means the bacterial cells move in the same direction.

Tumble means the bacterial cells move in a random direction. The bacterial cells

alternate between swim and tumble for the entire lifetime. The tumble movement is

formulated as follow:

)

i

i

ʸ

(

j

+

1

k

,

l

)

=

ʸ

(

j

,

k

,

l

)

+

C

(

i

)

ˆ

(

j

)

(3)

i

th

th

ʸ

(

j

,

k

,

l

)

denotes the current position of the

i

individual at the

j

chemotaxis

th

th

step,

k

reproduction step and

l

elimination-dispersal events.

is a random

ˆ

(
j

)

th

direction angle of the

j

chemotaxis step.

θ
i

i

If the cost at

ʸ

(

j

+

1

k

,

l

)

is better than the cost at

(

j

,

k

,

l

)

, the bacterium will

swim another step of size

(
C
in the same direction as the tumble movement did,

otherwise it is allowed to tumble in a random direction

)

. The process is repeated

until the number of maximum swimming length
N
is reached.

Swarming: Cell-released attractants are used to signal other cells that they should

swarm together. The cell also repels a nearby cell in the sense that it consumes nearby

nutrients and it is not physically possible to have two cells at the same locations. Thus

all cells will have a cell to cell attraction via attractant and cell to cell repulsion via

repellant. The cell to cell signaling in E.coli swarm is representing as formula (4):

ʸ

(
j

)

J

(

ʸ

,

p

(

j

,

k

,

l

))

=

cc

S

S

p

i

i

m

2

∑

J

(

ʸ

,

ʸ

(

j

,

k

,

l

)

=

∑

[

d

exp(

w

∑

(

ʸ

−

ʸ

)

)]

+

cc

attrac

tan

t

attrac

tan

t

m

(4)

i

=

1

i

=

1

m

=

1

S

p

i

m

2

∑
[

h

exp(

w

∑
(

ʸ

−

ʸ

)

)]

repellant

repellant

m

i

=

1

m

=

1