24-01-2013, 01:00 PM
Genetic Algorithm Optimization for Circular Microstrip Antenna
[attachment=48287]
Abstract
This paper discusses the problem of optimization in general, and in particular for circular microstrip
antenna. The general non specialized method known as Genetic Algorithm is described and applied to a specific
case. This method is particularly effective when the goal is to find an approximate global maxima in high
dimension, multi-modal function domains in a near optimal manner. The simulation results show the advantage
of Genetic Algorithm.
Introduction
The Research in the microstrip antenna’s domain have
been developed during the last years with the
miniaturization of the electronic systems and the
advent of data processing. These antennas were
largely used in spatial telecommunications, the
mobile communications, the radars, …
In the microstrip antenna’s domain, several numerical
tools for analysis problems have been developed.
They have been classified in two categories : the
rigorous approaches (integral equations, finite
difference time domain (FDTD)) [1], and the
approximated ones (cavity method). In this paper we
realize the optimization of circular microstrip antenna
responding to some constraints (frequency of the
fundamental mode, band pass) some more advanced
techniques, which give a global minimum, have been
retained. One of these new approaches, more and
more used, based on genetic algorithm (GA) method
[2] is well suited to our needs. The GA method, which
is able to optimize different natural variables, is the
most versatile approach. It can optimize the physical
(dimension of the patch, thickness of substrate,…)
and electric parameters (relative permittivity).
In this paper, we will use the DERNERYD model [3]
as an analysis method. Some results will be presented
in this article, and we will show the performance of
the proposed method.
Mutation
Mutation consists to modify in a random way and
with a small probability (0.01-0.1) the bit value of a
chromosome. In other words, a “1” becomes a “0”
and a “0” becomes a “1”.
Application
In order to show the feasibility of our approach, the
case of a circular microstrip antenna form was
studied. It is about an antenna of radius a, thickness
H posed on a substrate of permittivity εR
The objective is to find the values of the three
parameters : radius a, thickness H and εR , so that the
antenna satisfies the constraint (a resonant frequency
equal to 5 Ghz).
This research will be done by genetic algorithm,
coupled with the model of analysis given by
DERNERYD [3, 4].
Selection, reproduction
Each of the individuals is selected by its fitness value.
Reproduction consists in duplicating each individual
in ralation to the average of the performances for all
the chromosomes of population. Then individuals
which give the best results have a good probability to
be selected for the next generation.
Crossover
After the reproduction step, a crossover allows a
generation of new individuals. The crossover step
consists to cut two chromosomes, named parents, on a
random place, then the end of these two individuals
string is reversed and two chromosomes are created
and named children.
Conclusion
This article presents an approach allowing the
optimization of microstrip antennas. The technique
consists with used the genetic algorithm to determine
the optimal parameters of a microstrip antenna, with
circular radiant element, feeded with coaxial probe.
This approach has the advantage of escaping the local
solutions, it tend to produce global optimal results
without requiring a great deal of information about
the solution domain. However, the choice of the
function fitness is delicate, because it is the only link
between the physical problem to optimize and the
genetic algorithm.
[attachment=48287]
Abstract
This paper discusses the problem of optimization in general, and in particular for circular microstrip
antenna. The general non specialized method known as Genetic Algorithm is described and applied to a specific
case. This method is particularly effective when the goal is to find an approximate global maxima in high
dimension, multi-modal function domains in a near optimal manner. The simulation results show the advantage
of Genetic Algorithm.
Introduction
The Research in the microstrip antenna’s domain have
been developed during the last years with the
miniaturization of the electronic systems and the
advent of data processing. These antennas were
largely used in spatial telecommunications, the
mobile communications, the radars, …
In the microstrip antenna’s domain, several numerical
tools for analysis problems have been developed.
They have been classified in two categories : the
rigorous approaches (integral equations, finite
difference time domain (FDTD)) [1], and the
approximated ones (cavity method). In this paper we
realize the optimization of circular microstrip antenna
responding to some constraints (frequency of the
fundamental mode, band pass) some more advanced
techniques, which give a global minimum, have been
retained. One of these new approaches, more and
more used, based on genetic algorithm (GA) method
[2] is well suited to our needs. The GA method, which
is able to optimize different natural variables, is the
most versatile approach. It can optimize the physical
(dimension of the patch, thickness of substrate,…)
and electric parameters (relative permittivity).
In this paper, we will use the DERNERYD model [3]
as an analysis method. Some results will be presented
in this article, and we will show the performance of
the proposed method.
Mutation
Mutation consists to modify in a random way and
with a small probability (0.01-0.1) the bit value of a
chromosome. In other words, a “1” becomes a “0”
and a “0” becomes a “1”.
Application
In order to show the feasibility of our approach, the
case of a circular microstrip antenna form was
studied. It is about an antenna of radius a, thickness
H posed on a substrate of permittivity εR
The objective is to find the values of the three
parameters : radius a, thickness H and εR , so that the
antenna satisfies the constraint (a resonant frequency
equal to 5 Ghz).
This research will be done by genetic algorithm,
coupled with the model of analysis given by
DERNERYD [3, 4].
Selection, reproduction
Each of the individuals is selected by its fitness value.
Reproduction consists in duplicating each individual
in ralation to the average of the performances for all
the chromosomes of population. Then individuals
which give the best results have a good probability to
be selected for the next generation.
Crossover
After the reproduction step, a crossover allows a
generation of new individuals. The crossover step
consists to cut two chromosomes, named parents, on a
random place, then the end of these two individuals
string is reversed and two chromosomes are created
and named children.
Conclusion
This article presents an approach allowing the
optimization of microstrip antennas. The technique
consists with used the genetic algorithm to determine
the optimal parameters of a microstrip antenna, with
circular radiant element, feeded with coaxial probe.
This approach has the advantage of escaping the local
solutions, it tend to produce global optimal results
without requiring a great deal of information about
the solution domain. However, the choice of the
function fitness is delicate, because it is the only link
between the physical problem to optimize and the
genetic algorithm.