# A New Fuzzy Harmony Search Algorithm Using Fuzzy Logic for Dynamic Parameter Adaptation
## 5 Comparison between of Fuzzy Harmony Search Algorithm (FHS) and of Fuzzy Bat Algorithm (FBA)  
This section presents a comparison between two metaheuristic algorithms that apply fuzzy logic to dynamically adapt some of its parameters. In this case it was decided to choose the fuzzy harmony search algorithm with increasing parameters of pitch adjustment since, according to the three proposals that made in this paper, this one obtained better results. This was tested with six benchmark mathematical functions and ten dimensions in each of its harmonies (number of vector solution) or bats that were used; note that the results of the fuzzy bat algorithm was taken from the literature [6]. The following tables show the behavior of each of the methods. Table 13 shows the overall averages for each method according to the number of bats or harmonies used, as well as the best and the worst results obtained for the sphere function. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Function** & **Simple HS** & **FHS1** & **FHS2** & **FHS3** \\ \hline
**Spherical** & \(6.57\mathrm{E}-05\) & \(5.28\mathrm{E}-05\) & \(1.38\mathrm{E}-05\) & \(3.39\mathrm{E}-05\) \\
**[PERSON]** & \(4.88\mathrm{E}-04\) & \(6.33\mathrm{E}-07\) & \(1.76\mathrm{E}-11\) & \(9.52\mathrm{E}-12\) \\
**[PERSON]** & \(2.26\mathrm{E}-08\) & \(1.36\mathrm{E}-08\) & \(1.08\mathrm{E}-08\) & \(2.52\mathrm{E}-08\) \\
**[PERSON]** & \(1.18\mathrm{E}-04\) & \(7.87\mathrm{E}-05\) & \(9.55\mathrm{E}-06\) & \(1.73\mathrm{E}-04\) \\
**[PERSON]** & \(2.71\mathrm{E}-04\) & \(1.25\mathrm{E}-04\) & \(4.72\mathrm{E}-05\) & \(1.69\mathrm{E}-03\) \\
**Sum Square** & \(3.59\mathrm{E}-05\) & \(3.72\mathrm{E}-06\) & \(2.53\mathrm{E}-06\) & \(6.33\mathrm{E}-04\) \\
**Average** & \(1.63\mathrm{E}-04\) & \(4.35\mathrm{E}-05\) & \(1.22\mathrm{E}-05\) & \(4.22\mathrm{E}-04\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparison of results obtained with all the proposed methods. Figure 15: Plot of three proposed fuzzy HS. In Table 14, the overall averages for each method according to the number of bats or harmonies used can be observed, as well as the best and the worst results obtained for the Ackley function. In Table 15, the overall averages for each method according to the number of bats or harmonies used can be observed, as well as the best and the worst results obtained for the Zakharov function. In Table 16, the overall averages for each method according to the number of bats or harmonies used can be observed, as well as the best and the worst results obtained for the Zakharov function. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**FBA**} & \multicolumn{3}{c}{**FHS**} \\ \hline \multirow{2}{*}{
\begin{tabular}{c} **Num.** \\ **Bats** \\ \end{tabular} } & \multirow{2}{*}{**Best**} & \multirow{2}{*}{**Worst**} & \multirow{2}{*}{**Average**} & \multicolumn{2}{c}{**Num.**} & \multirow{2}{*}{**Best**} & \multirow{2}{*}{**Worst**} & \multirow{2}{*}{**Average**} \\  & & & & & & & \\ \hline
**2** & \(3.47\mathrm{E}-03\) & \(1.54\mathrm{E}+00\) & \(1.10\mathrm{E}-01\) & **2** & \(1.01\mathrm{E}-07\) & \(2.64\mathrm{E}-04\) & \(5.84\mathrm{E}-05\) \\
**5** & \(1.09\mathrm{E}-04\) & \(9.37\mathrm{E}-01\) & \(1.28\mathrm{E}-01\) & **5** & \(1.54\mathrm{E}-09\) & \(1.19\mathrm{E}-05\) & \(9.28\mathrm{E}-07\) \\
**10** & \(5.53\mathrm{E}-06\) & \(1.60\mathrm{E}-04\) & \(1.20\mathrm{E}-04\) & **10** & \(1.10\mathrm{E}-06\) & \(9.42\mathrm{E}-05\) & \(1.63\mathrm{E}-05\) \\
**20** & \(2.77\mathrm{E}-06\) & \(2.30\mathrm{E}-04\) & \(9.82\mathrm{E}-05\) & **20** & \(1.86\mathrm{E}-08\) & \(2.48\mathrm{E}-05\) & \(4.17\mathrm{E}-06\) \\
**30** & \(9.31\mathrm{E}-06\) & \(4.50\mathrm{E}-04\) & \(9.99\mathrm{E}-05\) & **30** & \(1.57\mathrm{E}-08\) & \(1.99\mathrm{E}-05\) & \(2.65\mathrm{E}-06\) \\
**40** & \(2.74\mathrm{E}-06\) & \(6.10\mathrm{E}-04\) & \(9.34\mathrm{E}-05\) & **40** & \(1.92\mathrm{E}-08\) & \(2.47\mathrm{E}-06\) & \(3.46\mathrm{E}-07\) \\ \hline \hline \end{tabular}
\end{table}