# 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  
In this section, the experimental results obtained by the Harmony Search algorithm and fuzzy harmony search are shown in separate tables of the 12 proposed fuzzy systems. The results obtained using the original method, with six benchmark mathematical functions, are presented in Table 2. It should be noted that the best, worst and average of 30 experiments are shown for each mathematical function. In Table 2, the overall averages obtained for each mathematical function are presented. The first column represents the best values of the experiments, the second column represents the worst values of the experiments and the third column represents the averages of the experiments with the original harmony search algorithm. The first proposal made by this method was to perform the dynamic adjustment of parameters applied to the first parameter of the algorithm, which is the harmony memory accepting (HMR). This was created to dynamically change this parameter in the range that indicates the literature, which is from 0 to 1. This methodology was applied to the six benchmark mathematical functions previously mentioned and 30 experiments were performed with each of these functions. Table 3 shows the results. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{3}{c}{**Simple Harmony Search**} \\ \hline
**Function** & **Best** & **Worst** & **Average** \\ \hline
**Spherical** & \(2.36\mathrm{E}-05\) & \(1.49\mathrm{E}-04\) & \(6.57\mathrm{E}-05\) \\
**[PERSON]** & \(1.47\mathrm{E}-11\) & \(1.31\mathrm{E}-02\) & \(4.88\mathrm{E}-04\) \\
**[PERSON]** & \(9.31\mathrm{E}-12\) & \(2.24\mathrm{E}-07\) & \(2.26\mathrm{E}-08\) \\
**[PERSON]** & \(8.72\mathrm{E}-06\) & \(4.54\mathrm{E}-04\) & \(1.18\mathrm{E}-04\) \\
**[PERSON]** & \(7.33\mathrm{E}-05\) & \(1.80\mathrm{E}-03\) & \(2.71\mathrm{E}-04\) \\
**[PERSON] Square** & \(4.82\mathrm{E}-06\) & \(1.05\mathrm{E}-04\) & \(3.59\mathrm{E}-05\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results obtained using the harmony search algorithm. Figure 14: Benchmark mathematical functions. In Table 3, the overall averages, as well as best and worst results obtained for each mathematical function and method can be found. The results obtained with the FHS1 using the range of 0 to 1 using rules increment and decrement are presented. Based on the previous experiments, the range of 0.7 to 1 for the HMR output was used. In the literature, it is recommended to use this parameter in the range from 0.7 to 0.95 to obtain better results, but in many existing works they use the range up to 0.99 and 1, hence the experiments were performed by trial and error. Table 4 shows the results obtained with this modification. In Table 4, the averages of the 30 experiments for each mathematical function are shown, in addition to the best and worst results obtained for each mathematical function and the overall average obtained in each function. The results of these experiments suggest the use of the range of 0.7 to 1 with the proposed method as shown in Table 5.  
In Table 5, the averages of the 30 experiments for each mathematical function are shown, as well as the best and worst results for each mathematical function and the overall average. The results are with the original algorithm and the best fuzzy system, in this case FHS1, with rules and increase in the output range from 0.7 to 1. The best results obtained are of the proposed method.