10-06-2013, 03:51 PM
A New Artificial Fish Swarm Algorithm for Dynamic Optimization Problems
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Abstract
Artificial fish swarm algorithm is one of the
swarm intelligence algorithms which performs based on
population and stochastic search contributed to solve
optimization problems. This algorithm has been applied in
various applications e.g. data clustering, neural networks
learning, nonlinear function optimization, etc. Several
problems in real world are dynamic and uncertain, which
could not be solved in a similar manner of static problems.
In this paper, for the first time, a modified artificial fish
swarm algorithm is proposed in consideration of dynamic
environments optimization. The results of the proposed
approach were evaluated using moving peak benchmarks,
which are known as the best metric for evaluating dynamic
environments, and also were compared with results of
several state-of-the-art approaches. The experimental results
show that the performance of the proposed method
outperforms that of other algorithms in this domain.
INTRODUCTION
Artificial fish swarm algorithm (AFSA) is one of the
algorithms inspired both from the nature and swarm
intelligence algorithms. AFSA was presented by Li Xiao
Lei in 2002[1]. This algorithm is an approach based on
swarm behaviors that was inspired from social behaviors
of fish swarm in the nature. This algorithm has some
characteristics such as high convergence rate, insensibility
to initial values, flexibility and high fault tolerance. AFSA
has been utilized in optimization applications e.g. PID
controller parameters setting[2] multi-objective
optimization[3], global optimization[4].
ARTIFICIAL FISH SWARM ALGORITHM
In water world, fishes can find areas that have more
foods, which is done with individual or swarm search by
fishes. According to this characteristic, artificial fish (AF)
model is represented by prey, free_move, swarm and
follow behaviors. AFs search the problem space by those
behaviors. The environment, which AF lives in,
substantially is solution space and other AF’s domain.
Food consistence degree in water area is AFSA objective
function. Finally, AFs reach to a point which its food
consistence degree is maxima (global optimum).
As it is observed in figure 1, AF perceives external
concepts with sense of sight. Current position of AF is
shown by vector X=(x1, x2, …, xn). The visual is equal to
sight field of AF and Xv is a position in visual where the
AF wants to go. Then if Xv has better food consistence
than current position of AF, it goes one step toward Xv
which causes change in AF position from X to Xnext, but if
the current position of AF is better than Xv, it continues
searching in its visual area.
THE PROPOSED ALGORITHM
In this section, a new algorithm based on artificial fish
swarm algorithm is presented for optimization in dynamic
environment. In proposed algorithm, parameters,
behaviors and AFSA procedure are modified to be
appropriate for optimization in dynamic environments. In
the proposed algorithm, prey, follow and swarm
behaviors are done for AFs which have main differences
with prey, follow and swarm behaviors in Standard
AFSA[5]. The reason to perform these changes is to adapt
AFSA for working in dynamic environments. In
following, after description of modified artificial fish
swarm algorithm (MAFSA), a new algorithm based on
MAFSA will be presented for dynamic environments.
MAFSA PROCEDURE
In MAFSA, for every AF, prey, follow and swarm
behaviors are performed in each iteration. In Standard
AFSA executing one of the standard swarm and standard
follow behaviors didn’t affect on AFs movement and
huge amount of computations were wasted.
Unlike standard AFSA, in MAFSA, all three
behaviors influence on movement of AFs and swarm
move toward better positions. In MAFSA, first, all AFs
perform prey behavior and their position is updated based
on this behavior procedure. By executing this behavior,
every AF can displace up to try_number times. Then, all
of them with respect to their new position and other AFs’
position which performed prey behavior, execute follow
behavior and all members except the best AF of swarm
move to a new location in direction of moving toward the
best found position by swarm. Then each AF performs
swarm behavior.
CONCLUSION
In this paper, for the first time, a method was proposed
for optimization in dynamic environments based on
artificial fish swarm algorithm. Results on moving peak
benchmark problem were compared with some other
known methods. In the proposed algorithm, it was tried to
satisfy all requirements of dynamic environments.
Experimental results showed that the proposed algorithm
has high ability in locating and tracking optimums,
appropriate convergence rate and local search ability.
Also, there are some relevant works to pursue in the
future. First, some work can be done to set a good
initialization before the algorithm start. Second,
adaptation of Visual with some learning algorithm will
also improve efficiency of the algorithm so much.