Nature Inspired Antenna Design
Particle Swarm Optimization of Antenna Elements and Arrays

Swarms of bees, flocks of birds,
schools of fish, and other animals in groups optimize their behavior via personal and group knowledge and information sharing 
Swarm intelligence,
one of the newest optimization techniques, was first introduced by James Kennedy and Russell C. Eberhart in 1995.
Kennedy and Eberhart studied the behavior of individuals from the social point of view:
individual behavior in groups.
PSO simply mimics the success in optimization as a group.
PSO is a stochastic, population based, robust multiobjective search algorithm. It does not require prior knowledge of the shape of the search space.
The algorithm is very simple and easy to implement and PSO has recently been shown to be useful for solving complex electromagnetics and antenna optimization problems.
..: References :..
1)
A Comparison of Particle Swarm Optimization and Genetic Algorithms for a Phased Array Synthesis Problem
by D. W. Boeringer and D. H. Werner
2003 IEEE International Symposium on Antennas and Propagation, Columbus, Ohio, June 2227.
ABSTRACT: Particle swarm optimization is a recently invented highperformance
optimizer that possesses several highly desirable attributes, including
the fact that the basic algorithm is very easy to understand and implement.
It is similar in some ways to genetic algorithms or evolutionary algorithms,
but generally requires only a few lines of code. In this paper, a particle
swarm optimizer is implemented and compared to a genetic algorithm for
phased array synthesis of a far field sidelobe notch, using amplitudeonly,
phaseonly, and complex tapering. The results show that some optimization
scenarios are better suited to one method versus the other (i.e. particle
swarm optimization performs better in some cases while genetic algorithms
perform better in others), which implies that the two methods traverse
the problem hyperspace differently. Although simple, the particle swarm
optimizer shows good possibilities for electromagnetic optimization.
2)
Particle Swarm Optimization Versus Genetic Algorithms for Phased Array Synthesis
by Daniel W. Boeringer and Douglas H. Werner
ABSTRACT: Particle swarm optimization is a recently invented highperformance
optimizer that is very easy to understand and implement. It is similar
in some ways to genetic algorithms or evolutionary algorithms, but requires
less computational bookkeeping and generally only a few lines of code.
In this paper, a particle
swarm optimizer is implemented and compared to a genetic algorithm for
phased array synthesis of a farfield sidelobe notch, using amplitudeonly,
phaseonly, and complex tapering. The results show that some optimization
scenarios are better suited to one method versus the other (i.e., particle
swarm optimization performs better in some cases while genetic algorithms
perform better in others), which implies that the two methods traverse
the problem hyperspace differently. The particle swarm optimizer shares
the ability of the genetic algorithm to handle arbitrary nonlinear cost
functions, but with a much simpler implementation it clearly demonstrates
good possibilities for widespread use in electromagnetic optimization.
3)
Particle Swarm Optimization of a Modified Bernstein Polynomial for Conformal Array Excitation Synthesis
by D. W. Boeringer and D. H. Werner
2004 IEEE International Symposium on Antennas and Propagation, Monterey, California, June 2026.
ABSTRACT: Bernstein polynomials are well known in the computer
graphics community as the basis functions of Bézier curves. Like
popular amplitude weighting functions such as Taylor weights, Bernstein
polynomials are nonnegative and decay smoothly away from a single maximum.
In this paper a modified Bernstein polynomial is introduced, defined with
just four parameters for ease and speed of optimization. A particle swarm
optimizer sets these four parameters to realize low sidelobe array amplitude
distributions for a conformal array at various scan angles. This yields
a novel method of generating realistic aperture weights, using the relatively
new technique of particle swarm optimization.
4)
EfficiencyConstrained Particle Swarm Optimization of a Modified Bernstein Polynomial for Conformal Array Excitation Amplitude Synthesis
by D. W. Boeringer and D. H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 53, No. 8, pp. 26622673, August 2005.
ABSTRACT: As various enabling technologies advance, conformal
phased arrays are finding more numerous applications. Because a
conformal array is curved, new far field pattern behaviors emerge
and many of the traditional linear and planar phased array synthesis
methods are not valid. This paper starts by reviewing the
equations for the far field of a curved phased array, and provides
a generalized definition of aperture efficiency appropriate for conformal arrays. A modified Bernstein polynomial, defined with just five parameters, is introduced which provides a flexible method to specify a variety of smooth unimodal amplitude distributions that are shown to give good sidelobe levels and aperture efficiencies.
By using particle swarm optimization of the modified Bernstein polynomial parameters constrained to provide a specified aperture efficiency, a family of aperture distributions and corresponding far field patterns is produced that allows aperture efficiency to be traded for sidelobe level.
5)
Miniature Threeelement Stochastic YagiUda Array Optimization via Particle Swarm Intelligence
by Zikri Bayraktar, P. L. Werner, and D. H. Werner
ABSTRACT: Particle Swarm Optimization (PSO) is a populationbased heuristic global search algorithm,
which can be successfully applied to multiobjective optimization problems. In essence, PSO mimics the collective
learning of individuals when they are in groups. Recently, PSO has been introduced to the electromagnetics community
and shown to be very effective for optimization of complex antenna engineering problems [1, 2]. The purpose of this paper
is to investigate the performance of PSO when applied to the optimization and miniaturization of threeelement YagiUda arrays.
6)
The Design of Miniature ThreeElement Stochastic YagiUda Arrays Using Particle Swarm Optimization
by Zikri Bayraktar, P. L. Werner and D. H. Werner
IEEE Antennas and Wireless Propagation Letters. Volume 5, Issue 1, pp. 22  26, Dec 2006.
ABSTRACT: A fixed grid structure of reduced length is employed to generate threeelement miniature stochastic YagiUda arrays.
Particle swarm optimization (PSO) is utilized to alter the shape and the element distances for optimum forward gain, good
fronttoback ratio, and 2:1 or better voltage standing wave ratio (VSWR). Simulation results of PSO are compared with binary valued
genetic algorithm (GA) optimized designs and with a conventional threeelement YagiUda array.
7)
Bézier Representations for the Multiobjective Optimization of Conformal Array Amplitude Weights
by Daniel W. Boeringer and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 54, No. 7, pp. 19641970, July 2006.
ABSTRACT: For conformal phased arrays, generally the excitation amplitude of the array elements must be
adjusted in order to maintain low sidelobes as the array is scanned. While the desired phase weights for maximum
gain are deterministically set by the array geometry and scan angle, the representation of optimum low sidelobe
amplitude weights remains an open problem. Following up on prior work using the efficiencyconstrained optimization
of a modified Bernstein polynomial for low sidelobe conformal array synthesis, a Bézier surface is shown to provide a good representation
of the optimized amplitude weights with a reduced number of
parameters, while demonstrating constraint multiobjective optimization
of conformal aperture efficiency versus sidelobe level.
These results are extended to include a Bézier volume representation
for the multiobjective optimization of conformal aperture efficiency versus both sidelobe level and scan angle.
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