# MAOA: A Swift and Effective Optimization Algorithm for Linear Antenna Array Design
## 4 Results and Discussion
### Statistical Validation  
The Wilcoxon rank sum test [33] is applied for estimating the level of difference in two independent samples, this then used here to analyze the authenticity of the proposed MAOA. Here, the optimization algorithm is carried out for 15 independent runs with 1000 iteration on each run, using this test the performance of the proposed algorithm is analyzed as compared to other applied algorithms. The level of significance to perform this test is decided as 5%. The outcome of the test for the ten different designs of LAA has been outlined in Table 15. The outcome of this analysis reveals that MAOA algorithm outperforms the other intelligent optimization algorithms (ALO, AOA, PSO, GWO, GOA, SMO, BBO, DA, STO, and DBO). In most cases, higher R+ values are provided by MAOA indicating its superior performance over the other algorithm. In some cases, R- is higher for MAOA, but in overall comparison MAOA provides better optimal values of position and current amplitude than other algorithms. Figures 25 and 26 show the results of [PERSON] ranking tests for all the optimization algorithms across all ten designs of LAA with an overall confidence level of 95%. The results show that the proposed MAOA presents good ranking in most of the designs which signifies its suitability in optimizing the complex electromagnetic problems and are thus immerge as effective tool for performing the antenna array pattern synthesis.  
Figure 23: Inset Feed Patch Linear Antenna Array.  
Figure 24: Normalized Array Pattern of design 6 in EM Simulator.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Design** & **Algorithm** & **R\({}^{+}\)** & **R\({}^{-}\)** & **Result** \\ \hline \multirow{4}{*}{1} & MAOA vs. PSO & 1000 & 000 & + \\  & MAOA vs. GOA & 1000 & 000 & + \\  & MAOA vs. SMO & 1000 & 000 & + \\ \hline \multirow{4}{*}{2} & MAOA vs. ALO & 990 & 010 & + \\  & MAOA vs. PSO & 1000 & 000 & + \\  & MAOA vs. GWO & 886 & 114 & + \\ \hline \multirow{4}{*}{3} & MAOA vs. ALO & 954 & 046 & + \\  & MAOA vs. AOA & 1000 & 000 & + \\ \hline \multirow{4}{*}{4} & MAOA vs. ALO & 080 & 920 & – \\  & MAOA vs. AOA & 971 & 029 & + \\  & MAOA vs. DA & 116 & 884 & – \\ \hline \multirow{4}{*}{5} & MAOA vs. ALO & 663 & 337 & + \\  & MAOA vs. DA & 1000 & 000 & + \\  & MAOA vs. STO & 990 & 010 & + \\ \hline \multirow{4}{*}{6} & MAOA vs. DA & 1000 & 000 & + \\  & MAOA vs. STO & 989 & 011 & + \\  & MAOA vs. DBO & 634 & 366 & + \\ \hline \multirow{4}{*}{7} & MAOA vs. AOA & 914 & 086 & + \\  & MAOA vs. DA & 178 & 882 & – \\  & MAOA vs. BBO & 1000 & 000 & + \\ \hline \multirow{4}{*}{8} & MAOA vs. AOA & 884 & 116 & + \\  & MAOA vs. STO & 894 & 106 & + \\ \hline \multirow{4}{*}{9} & MAOA vs. ALO & 955 & 045 & + \\  & MAOA vs. AOA & 962 & 038 & + \\  & MAOA vs. STO & 993 & 007 & + \\ \hline \multirow{4}{*}{10} & MAOA vs. ALO & 000 & 1000 & – \\  & MAOA vs. DA & 310 & 690 & – \\  & MAOA vs. STO & 743 & 257 & + \\ \hline \end{tabular}
\end{table}
Table 15: Outcomes of the Wilcoxon rank sum test for different designs.  
Figure 25: Friedman ranking of optimization algorithms used for position optimization of LAA.