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Communication & Space
Sciences Laboratory

Nature Inspired Antenna Design

Radiation Pattern Synthesis via Genetic Algorithms


Arbitrary beam with limited ripple synthesized for two different types of array elements using an adaptive GA. (a) 50-element phased array with directive sources, and (b) 50-element phased array with isotropic sources. 
Insets: optimized amplitude and phase weights for each case.


..: References :..

1-) Adaptive Mutation Parameter Toggling Genetic Algorithm for Phase-only Array Synthesis
by D.W. Boeringer and D.H. Werner

ABSTRACT: A genetic algorithm that speeds convergence for phased array phase-only synthesis by adaptively toggling between nine mutation parameter pairs is illustrated. This adaptive algorithm outperforms any of the corresponding nine static cases where these same mutation parameters are held constant throughout the optimization process.




2-) Genetic Algorithms with Adaptive Parameters for Phased Array Synthesis
by D. W. Boeringer and D. H. Werner
2003 IEEE International Symposium on Antennas and Propagation, Columbus, Ohio, June 22-27.

ABSTRACT: Motivated by Darwin's theories of evolution and the concept of "survival of the fittest", genetic algorithms are commonly used to solve many optimization and synthesis problems. An important issue facing the user is the selection of genetic algorithm parameters, such as mutation rate, mutation range, and number of crossovers. This paper demonstrates a genetic algorithm that simultaneously adapts these parameters during the optimization process, which is shown to outperform its best static counterpart when used to synthesize phased array weights to satisfy a specified far field sidelobe envelope. When compared to conventional static parameter implementations, computation time is saved in two ways: (1) The algorithm converges faster and (2) the need to tune parameters by hand (generally done by repeatedly running the code with different parameter choices) is reduced.




3-) 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 22-27.

ABSTRACT: Particle swarm optimization is a recently invented high-performance 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 amplitude-only, phase-only, 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.




4-) Synthesis of Phased Array Amplitude Weights for Stationary Sidelobe Envelopes Using Genetic Algorithms
by D.W. Boeringer, D.W. Machuga and D.H. Werner
2001 IEEE International Symposium on Antennas and Propagation, Boston, Massachusetts, July 8-13.

ABSTRACT: This paper describes the application of genetic algorithms to the synthesis of phased array amplitude weights to satisfy a particular stationary sidelobe specification. By 'stationary sidelobe specification' we mean that the sidelobe envelope requirement does not move when the main beam is scanned. It is shown that for small scan angles, the given sidelobe requirements can be satisfied with less taper loss and tighter beamwidth than Taylor weighting, by permitting the close-in sidelobes to rise up to the specified envelope. An arbitrary 70 dB notch in the far sidelobes may be included with minimal additional taper loss or beam broadening. A brief description of the genetic algorithm is provided.




5-) Genetically Optimized Two-Dimensional Fractal-Random Arrays
by Joshua S. Petko and D. H. Werner
2003 IEEE AP-S International Symposium on Antennas and Propagation and USNC/URSI North American Radio Science Meeting, URSI Digest, p. 447, Columbus, Ohio, June 22-27, 2003.
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6-) 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 high-performance 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 far-field sidelobe notch, using amplitude-only, phase-only, 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.




7-) Progressive Evolution of Fractal Random Arrays by Generator Mitosis
by Joshua S. Petko and D. H. Werner
2004 IEEE International Symposium on Antennas and Propagation, Monterey, California, June 20-26.




8-) A Simultaneous Parameter Adaptation Scheme for Genetic Algorithms With Application to Phased Array Synthesis
by Daniel W. Boeringer, Douglas H. Werner and David W. Machuga
IEEE Transactions on Antennas and Propagation, Vol. 53, No. 1, pp.356-371, January 2005.

ABSTRACT: Genetic algorithms are commonly used to solve many optimization and synthesis problems. An important issue facing the user is the selection of genetic algorithm parameters, such as mutation rate, mutation range, and number of crossovers. This paper demonstrates a real-valued genetic algorithm that simultaneously adapts several such parameters during the optimization process. This adaptive algorithm is shown to outperform its static counterparts when used to synthesize the phased array weights to satisfy specified far-field sidelobe constraints, and can perform amplitude-only, phase-only, and complex weight synthesis. When compared to conventional static parameter implementations, computation time is saved in two ways: 1) The algorithm converges faster and 2) the need to tune parameters by hand (generally done by repeatedly running the code with different parameter choices) is greatly reduced. By requiring less iteration to solve a given problem, this approach may benefit electromagnetic optimization problems with expensive cost functions, since genetic algorithms generally require many function evaluations to converge. The adaptive process also provides insight into the qualitative importance of parameters, and dynamically adjusting the mutation range is found to be especially beneficial.




9-) The Evolution of Optimal Linear Polyfractal Arrays Using Genetic Algorithms
by Joshua S. Petko and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 53, No. 11, pp.3604-3615, November 2005.

ABSTRACT: Recently, in order to successfully combine the positive attributes of both periodic and random arrays into one design, a novel class of arrays, known as fractal-random arrays, has been introduced. In addition, several researchers have successfully used genetic algorithms, robust global optimization techniques based on natural selection, to find solutions to complex array layout problems. This paper introduces a type of nature-based design process that applies a specially formulated genetic algorithm to evolve optimal layouts of an important subset of fractal-random arrays, which we call polyfractal arrays. Also, this paper discusses
how the underlying self-similar properties of polyfractal arrays can be exploited to increase the speed of the associated array factor calculations. This speed increase dramatically reduces the time required for the genetic algorithm to converge thereby making it possible to effectively evolve optimal array configurations which are much larger than has been previously possible. Moreover, the fractal-random properties of these polyfractal arrays are shown to provide substantially wider bandwidth performance than their conventional counterparts. Finally, several design examples of genetically optimized linear polyfractal arrays with narrow beamwidths, improved sidelobe suppression and wide bandwidths are presented.




10-) Pareto Optimization of Planar Fractal-Random Arrays using the Strength Pareto Evolutionary Algorithm and Generator Duplication
by J. S. Petko and D. H. Werner

ABSTRACT: Many complex design problems require the optimization of more than one parameter. Often, a composite fitness function is created for use in a genetic algorithm by simply setting the fitness function’s value equal to a weighted sum of several parameters. However, the weighted sum is a crude method of finding optimal solutions and limits the results to a small subset of possible solutions. Ideally, when faced with optimization problems of more than one parameter, engineers would like to compare the solutions which lie upon the Pareto front (i.e. the set of all non-dominated solutions). In this paper, we study how to evolve planar fractal-random arrays using the methods developed for linear fractal-random array optimization [1] and apply them to an existing multi-objective genetic algorithm, the Strength Pareto Evolutionary Algorithm [2].




11-) An Autopolyploidy-Based Genetic Algorithm for Enhanced Evolution of Linear Polyfractal Arrays
by J. S. Petko and D. H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 55, No. 3, pp. 583 - 593, March 2007.

ABSTRACT: There has been considerable recent interest in techniques for the optimization of large- antenna arrays. Unfortunately, the successful development of such techniques has been hindered by the large number of independent parameters that must be optimized and the complexity of the calculations needed for the electromagnetic evaluation of large- arrays. One promising new design methodology for large- arrays which has recently been introduced is based on properties of a subset of fractal-random arrays called polyfractal arrays. Polyfractal arrays have many embedded self-similar structures, thereby allowing very large and seemingly complex array layouts to be described with only a small set of independent parameters. In addition, by effectively utilizing the self-similarity of polyfractal arrays, a considerable reduction can be achieved in the amount of time required to evaluate the radiation patterns of largearrays. This paper introduces a type of nature-based design process that applies a specially formulated genetic algorithm (GA) technique to evolve optimal polyfractal array layouts. The most unique aspect of this optimization technique is a new autopolyploidy-based chromosome expansion that maximizes the efficiency of the GAs. Simple polyfractal geometries are used in the initial stage or first epoch of the optimization because the number of independent parameters is small and the computation times are relatively fast. After the optimization converges for the first epoch, more complicated descriptions of these polyfractal arrays are introduced to provide additional independent parameters for the optimizer as it progresses through later epochs of evolution. This process has been shown to be very effective in creating optimized large- arrays, the largest example considered here being a 1616-element linear array with a -24.30-dB sidelobe level and a 0.056° half-power beamwidth.




12-) Pareto Optimization of Thinned Planar Arrays With Elliptical Mainbeams and Low Sidelobe Levels
by J. S. Petko and D. H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 59, No. 5, pp. 1748 - 1751, May 2011.

ABSTRACT: A multi-objective Pareto genetic algorithm design methodology is applied to thinned planar arrays to simultaneously minimize peak side-lobe levels and target an elliptical mainbeam with specific minimum and maximum half-power beamwidths. This new radiation pattern synthesis technique for thinned planar arrays provides antenna engineers with a set of tradeoffs between low side-lobe levels and close adherence to mainbeam design objectives (i.e., the specified half-power beamwidths corresponding to the major and minor axes of an elliptical mainbeam). One Pareto optimization example is presented for a thinned low side-lobe planar array with a desired minimum and maximum beamwidth of 8.4° and 12° respectively. Two designs from the Pareto front are discussed, one with a -20.92 dB side-lobe level and beamwidths between 11.5° and 7.5° and a second with a -18.97 dB side-lobe level with beamwidths between 12 ° and 7.93 °.




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