Page 107 - IJOCTA-15-2
P. 107
A. Ebrahimzadeh, R. Khanduzi, A. Jajarmi / IJOCTA, Vol.15, No.2, pp.294-310 (2025)
the better solutions (water flow), soil im- U min are the most significant and most
permeability coefficient, and its impact on minor amounts of control variables of the
flooding. The direction indicates the best NLP. Also, water infiltration in the soil
mass of water (best solution), where U best makes the water sink or become trapped
indicates the exact slope of the water flow in the water ditches and propagate around
path. Thus, the U i -th mass travels nor- or evaporate, decreasing the probability of
mally to the slope and finds an approxi- overflow. This relation indicates that the
mate value of U best , and the goal is to de- smaller or better the objective function of
crease the distance between the U i -th and the mass amount, the smaller the infiltra-
the best mass, namely, it travels around tion rate, and the greater the probability
U best about U j −U i . We compute this gen- of overflow:
eral momentum relation and then proceed J(U i ) − J min 2
as follows: Pe i = . (56)
J max − J min
U i new = U best + rand × (U j − U i ) , (53) In the equation (56), J min and J max show
in which rand creates random values from the best and worst values of the objec-
interval [0, 1] to the dimension of D. The tive function that was found for this run
of FBMO. Water erosion from the pool
NLP has a value of j = 1 : D, and U j
is the jth mass of the crowd at random. reduces the probability of overflow in
Concerning the relation (53), the water FBMO. The below code shows this step
mass travels toward the path’s slope and for the ith mass:
typically toward a better mass. Indeed,
water travels towards the river due to the if randG > rand + Pe i
pressure behind it, not the slope. There- Pk randG
fore, by increasing the river’s water flow, U i new = U i + ×
Iter
floods may occur. This erosion coefficient
(rand × (U max − U min ) + U min )
concerning the repetitions of the FBMO
is modeled based on the relation (54): else
"
1.2 new
Pk = k+ U i = U best + rand × (U j − U i )
Iter
end
#
1 Iter max
ln k + ,
So, a new situation for the ith mass, i.e.,
Iter max × Iter 4
4 U new , is compared to the previous situa-
(54) i
√ tion and altered if it is better.
2
where k = Iter max × Iter + 1. In this (2) Step 2 (A Growth and Reduction in the
relation, Pk is the water erosion coeffi- Crowd): Rainfall, snowmelt, or fountains
cient, and Iter max indicates the maximum replenish the water in a pool. Water evap-
number of FBMO repetitions; Iter indi- oration occurs when it sinks into the land
cates the current repetition of the FBMO. or becomes stuck in water ditches. We
On the other hand, the flood phenomenon have reversed these two situations. This
is randomly generated by a rand value, means that Ne number of masses vapor-
which will be the relation of motion of the ize, which are the most weak. Addition-
masses during the flood as in the relation ally, when we add Ne masses, the total
(55): number of masses remains constant. In re-
turn, the probability of the event in these
Pk randG
U i new = U i + × two situations (Pt) is the same:
Iter (55)
rand
(rand × (U max − U min ) + U min ) . Pt = sin . (57)
Iter
The water masses are collected from the
These new masses will alter the worst an-
pool on this border and the other bor- swers, and they will be in the best situa-
der of the region at random, determined
by the value of the water erosion coeffi- tion:
cient. In addition, randG is a Gaussian new
U = U best + rand×
distribution from the interval [−∞, +∞], e (58)
which is one dimension, and U max and (rand × (U max − U min ) + U min ),
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