222
A. V. Panteleev and M. M. S. Karane
The first and third phases require one-dimensional maximization of parametric
curves. The swarm intelligence method called as Krill Herd [10, 11] is used for
maximization, but it was possible to use classical algorithms for one-dimensional
maximization, for example, the dichotomy method or the golden-section search. Krill
Herd method is based on the results of the krill packs behavior analysis, resembling
shrimps. Their positions change under the influence of three factors: the presence
of other members of the population, need to search for food, and random walks.
Usually the movement of krill population is determined by two goals: the increase
in the density of krill and attainment of food. At the beginning of the process, a
population N P
is generated from individuals on interval t ∈ [0, 1] using a uniform
distribution. It is assumed that the motion of the j th member of the population occurs
according to Eq. 16.8, where x
j is the position, V
j is the speed, which consists of
three terms.
dx
j
dt
= V
j
(16.8)
The first term is determined by the influence of neighbors (members of the population that belong to certain neighborhood of jth element of a certain radius), the
best element in the entire population, and information about its former speed. The
second term is determined by the movement toward the food source (the “center
of mass” of the population is taken for it), information about the former speed in
search of food, and the memory of its best result for all the iterations. The third term
imitates the random walks of the individual, which decrease with increasing number
of iterations. To revive the search process, the cross and mutation operations are used
in other evolutionary methods, as well as, the method of differential evolution are
applied. The procedure for finding the maximum of the interpolation curve ends when
the specified number of iterations is reached. And as an answer from the last krill
population, the individual that corresponds to the smallest value of the parametric
curve f is selected, and a new member x
j is added to the original population.
The hybrid multi-agent method of interpolation search finishes work after the
specified number of iterations is passed. As an approximate solution to the problem,
an individual from the last population with the greatest value of the objective function
is selected.
Solution search algorithm
Step 1
Set the method parameters: NP is the number of members in the population, M 1 is the number of points obtained using the Bezier curves, M 2 is
the number of points obtained using B-spline curves, PRT is the parameter that determines the search activity by coordinate, nstep is the number
of possible positions of the population members, b 2 is the number of individuals (worst) to reduce population, and I max is the maximum number
of iterations. Let I = 1 (iteration count).
A. V. Panteleev and M. M. S. Karane
The first and third phases require one-dimensional maximization of parametric
curves. The swarm intelligence method called as Krill Herd [10, 11] is used for
maximization, but it was possible to use classical algorithms for one-dimensional
maximization, for example, the dichotomy method or the golden-section search. Krill
Herd method is based on the results of the krill packs behavior analysis, resembling
shrimps. Their positions change under the influence of three factors: the presence
of other members of the population, need to search for food, and random walks.
Usually the movement of krill population is determined by two goals: the increase
in the density of krill and attainment of food. At the beginning of the process, a
population N P
is generated from individuals on interval t ∈ [0, 1] using a uniform
distribution. It is assumed that the motion of the j th member of the population occurs
according to Eq. 16.8, where x
j is the position, V
j is the speed, which consists of
three terms.
dx
j
dt
= V
j
(16.8)
The first term is determined by the influence of neighbors (members of the population that belong to certain neighborhood of jth element of a certain radius), the
best element in the entire population, and information about its former speed. The
second term is determined by the movement toward the food source (the “center
of mass” of the population is taken for it), information about the former speed in
search of food, and the memory of its best result for all the iterations. The third term
imitates the random walks of the individual, which decrease with increasing number
of iterations. To revive the search process, the cross and mutation operations are used
in other evolutionary methods, as well as, the method of differential evolution are
applied. The procedure for finding the maximum of the interpolation curve ends when
the specified number of iterations is reached. And as an answer from the last krill
population, the individual that corresponds to the smallest value of the parametric
curve f is selected, and a new member x
j is added to the original population.
The hybrid multi-agent method of interpolation search finishes work after the
specified number of iterations is passed. As an approximate solution to the problem,
an individual from the last population with the greatest value of the objective function
is selected.
Solution search algorithm
Step 1
Set the method parameters: NP is the number of members in the population, M 1 is the number of points obtained using the Bezier curves, M 2 is
the number of points obtained using B-spline curves, PRT is the parameter that determines the search activity by coordinate, nstep is the number
of possible positions of the population members, b 2 is the number of individuals (worst) to reduce population, and I max is the maximum number
of iterations. Let I = 1 (iteration count).