Page 163 - {PDF Title}

Blockchain for secure e-health data in smart cities

the algorithm to miss the optimal solution, whereas too Here, l individual at T + 1 iteration is signified by
th
much exploitation may result in getting stuck in local Z T +1 , whereas Z T symbolizes the current optimal
best
l
minima. Therefore, to overcome these challenges, we individual, and γ and γ symbolize weighting
2
1
included the concept of STO in our work. coefficients. The extent to which tuna follows the
The new algorithm, including the concepts of
SBO and TSA, is termed STI-TSA. The hybrid TSA optimal and prior individual is assessed by co, whereas
33
32
with SBO could attain faster convergence and create T and T max signify the iteration count and
high-quality solutions, including diverse optimizing maximal iteration, and b signifies the random figure
approaches. In addition, STI-TSA could balance both between 0 and 1.
local and global searches. Each tuna can more effectively utilize the search
(i) Initialization: TSA begins with the arbitrary phase when swimming in a spiral pattern around the
generation of initial populations as shown in bait. This strategy allows the tuna to cover a larger area,
Equation IX, where, Z points out initial enhancing TSA’s potential to explore the search space
in
l
individuals, LB and UB point out lower and upper
limits, O points out the tuna population, and rnd on a global scale, as stated in Equation XV.
points out random values between 0 and 1
. Z T . Z T Z l Z . T , l 1
T

Z rnd UB LB. LB l, 12 O (IX) Z l T 1 1 rnd rnd 2 l
in
, ...
1
l
T
T T
. Z T rnd . Z T rnd Z l 2 Z . l1 l 23, ,..., O
(ii) Spiral foraging: The entire school of fish forms a (XV)
tight configuration by continuously changing its
swimming direction to prevent predators from The symbol Z T rnd represents an arbitrary reference
latching onto a victim. At that point, the tuna group point in the field of search space. The TSA changes the
forms a tight spiral shape to pursue the prey. Although spiral foraging indicators from arbitrary to optimum
many fish possess a sense of direction, when a ones as the iteration rises. It may be found numerically
small group of fish begins swimming in a certain in Equation XVI.
direction, other fish in the vicinity often follow
T
suit. The fish in the leading group share a common . Z T rnd . Z T rnd Z l

1
objective and initiate the hunt. Furthermore, all tuna T
communicate with each other. The mathematical 2 Z . l , l 1, , if rnd T ,
1
formula for spiral foraging behavior is provided in . Z T . Z T Z l l T max
T
Equation X. rnd rnd
T

. Z T . Z T Z l Z . T , l 1 Z l T 1 2 Z . l1 , l 23,,..., O,
T
1

T
Z l T 1 1 best best 2 l . Z best . Z T best Z l T
1

T
. Z T . Z T T Z l Z . T l 23, ,..., O T
best best 2 l1 2 Z . l l , 1 T
(X) Z T Z T Z T ,if rnd T ,

The computation of γ , γ , δ, and le are shown in . best . best l max
1
2
1
Equation XI to Equation XIV. 2 Z . T l 1 l , 23,,....,O (XVI)

T
co 1 . (XI) (iii) Proposed parabolic foraging: Here, tuna forms
co
1 T max a parabolic shape using food as a point of
1 1 . T (XII) reference. They also search their surroundings in
co
co
T
2 search of nourishment. Two methods were used
max
simultaneously, with the assumption that each had a
δ = w .cos (2πb) (XIII) 50% chance of being selected. Its numerical version
ble
T 1 is given in Equation XVII. tf is an arbitrary number
T
1
3cos
le w max (XIV) with a value of either −1 or 1.
Volume 22 Issue 1 (2025) 157 doi: 10.36922/AJWEP025040017