# A New Optimization Algorithm Based on the Fungi Kingdom Expansion Behavior for Antenna Applications

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## Abstract

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## 1. Introduction

## 2. Fungi Kingdom Expansion Behavior

- (a)
- Immobile biomass expansion: which represents the materials that are used to build the hyphae and the tubes inside them.
- (b)
- Mobile biomass expansion: this part represents the material flowing through the tubes of the hyphae to provide nutrition to the terminal of the hyphae.

## 3. Implementation of the Fungi Kingdom Expansion (FKE) Algorithm

**i**-th fungus where $i=\left[1,\text{}2,\text{}\dots ,\text{}Pop\right]$, and $Pop$ represents the population size of the fungi kingdom. The initial population distribution can be determined by randomly ($Rand$) spreading spores within the maximum allowed distance (${x}_{max}$) and the minimum allowed distance (${x}_{min}$) as given below:

**Mode 1:**Chaotic Expansion Mode

**Mode 2:**Deterministic Expansion Mode

**Mode 3:**Random Dispersion

Algorithm 1 Fungi kingdom Expansion |

1: Set the moisture-temperature range and the location range. |

2: Set the number of hyphae |

3: Set the fungi kingdom size and the dimension. |

4: Set the random dispersion number (DIS). |

5: Initialize the location of each fungus from Equation (1). |

6: Subject the locations to a certain fitness function. |

7: Determine the current best location. |

8: Apply Equation (3) for the entire population and entire iterations. |

9: While (iter < itermax) |

10: % The immobile mass expansion |

11: For i = 1: fungi kingdom size |

12: For j = 1: number of hyphae |

13: Apply Equation (2) with the aid of Equation (3) |

14: End j |

15: Subject the hyphae to a fitness function then pick the best hyphen only. |

16: % The mobile mass expansion |

17: Compute (MT) from Equation (6) |

18: Compute (cond) from Equation (5) |

19: Apply Equation (4) |

20: End i |

21: Subject the new locations to the fitness function |

22: If the new best location is better than the older one |

23: The new best is the global best |

24: End If |

25: Randomly spread the worst (DIS) locations |

26: Subject the new population to the fitness function to determine the global best. |

27: End While |

## 4. Engineering Applications: Antenna Array Beamforming

**H**denotes the Hermitian transpose, and $\mathit{a}\left(\mathsf{\Phi}\right)$ represents the steering vector of the antenna at any azimuth angle ($\mathsf{\Phi}$):

- Array size is 20-element.
- Fungi population size is 50.
- $M{T}_{min}=20$ and $M{T}_{max}=60$.
- Immobile expansion factor $IEF=0.01$.
- Number of hyphae $hyp=10$.
- Fungi dispersion = 5.
- Number of runs = 30.

- Linear Optimization: by optimizing the magnitude of the weight vector.
- Nonlinear optimization: by optimization the inter-element spacing d.

#### 4.1. Side Lobe Reduction

#### 4.1.1. Side Lobe Reduction by Optimizing the Excitation Magnitude

#### 4.1.2. Side Lobe Reduction by Optimizing the Enter Element Spacing

#### 4.2. Flat-Top Pattern

#### 4.2.1. Step 1: Flat-Top Pattern Regardless the SLR

#### 4.2.2. Step 2: Flat-Top Pattern with Reduced Side Lobes

#### 4.3. Triangular Beam Pattern

#### 4.3.1. Step 1: Triangular Beam Regardless the Side Lobe Level

#### 4.3.2. Step 2: Triangular Pattern with Reduced Side Lobes

#### 4.4. Anti-Jamming System

## 5. Results Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**The normalized array factor for 2- element array antenna (

**a**) using uniform distribution and (

**b**) using FKE optimization.

**Figure 4.**The normalized array factor for 20 element array antenna by optimizing the inter-element spacing of the array antenna using FKE algorithm.

**Figure 5.**The normalized flat-top array factor for 20 element array antenna by modifying the excitation amplitude of the array antenna using FKE algorithm.

**Figure 6.**The normalized array factor for 20 element array antenna by modifying the inter-element spacing of the array antenna using FKE.

**Figure 7.**The normalized triangular-shaped array factor for 20 element array antenna by modifying the excitation amplitude of the array antenna using FKE.

**Figure 8.**The normalized triangular array factor for 20 element array antenna by modifying the inter-element spacing of the array antenna using FKE algorithm.

**Figure 9.**Smart antenna system with M-antenna elements [39].

**Figure 10.**The normalized array factor for 20-element anti-jamming antenna by optimizing the excitation amplitude of the array antenna using FKE algorithm.

**Table 1.**The success rate (SR) of the proposed FKE algorithm, PSO, and GA for the sidelobe reduction using the magnitude of the excitation current (No. of runs = 30).

Algorithm | Best SLR (dB) | SR % |
---|---|---|

FKE (30 iterations) | 25.6023 | 100 |

PSO (300 iterations) | 24.6177 | 73.33 |

GA (300 iterations) | 24.8263 | 66.67 |

Element No. | Excitation Magnitude |
---|---|

1 | 0.3963 |

2 | 0.3788 |

3 | 0.4980 |

4 | 0.4905 |

5 | 0.5334 |

6 | 0.7778 |

7 | 0.8593 |

8 | 0.8714 |

9 | 0.9791 |

10 | 0.9578 |

11 | 0.9376 |

12 | 1.0000 |

13 | 0.9482 |

14 | 0.7375 |

15 | 0.8107 |

16 | 0.6890 |

17 | 0.6734 |

18 | 0.3582 |

19 | 0.4529 |

20 | 0.4590 |

**Table 3.**The success rate (SR) of the proposed FKE algorithm, PSO, and GA for the sidelobe reduction using the inter-element spacing (No. of runs = 30).

Algorithm | Best SLR (dB) | SR % |
---|---|---|

FKE (30 iterations only) | 24.0017 | 100 |

PSO (300 iterations) | 22.5721 | 40 |

GA (300 iterations) | 22.3245 | 33.33 |

**Table 4.**The best normalized value of inter-element spacing with respect to the wavelength (λ) using FKE.

Element No. | Normalized Element Spacing |
---|---|

1–2 | 0.8138 |

2–3 | 0.7410 |

3–4 | 0.5958 |

4–5 | 0.3971 |

5–6 | 0.4453 |

6–7 | 0.4016 |

7–8 | 0.3914 |

8–9 | 0.3398 |

9–10 | 0.4283 |

10–11 | 0.2739 |

11–12 | 0.3961 |

12–13 | 0.3602 |

13–14 | 0.3708 |

14–15 | 0.3773 |

15–16 | 0.4626 |

16–17 | 0.5098 |

17–18 | 0.4441 |

18–19 | 0.6857 |

19–20 | 0.7318 |

**Table 5.**The success rate (SR) of the proposed FKE algorithm, PSO, and GA for the flat-top pattern. (No. of runs = 30).

Flat-Top Regardless SLR | Flat-Top with Reduced Side Lobes | ||||
---|---|---|---|---|---|

Algorithm | Best Flat-Top Ripple (dB) | SR % | Algorithm | Best SLR (dB) | SR % |

FKE 50 iterations only | 0.1044 | 100 | FKE 30 iterations only | 23.4612 | 100 |

PSO 500 iterations | 0.2785 | 56.67 | PSO 300 iterations | 21.6342 | 43.33 |

GA 500 iterations | 0.2255 | 46.67 | GA 300 iterations | 20.8564 | 30 |

**Table 6.**The best normalized value of the amplitude of the excitation current and element spacing with respect to λ using FKE for flat-top pattern.

Flat-Top Regardless SLR | Flat-Top with Reduced Side Lobes | ||
---|---|---|---|

Element No. | Excitation Amplitude | Element No. | Normalized Element Spacing |

1 | −0.0126 | 1–2 | 0.3906 |

2 | −0.3447 | 2–3 | 0.6579 |

3 | −0.0309 | 3–4 | 0.6475 |

4 | 0.6800 | 4–5 | 0.4998 |

5 | 0.8999 | 5–6 | 0.2645 |

6 | 0.7992 | 6–7 | 0.3324 |

7 | 1.0000 | 7–8 | 0.3306 |

8 | 0.9985 | 8–9 | 0.4204 |

9 | 0.9001 | 9–10 | 0.4749 |

10 | 0.2385 | 10–11 | 0.4494 |

11 | −0.1494 | 11–12 | 0.4343 |

12 | −0.2813 | 12–13 | 0.2418 |

13 | 0.0128 | 13–14 | 0.2037 |

14 | −0.3478 | 14–15 | 0.6407 |

15 | −0.2256 | 15–16 | 0.3431 |

16 | 0.3540 | 16–17 | 0.5052 |

17 | 0.1807 | 17–18 | 0.1562 |

18 | −0.1175 | 18–19 | 0.4494 |

19 | 0.3787 | 19–20 | 0.1466 |

20 | −0.3687 |

**Table 7.**The success rate (SR) of the proposed FKE algorithm, PSO, and GA for the triangular pattern. (No. of runs = 30).

Triangular Pattern Regardless SLR | Triangular Pattern with Reduced Side Lobes | ||||
---|---|---|---|---|---|

Algorithm | Best Triangular Pattern Ripple (dB) | SR % | Algorithm | Best SLR (dB) | SR % |

FKE (50 iterations only) | 0.6345 | 100 | FKE 30 iterations only | 19.0123 | 100 |

PSO (500 iterations) | 0.7353 | 96.67 | PSO 300 iterations | 20.2093 | 30 |

GA (500 iterations) | 0.6453 | 93.33 | GA 300 iterations | 19.5364 | 36.67 |

**Table 8.**The best normalized value of the amplitude of the excitation current and element spacing with respect to λ using FKE for triangular pattern.

Triangular Pattern Regardless SLR | Triangular Pattern with Reduced Side Lobes | ||
---|---|---|---|

Element No. | Excitation Amplitude | Element No. | Normalized Element Spacing |

1 | 0.8004 | 1–2 | 0.3906 |

2 | 0.2412 | 2–3 | 0.6579 |

3 | −0.2876 | 3–4 | 0.6475 |

4 | −0.2911 | 4–5 | 0.4998 |

5 | 0.1939 | 5–6 | 0.2645 |

6 | 0.0115 | 6–7 | 0.3324 |

7 | −0.0081 | 7–8 | 0.3306 |

8 | 0.3175 | 8–9 | 0.4204 |

9 | 0.4632 | 9–10 | 0.4749 |

10 | 0.6449 | 10–11 | 0.4494 |

11 | 0.9564 | 11–12 | 0.4343 |

12 | 1.0000 | 12–13 | 0.2418 |

13 | 0.6030 | 13–14 | 0.2037 |

14 | 0.8111 | 14–15 | 0.6407 |

15 | 0.4692 | 15–16 | 0.3431 |

16 | −0.1326 | 16–17 | 0.5052 |

17 | −0.0892 | 17–18 | 0.1562 |

18 | 0.3432 | 18–19 | 0.4494 |

19 | 0.3022 | 19–20 | 0.1466 |

20 | 0.3836 |

**Table 9.**The success rate (SR) of the proposed FKE algorithm, PSO, and GA for the anti-jamming smart antenna system (No. of runs = 30).

Algorithm | SR % |
---|---|

FKE (30 iterations only) | 100 |

PSO (300 iterations) | 100 |

GA (300 iterations) | 100 |

**Table 10.**The best normalized value of the magnitude of the excitation current using FKE algorithm for anti-jamming optimization.

Element No. | Excitation Amplitude |
---|---|

1 | 0.2876 |

2 | 0.5281 |

3 | 0.7154 |

4 | 1.0000 |

5 | 0.6386 |

6 | 0.7782 |

7 | 0.5270 |

8 | 0.5188 |

9 | 0.5191 |

10 | 0.3633 |

11 | 0.3661 |

12 | 0.3836 |

13 | 0.4718 |

14 | 0.4543 |

15 | 0.7104 |

16 | 0.7682 |

17 | 0.9019 |

18 | 0.9885 |

19 | 0.4997 |

20 | 0.4370 |

**Table 11.**The average CPU time, average memory size, and the average SR of FKE algorithm compared to that of the PSO and GA.

Algorithm | Average CPU Time (s) | Average Memory Size (byte) | Average SR % |
---|---|---|---|

FKE (30 iterations) | 30.863 | 4,046,848 | 100 |

PSO (300 iterations) | 31.387 | 2,072,576 | 62.857 |

GA (300 iterations) | 28.614 | 1,975,724 | 58.906 |

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## Share and Cite

**MDPI and ACS Style**

Alnahwi, F.M.; Al-Yasir, Y.I.A.; Sattar, D.; Ali, R.S.; See, C.H.; Abd-Alhameed, R.A.
A New Optimization Algorithm Based on the Fungi Kingdom Expansion Behavior for Antenna Applications. *Electronics* **2021**, *10*, 2057.
https://doi.org/10.3390/electronics10172057

**AMA Style**

Alnahwi FM, Al-Yasir YIA, Sattar D, Ali RS, See CH, Abd-Alhameed RA.
A New Optimization Algorithm Based on the Fungi Kingdom Expansion Behavior for Antenna Applications. *Electronics*. 2021; 10(17):2057.
https://doi.org/10.3390/electronics10172057

**Chicago/Turabian Style**

Alnahwi, Falih M., Yasir I. A. Al-Yasir, Dunia Sattar, Ramzy S. Ali, Chan Hwang See, and Raed A. Abd-Alhameed.
2021. "A New Optimization Algorithm Based on the Fungi Kingdom Expansion Behavior for Antenna Applications" *Electronics* 10, no. 17: 2057.
https://doi.org/10.3390/electronics10172057