# Antenna Design by Means of the Fruit Fly Optimization Algorithm

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## Abstract

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## 1. Introduction

## 2. Description of the Algorithm

- The swarm is positioned at the location $({X}^{\left(0\right)};{Y}^{\left(0\right)})$, with a given smell concentration $Smel{l}^{\left(0\right)}$. For each fly i in the swarm:
- The fly moves around a random distance, searching for food by using the osphresis:$${X}^{\left(i\right)}={X}^{\left(0\right)}+{R}^{X},{Y}^{\left(i\right)}={Y}^{\left(0\right)}+{R}^{Y},$$
- The smell concentration judgement value is defined as the reciprocal of the distance to the origin of coordinates:$${S}^{\left(i\right)}=\frac{1}{\sqrt{{\left({X}^{\left(i\right)}\right)}^{2}+{\left({Y}^{\left(i\right)}\right)}^{2}}}$$
- Compute the smell concentration of the fly’s current location by using the smell concentration function (equivalent to a fitness function):$$Smel{l}^{\left(i\right)}=Function({S}^{\left(i\right)})$$

- Look for the specific fly I with the best smell concentration. If this value is better than the value in the initial location of the swarm $({X}^{\left(0\right)};{Y}^{\left(0\right)})$ then move the swarm towards the position of the fly I by using the vision sense:$${X}^{\left(0\right)}={X}^{\left(I\right)},{Y}^{\left(0\right)}={Y}^{\left(I\right)}$$

## 3. Numerical Examples

#### 3.1. Application to Array Factor Synthesis

- Flies per swarm: 20.
- Total smell function evaluations: 5000.

#### 3.2. Application to Horn Antennas

- Radii: 0.15 mm
- Lengths: $0.15\xb7{\lambda}_{0}$
- Angle: ${0.25}^{\circ}$

#### 3.3. Statistical Analysis of the Results

#### 3.4. Comparison with a Genetic Algorithm

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

FOA | Fruit fly Optimization Algorithm |

SLL | Side Lobe Level |

TE | Transverse Electric |

TM | Transverse Magnetic |

GA | Genetic Algorithm |

## References

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**Figure 9.**Normalized radiation pattern at 94 GHz of the of the optimized Potter Horn (Diagonal Plane, Copolar Component).

**Figure 10.**Normalized radiation pattern at 94 GHz of the of the optimized Potter Horn (Diagonal Plane, Crosspolar Component).

**Figure 17.**Comparison of the results provided by the implemented FOA and a commercial implementation of a GA. ${\overline{Smell}}_{FOA}$ = 1.73, ${\sigma}_{FOA}$ = 0.41, ${\overline{Smell}}_{GA}$ = 1.71, ${\sigma}_{GA}$ = 0.49. Mean value (${\overline{Smell}}_{x}$) and variance (${\sigma}_{x}$) of the Smell function results.

Parameter | Initial / Dolph | FOA |
---|---|---|

${d}_{1}$ | $0.250{\lambda}_{0}$ | $0.2029{\lambda}_{0}$ |

${d}_{2}$ | $0.750{\lambda}_{0}$ | $0.5260{\lambda}_{0}$ |

${d}_{3}$ | $1.250{\lambda}_{0}$ | $1.0812{\lambda}_{0}$ |

${d}_{4}$ | $1.750{\lambda}_{0}$ | $1.6361{\lambda}_{0}$ |

${d}_{5}$ | $2.250{\lambda}_{0}$ | $2.2917{\lambda}_{0}$ |

Parameter | Initial | FOA | Simplex |
---|---|---|---|

${d}_{1}$ | $0.250{\lambda}_{0}$ | $0.0789{\lambda}_{0}$ | $0.2710{\lambda}_{0}$ |

${d}_{2}$ | $0.750{\lambda}_{0}$ | $0.3149{\lambda}_{0}$ | $0.7540{\lambda}_{0}$ |

${d}_{3}$ | $1.250{\lambda}_{0}$ | $0.8228{\lambda}_{0}$ | $1.2320{\lambda}_{0}$ |

${d}_{4}$ | $1.750{\lambda}_{0}$ | $0.7631{\lambda}_{0}$ | $1.6840{\lambda}_{0}$ |

${d}_{5}$ | $2.250{\lambda}_{0}$ | $1.4619{\lambda}_{0}$ | $2.2580{\lambda}_{0}$ |

Parameter | Initial | FOA | Simplex |
---|---|---|---|

${r}_{2}$ | 1.50 mm | 1.70 mm | 1.64 mm |

${L}_{2}$ | 1.60 mm | 6.11 mm | 2.78 mm |

${r}_{3}$ | 1.95 mm | 2.44 mm | 2.13 mm |

${L}_{3}$ | 3.99 mm | 2.64 mm | 2.76 mm |

$\theta $ | ${6.5}^{\circ}$ | ${5.29}^{\circ}$ | ${7.72}^{\circ}$ |

Parameter | Lower Boundary | Upper Boundary |
---|---|---|

${r}_{2}$ | 1.13 mm | 9.57 mm |

${L}_{2}$ | 1.00 mm | 10.00 mm |

${r}_{3}$ | 1.13 mm | 9.57 mm |

${L}_{3}$ | 1.00 mm | 10.00 mm |

$\theta $ | ${2.0}^{\circ}$ | ${10.0}^{\circ}$ |

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**MDPI and ACS Style**

Polo-López, L.; Córcoles, J.; Ruiz-Cruz, J.A.
Antenna Design by Means of the Fruit Fly Optimization Algorithm. *Electronics* **2018**, *7*, 3.
https://doi.org/10.3390/electronics7010003

**AMA Style**

Polo-López L, Córcoles J, Ruiz-Cruz JA.
Antenna Design by Means of the Fruit Fly Optimization Algorithm. *Electronics*. 2018; 7(1):3.
https://doi.org/10.3390/electronics7010003

**Chicago/Turabian Style**

Polo-López, Lucas, Juan Córcoles, and Jorge A. Ruiz-Cruz.
2018. "Antenna Design by Means of the Fruit Fly Optimization Algorithm" *Electronics* 7, no. 1: 3.
https://doi.org/10.3390/electronics7010003