# A New Fuzzy Harmony Search Algorithm Using Fuzzy Logic for Dynamic Parameter Adaptation
## 4 Experiment Results Comparison of the Simple Harmony Search Algorithm with Fuzzy Harmony Search
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{6}{c}{**FHS3 Rules Increase in Range 0.7 to 1**} & \multicolumn{6}{c}{**FHS3 Rules Decrease in Range 0.7 to 1**} \\ \hline \hline
**Function** & **Best** & **Worst** & **Average** & **Function** & **Best** & **Worst** & **Average** \\ \hline
**Spherical** & \(3.74\mathrm{E}-06\) & \(1.11\mathrm{E}-04\) & \(3.39\mathrm{E}-05\) & **Spherical** & \(2.03\mathrm{E}-06\) & \(5.68\mathrm{E}-05\) & \(1.59\mathrm{E}-05\) \\
**Rosenbrock** & \(3.55\mathrm{E}-15\) & \(1.08\mathrm{E}-10\) & \(9.52\mathrm{E}-12\) & **Rosenbrock** & \(2.55\mathrm{E}-14\) & \(8.56\mathrm{E}-11\) & \(9.30\mathrm{E}-12\) \\
**Rastrigin** & \(3.52\mathrm{E}-11\) & \(1.62\mathrm{E}-07\) & \(2.52\mathrm{E}-08\) & **[PERSON]** & \(7.60\mathrm{E}-12\) & \(3.66\mathrm{E}-07\) & \(3.51\mathrm{E}-08\) \\
**[PERSON]** & \(1.12\mathrm{E}-05\) & \(6.40\mathrm{E}-04\) & \(1.73\mathrm{E}-04\) & **[PERSON]** & \(1.53\mathrm{E}-06\) & \(6.25\mathrm{E}-04\) & \(1.68\mathrm{E}-04\) \\
**[PERSON]** & \(9.73\mathrm{E}-05\) & \(1.14\mathrm{E}-01\) & \(1.69\mathrm{E}-03\) & **[PERSON]** & \(3.46\mathrm{E}-05\) & \(1.80\mathrm{E}+00\) & \(8.79\mathrm{E}-02\) \\
**Sum Square** & \(6.43\mathrm{E}-05\) & \(2.00\mathrm{E}-03\) & \(6.33\mathrm{E}-04\) & **Sum Square** & \(2.87\mathrm{E}-05\) & \(9.26\mathrm{E}-04\) & \(2.52\mathrm{E}-04\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of results obtained with FHS 3 using fuzzy logic rules for increasing and decreasing using the range 0.7 to 1 for the two outputs. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{6}{c}{**FHS3 Rules Increase in Range 0 to 1**} & \multicolumn{6}{c}{**FHS3 Rules Decrease in Range 0 to 1**} \\ \hline \hline
**Function** & **Best** & **Worst** & **Average** & **Function** & **Best** & **Worst** & **Average** \\ \hline
**Spherical** & \(1.44\mathrm{E}-05\) & \(2.33\mathrm{E}+00\) & \(4.96\mathrm{E}-01\) & **Spherical** & \(1.30\mathrm{E}-03\) & \(4.60\mathrm{E}-01\) & \(1.23\mathrm{E}-01\) \\
**Rosenbrock** & \(5.20\mathrm{E}-11\) & \(5.28\mathrm{E}-06\) & \(1.34\mathrm{E}-07\) & **Rosenbrock** & \(2.14\mathrm{E}-12\) & \(6.50\mathrm{E}-09\) & \(5.46\mathrm{E}-10\) \\
**Rastrigin** & \(1.66\mathrm{E}-06\) & \(1.13\mathrm{E}+00\) & \(1.28\mathrm{E}-01\) & **Rastrigin** & \(6.60\mathrm{E}-10\) & \(2.63\mathrm{E}-06\) & \(2.80\mathrm{E}-07\) \\
**[PERSON]** & \(1.70\mathrm{E}-03\) & \(4.04\mathrm{E}+00\) & \(8.59\mathrm{E}-01\) & **[PERSON]** & \(1.50\mathrm{E}-03\) & \(4.86\mathrm{E}-01\) & \(1.32\mathrm{E}-01\) \\
**[PERSON]** & \(5.00\mathrm{E}-05\) & \(8.30\mathrm{E}-01\) & \(6.35\mathrm{E}-02\) & **[PERSON]** & \(8.77\mathrm{E}-01\) & \(2.23\mathrm{E}+01\) & \(7.02\mathrm{E}+00\) \\
**Sum Square** & \(8.42\mathrm{E}-05\) & \(9.40\mathrm{E}-04\) & \(3.40\mathrm{E}-04\) & **Sum Square** & \(1.74\mathrm{E}-02\) & \(6.79\mathrm{E}+00\) & \(1.34\mathrm{E}+00\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of results obtained with FHS 3 using fuzzy logic rules for increasing and decreasing using the range 0 to 1 for the two outputs. The results of an analysis of Tables 2-11 applying the three proposed fuzzy systems to benchmark mathematical functions using the output range of 0 to 1 with increment and decrement rules, as well as the range of 0.7 to 1 with rules in increment and decrement, are compared in Table 12.  
In Table 12, the overall averages obtained for each mathematical function of the three proposed fuzzy methods can be found. Figure 15 shows the data plot of the three proposals; it is noteworthy that the best algorithm is the fuzzy harmony search with dynamic adjustment of the _PArate_ parameter (FHS2). Based on these experiments of the proposed methods and the original method (with parameters by trial and error), the conclusion is that, for the best results, the most effective range is from 0.7 to 1 and with the rules in increase.