226
A. V. Panteleev and M. M. S. Karane
Place individuals of the current population increasing the value of the
fitness function I t = {x
(1)
, . . . , x
(N P)
}, where N P = b 1 + b 2 , f (x
(1)
) =
f max . Delete the last b 2 individuals (with the worst value of the fitness
function).
Increase the number of iterations it = it + 1.
The result of Step 7 is a reduced population.
Step 8
Execute the replenishment of population.
Step 8.1 Perform this step b 2 times. Generate a population consisting of b 2
individuals on a set D using a uniform distribution: x
1
, . . . , x
b 2 .
Step 8.2 Order the individuals of the population in ascending order of the fitness
function value: I t = {x
(1)
, . . . , x
(N P)
}, where N P = b 1 + b 2 , f (x
(1)
) =
f max .
Step 9
Check the stop conditions of global search.
If it < I max , then continue search, go to Step 4.
If it ≥ I max , then finish search, go to Step 10.
Step 10 Select the solution from the last population.
Stop the algorithm. As an approximate solution to the problem f (x
∗
) =
max
x∈D
f (x), select individual with the greatest value of the fitness function
from the current population: x
∗ ∼ = ˜
x
∗
= arg max
j=1,...,N P
f (x
j
).
Recommendations on the parameters selection. Size of the population N P determines a number of calculations of the objective function at each iteration. For a task
with a large range of feasible solutions, it is recommended to take a larger parameter
value NP. Recommended value for this parameter is N P ∈ [30, 40].
The number of iterations I max determines how long the search for new solutions will continue. The more I max , the more accurate the solution could be found.
Recommended values for the considered set of standard functions depending on the
complexity of the function are I max ∈ [100, 300].
The number of points M 1 obtained using the Bezier curves in the interpolation
search phase. When maximizing the objective function along the parametric curve,
M 1 agents are formed. Recommended value for this parameter is M 1 ∈ [2, 5].
The number of points M 2 obtained using B-spline during the interpolation search
phase. When maximizing the objective function along the parametric curve, M 2
agents are formed. This curve is used to explore new areas. Recommended value for
this parameter is M 2 ∈ [4, 6].
Parameter PRT determines the activity of searching by coordinate during migration of group agents. The parameter sets the search direction. Recommended value
for this parameter is P RT ∈ [0.005, 0.06].
The number nstep defines the possible positions of the population members during
the migration of the population. The parameter determines how many steps an individual will take in the direction to the leader. Recommended value for this parameter
is nstep ∈ [3, 7].
A. V. Panteleev and M. M. S. Karane
Place individuals of the current population increasing the value of the
fitness function I t = {x
(1)
, . . . , x
(N P)
}, where N P = b 1 + b 2 , f (x
(1)
) =
f max . Delete the last b 2 individuals (with the worst value of the fitness
function).
Increase the number of iterations it = it + 1.
The result of Step 7 is a reduced population.
Step 8
Execute the replenishment of population.
Step 8.1 Perform this step b 2 times. Generate a population consisting of b 2
individuals on a set D using a uniform distribution: x
1
, . . . , x
b 2 .
Step 8.2 Order the individuals of the population in ascending order of the fitness
function value: I t = {x
(1)
, . . . , x
(N P)
}, where N P = b 1 + b 2 , f (x
(1)
) =
f max .
Step 9
Check the stop conditions of global search.
If it < I max , then continue search, go to Step 4.
If it ≥ I max , then finish search, go to Step 10.
Step 10 Select the solution from the last population.
Stop the algorithm. As an approximate solution to the problem f (x
∗
) =
max
x∈D
f (x), select individual with the greatest value of the fitness function
from the current population: x
∗ ∼ = ˜
x
∗
= arg max
j=1,...,N P
f (x
j
).
Recommendations on the parameters selection. Size of the population N P determines a number of calculations of the objective function at each iteration. For a task
with a large range of feasible solutions, it is recommended to take a larger parameter
value NP. Recommended value for this parameter is N P ∈ [30, 40].
The number of iterations I max determines how long the search for new solutions will continue. The more I max , the more accurate the solution could be found.
Recommended values for the considered set of standard functions depending on the
complexity of the function are I max ∈ [100, 300].
The number of points M 1 obtained using the Bezier curves in the interpolation
search phase. When maximizing the objective function along the parametric curve,
M 1 agents are formed. Recommended value for this parameter is M 1 ∈ [2, 5].
The number of points M 2 obtained using B-spline during the interpolation search
phase. When maximizing the objective function along the parametric curve, M 2
agents are formed. This curve is used to explore new areas. Recommended value for
this parameter is M 2 ∈ [4, 6].
Parameter PRT determines the activity of searching by coordinate during migration of group agents. The parameter sets the search direction. Recommended value
for this parameter is P RT ∈ [0.005, 0.06].
The number nstep defines the possible positions of the population members during
the migration of the population. The parameter determines how many steps an individual will take in the direction to the leader. Recommended value for this parameter
is nstep ∈ [3, 7].