### Abstract

There has been considerable recent interest in techniques for the optimization of large-N 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-N arrays. One promising new design methodology for large-N 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 large-N arrays. 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-N 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.

Original language | English (US) |
---|---|

Pages (from-to) | 583-593 |

Number of pages | 11 |

Journal | IEEE Transactions on Antennas and Propagation |

Volume | 55 |

Issue number | 3 I |

DOIs | |

State | Published - Mar 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

}

*IEEE Transactions on Antennas and Propagation*, vol. 55, no. 3 I, pp. 583-593. https://doi.org/10.1109/TAP.2007.891507

**An autopolyploidy-based genetic algorithm for enhanced evolution of linear polyfractal arrays.** / Petko, Joshua S.; Werner, Douglas H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An autopolyploidy-based genetic algorithm for enhanced evolution of linear polyfractal arrays

AU - Petko, Joshua S.

AU - Werner, Douglas H.

PY - 2007/3/1

Y1 - 2007/3/1

N2 - There has been considerable recent interest in techniques for the optimization of large-N 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-N arrays. One promising new design methodology for large-N 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 large-N arrays. 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-N 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.

AB - There has been considerable recent interest in techniques for the optimization of large-N 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-N arrays. One promising new design methodology for large-N 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 large-N arrays. 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-N 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.

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U2 - 10.1109/TAP.2007.891507

DO - 10.1109/TAP.2007.891507

M3 - Article

AN - SCOPUS:34047196043

VL - 55

SP - 583

EP - 593

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 3 I

ER -