D.W. Boeringer

Particle swarm optimization versus genetic algorithms for phased array synthesis

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.

Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning

The scan volume of a thinned periodic linear phased array is proportional to the spacing between array elements. As the spacing between elements increases beyond a half wavelength, the scan range of the array will be significantly reduced due to the appearance of grating lobes. This paper investigates a method of creating thinned aperiodic linear phased arrays through the application of genetic algorithms that will suppress the grating lobes with increased steering angles. In addition, the genetic algorithm will place restrictions on the driving-point impedance of each element so that they are well behaved during scanning. A genetic algorithm approach is also introduced for the purpose of evolving an optimal set of matching networks. Finally, an efficient technique for evaluating the directivity of an aperiodic array of half-wave dipoles is developed for use in conjunction with genetic algorithms.

A simultaneous parameter adaptation scheme for genetic algorithms with application to phased array synthesis

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.

Efficiency-constrained particle swarm optimization of a modified bernstein polynomial for conformal array excitation amplitude synthesis

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.

A comparison of particle swarm optimization and genetic algorithms for a phased array synthesis problem

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. 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 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.

Bezier representations for the multiobjective optimization of conformal array amplitude weights

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 efficiency-constrained optimization of a modified Bernstein polynomial for low sidelobe conformal array synthesis, a Bezier surface is shown to provide a good representation of the optimized amplitude weights with a reduced number of parameters, while demonstrating e-constraint multi-objective optimization of conformal aperture efficiency versus sidelobe level. These results are extended to include a Bezier volume representation for the multiobjective optimization of conformal aperture efficiency versus both sidelobe level and scan angle.

Thinned aperiodic linear phased array optimization for reduced grating lobes during scanning with input impedance bounds

The scan volume of a thinned periodic linear phased array is proportional to the spacing between array elements. As the spacing between elements increases beyond a half wavelength, the scan range of the array will be significantly reduced due to the appearance of grating lobes. This paper investigates a method of creating thinned aperiodic, linear phased arrays through genetic algorithms that suppress the grating lobes with increased steering angles. In addition the genetic algorithm places restrictions on the driving point impedance of each element so that they are well behaved during scanning.

Particle swarm optimization of a modified Bernstein polynomial for conformal array excitation synthesis

Bernstein polynomials are well known in the computer graphics community as the basis functions of Bezier curves. Like popular amplitude weighting functions, such as Taylor weights, Bernstein polynomials are nonnegative and decay smoothly from a single maximum. 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 array sidelobe 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.

Matching network design using genetic algorithms for impedance constrained thinned arrays

This paper investigates a technique for optimizing matching networks for thinned aperiodic dipole arrays to achieve a 2:1 or better VSWR for each antenna element over the entire scan range of the array. The thinned array is optimized via a genetic algorithm to have a suppressed grating lobe over the scan range of the array. In addition, the genetic algorithm places restrictions on the driving point impedance of each element so that they are well behaved during scanning. The impedance constraint allows a three element reactive matching network to be optimized for each element of the array using a separate genetic algorithm.

Bezier surface optimization of amplitude weights for a curtain array

A multilayer dipole curtain array topology is presented and amplitude weights are synthesized to meet a specified sidelobe envelope. While direct optimization of the amplitude weights with a genetic algorithm meets the sidelobe requirement, the resulting optimized weights are observed to be highly oscillatory, which can lead to practical implementation problems. Better results are found when the genetic algorithm is used to synthesize the control points of Bezier surfaces, which are then sampled to produce aperture weights. The smoothing properties of the Bezier formulation encourage smooth continuous weighting functions and the genetic algorithm operates efficiently because of the close geometric proximity of the synthesized control points to the resulting curve. The method can be extended to arbitrary arrays, including conformal and volumetric arrays