# 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} \hline \hline \multicolumn{6}{c}{**FHS1 Rules Increase in Range 0.7 to 1**} & \multicolumn{3}{c}{**FHS1 Rules Decrease in Range 0.7 to 1**} \\ \hline \hline
**Function** & **Best** & **Worst** & **Average** & **Function** & **Best** & **Worst** & **Average** \\ \hline
**Spherical** & \(2.45\mathrm{E}-09\) & \(3.52\mathrm{E}-04\) & \(5.28\mathrm{E}-05\) & **Spherical** & \(4.94\mathrm{E}-04\) & \(2.91\mathrm{E}-01\) & \(5.12\mathrm{E}-02\) \\
**Rosenbrock** & \(2.95\mathrm{E}-11\) & \(6.88\mathrm{E}-05\) & \(6.33\mathrm{E}-07\) & **Rosenbrock** & \(1.81\mathrm{E}-13\) & \(1.35\mathrm{E}-08\) & \(1.88\mathrm{E}-09\) \\
**[PERSON]** & \(1.06\mathrm{E}-11\) & \(9.32\mathrm{E}-08\) & \(1.36\mathrm{E}-08\) & **[PERSON]** & \(1.32\mathrm{E}-09\) & \(2.07\mathrm{E}-06\) & \(1.88\mathrm{E}-07\) \\
**[PERSON]** & \(1.00\mathrm{E}-09\) & \(5.09\mathrm{E}-04\) & \(7.87\mathrm{E}-05\) & **[PERSON]** & \(3.31\mathrm{E}-05\) & \(1.40\mathrm{E}-03\) & \(4.60\mathrm{E}-04\) \\
**[PERSON]** & \(1.30\mathrm{E}-13\) & \(9.54\mathrm{E}-04\) & \(1.25\mathrm{E}-04\) & **[PERSON]** & \(3.55\mathrm{E}-01\) & \(1.27\mathrm{E}+01\) & \(3.41\mathrm{E}+00\) \\
**Sum Square** & \(2.30\mathrm{E}-09\) & \(5.70\mathrm{E}-05\) & \(3.72\mathrm{E}-06\) & **Sum Square** & \(1.58\mathrm{E}-02\) & \(5.47\mathrm{E}+00\) & \(9.28\mathrm{E}-01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results obtained with FHS1 using fuzzy logic to increase and decrease _HMR_ with a range from 0.7 to 1, applied to six benchmark mathematical functions. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{6}{c}{**FHS1 Rules Increase in Range 0 to 1**} & \multicolumn{3}{c}{**FHS1 Rules Decrease in Range 0 to 1**} \\ \hline \hline
**Function** & **Best** & **Worst** & **Average** & **Function** & **Best** & **Worst** & **Average** \\ \hline
**Spherical** & \(1.22\mathrm{E}-04\) & \(1.31\mathrm{E}-01\) & \(4.71\mathrm{E}-03\) & **Spherical** & \(2.10\mathrm{E}-03\) & \(4.90\mathrm{E}-01\) & \(1.19\mathrm{E}-01\) \\
**Rosenbrock** & \(1.18\mathrm{E}-12\) & \(9.24\mathrm{E}-06\) & \(3.04\mathrm{E}-07\) & **Rosenbrock** & \(4.46\mathrm{E}-16\) & \(2.01\mathrm{E}-09\) & \(1.18\mathrm{E}-10\) \\
**Rastrigin** & \(2.65\mathrm{E}-07\) & \(2.00\mathrm{E}+00\) & \(5.69\mathrm{E}-02\) & **[PERSON]** & \(4.70\mathrm{E}-10\) & \(3.23\mathrm{E}-06\) & \(3.35\mathrm{E}-07\) \\
**[PERSON]** & \(8.23\mathrm{E}-05\) & \(4.35\mathrm{E}-01\) & \(1.72\mathrm{E}-01\) & **[PERSON]** & \(6.64\mathrm{E}-05\) & \(1.80\mathrm{E}-03\) & \(6.50\mathrm{E}-04\) \\
**[PERSON]** & \(2.00\mathrm{E}-03\) & \(1.38\mathrm{E}-02\) & \(2.04\mathrm{E}+00\) & **[PERSON]** & \(1.01\mathrm{E}+00\) & \(1.47\mathrm{E}+01\) & \(6.67\mathrm{E}+00\) \\
**Sum Square** & \(4.30\mathrm{E}-04\) & \(1.00\mathrm{E}+00\) & \(3.33\mathrm{E}-02\) & **Sum Square** & \(3.70\mathrm{E}-02\) & \(9.08\mathrm{E}+00\) & \(2.38\mathrm{E}+00\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of results obtained with the FHS1 using fuzzy logic to increase and decrease of the HMR parameter in the range 0 to 1.