IEEE Robotics & Automation Magazine - December 2023 - 33

of USMA is discussed in detail as follows and is also depicted
in Figure 3.
1) Initially, the USMA approaches food and determines
the best location in all possible directions by applying
the Levy distribution function. This enables the algorithm
to explore the position change behavior in the
solution space effectively according to the essence in
the air. The mathematical calculation to simulate the
contraction pattern and structure is shown in (1).
Y^t + 1h
= )
YY Y
Y
zA B
$$
^ +-v
^ h,
tfzW tt LevD d
fc tLev Dd
h
^
$
^ h ^^ h1
^
hh,
h $
.
(1)
Here, t represents the current iteration, Yv is the current
position of the slime mould, YtA^h and YtB^h
depict the two individuals, arbitrarily chosen from the
slime mould, fz is an attribute with a range of [-b, b],
fc decreases linearly from 1 to 0, showing whether to
approach the food source or to determine some other
source, YZ shows the current location of an individual
with the highest odor concentration, Wv
determines the
weight factor of the slime, and Levy D^h represents the
level of diffusion vector. The mathematical formula for d
is shown in (2).
dZkbf=-^h
tanh
=12 f Zk
,, , ,
.
(2)
Here,kn ^h represents the fitness of Yv , and
bf shows the best fitness acquired so far. As fz = [-b, b],
"" b is shown in (3) and Wv
b
W^ascendh
=
Z
[
\
]
]]
]
]
11
11
+ LevDh
^
- LevDh
^
$
$
log
log
c +=rank
if Zk
oF Zk- ^ h
oF lF
-
c
oF k^ h
oF lF
- Z
-
m
+ m
first half of the population
otherwise
,
,
^^= SortZ .
^ h
(4)
Wascendhh (5)
Here, tmax represents the maximum number of iterations,
oF shows the acquired optimal fitness value at the current
iteration, lF determines the acquired least fitness value at
the current iteration, and Wascend ^hdenotes the sorted
sequence of fitness value, where a log is utilized to balance
the frequency and the rate of change of the contraction
value. Thus, according to the obtained best location, the
search of an individual can be updated by tuning the considered
parameters and through a guided direction to reach
the optimal value in the hyperdimensional space. The
dynamic path enhances the exploration and contraction
mode of the slime mould.
2) Further, the wrapping of food is based on the association
formed between the structure of the venous tissue and the
=- +
`` jj
arctanh
1
tmax
is presented in (4).
t
(3)
Here, UB and LB show the lower and upper bounds of a
certain search range, ra, and r represents a random value
ranging between 0 and 1.
3) USMA operates in the foraging method by mimicking the
behavior and morphological variations of SMA. The morphological
pattern varies with three contraction formation
phases of the slime. The cytoplasmic motion in the veins
depends upon the propagation wave oscillation for better
search or accumulation of the food concentration.
OPTIMAL VISUAL WORDS GENERATION USING USMA
The proposed USMA-BOF algorithm obtains the optimal
bag of visual words by applying the USMA-based clustering
algorithm to determine the cluster centroid. The formulated
visual words are aggregated to establish a codebook using
feature descriptors.
The USMA-based clustering approach is detailed next.
1) At an initial stage, an N-dimensional feature vector is
obtained by extracting various statistical-, texture-, and
shape-based features. Here, 107 features are extracted
from healthy and unhealthy leaf images.
2) The USMA-BOF algorithm computes the optimal set of
visual features using the following steps:
a) Using k-means clustering, the group of collected features
stated as
" aa am12 f , where aZ im is
,,
,
,
" rr rk12 f , where rZ .
k ! N
i e
N
=1to
,
used to create k clusters with cluster centroids
,,
b) We determine the population of slime moulds such that
each slime mould is a k-dimensional vector of features
that are near to the cluster heads returned by k-means.
c) We evaluate the fitness of each slime mould by applying
the objective function shown in (7).
m
ar =
k
Minimize mkb^h // ar
j
,,
i 11
==
where b shows the consistency of the cluster to reduce
compactness.
d) We compute the best solution by enhancing the position
and search pattern of the slime mould using USMA.
e) A repetition of steps c and d is performed until the termination
condition is met.
f) We output the best optimal solution or position.
DECEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
33
mk
2
(7)
concentration of food. It is observed that the higher the
concentration of the food, the greater the weight region
will be and vice versa, thus also exploring another
region. In the exploitation phase, the updated location is
enhanced by providing a guided direction for food while
in searching mode rather than trapping in a local optimum.
The best optimal position or value is determined
using the mathematical formula in (6) as follows:
YY YY
Y
) = *
fc $
^ h,
t
ra UB LB LB
tfzW tt
zA B
$
^ -+ ,
h
^ h+- ,
$$
^ ^^ ^
^
v hhh
rz
LevD d
LevD d
1
h
h
1
$
.
(6)
IEEE Robotics & Automation Magazine - December 2023

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