# A New Fuzzy Harmony Search Algorithm Using Fuzzy Logic for Dynamic Parameter Adaptation
## 7 Conclusions  
The harmony search (HS) algorithm is a relatively new method which can solve various kinds of problems in an easy and effective manner, as it requires many complex calculations. HS can handle the discrete and continuous variables and can be applied to linear and nonlinear functions.  
Currently, the parameters of the algorithms are set by trial and error. In this paper, a new algorithm was proposed to achieve better convergence and not stay in local optima.  
This paper presents a new algorithm to search for harmony with adjustable fuzzy parameters, in order for the fuzzy system to dynamically move the parameters of this algorithm and subsequently obtain a faster convergence and better results than the original method and others existing in the literature.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(W^{-}\) & \(W^{+}\) & \(W\) & **Level Significance** & **m = Degrees of Freedom** & **W0 = W \(\alpha\), m** \\ \hline
0 & 21 & 0 & 0.05 & 6 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 20: Values of parameters for the statistical test.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **F1** & **F2** & & & & \\ \hline
**Function** & **No.** & **FBA** & **FHS** & **Difference** & **abs (Difference)** & **Rank** & **Sign** & **Signed Rank (+)** \\ \hline
**Spherical** & 1 & \(3.97\mathrm{E}-02\) & \(1.38\mathrm{E}-05\) & \(3.97\mathrm{E}-02\) & \(3.97\mathrm{E}-02\) & 1 & 1 & 1 \\
**[PERSON]** & 2 & \(6.85\mathrm{E}-01\) & \(1.76\mathrm{E}-11\) & \(6.85\mathrm{E}-01\) & \(6.85\mathrm{E}-01\) & \(6\) & 1 & 6 \\
**[PERSON]** & 3 & \(3.68\mathrm{E}-01\) & \(1.08\mathrm{E}-08\) & \(3.68\mathrm{E}-01\) & \(3.68\mathrm{E}-01\) & 4 & 1 & 4 \\
**[PERSON]** & 4 & \(3.66\mathrm{E}-01\) & \(9.55\mathrm{E}-06\) & \(3.65\mathrm{E}-01\) & \(3.65\mathrm{E}-01\) & 3 & 1 & 3 \\
**[PERSON]** & 5 & \(3.32\mathrm{E}-01\) & \(4.72\mathrm{E}-05\) & \(3.32\mathrm{E}-01\) & \(3.32\mathrm{E}-01\) & 2 & 1 & 2 \\
**Sum Square** & 6 & \(4.40\mathrm{E}-01\) & \(1.38\mathrm{E}-05\) & \(4.40\mathrm{E}-01\) & \(4.40\mathrm{E}-01\) & 5 & 1 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 19: Parameters for the Wilcoxon statistical test.  
The paper proposed three different fuzzy systems to initially move each parameter independently of the algorithm. The harmony memory accepting (_HMR_) parameter provides exploitation ability to the algorithm, and pitch adjustment (_PArate_) is controlled by the scanning algorithm; it has a combination of both parameters and each of the changes make mathematical functions applied it to benchmark to test the efficiency of the algorithm.  
Finally, an analysis of the results of each of the proposed methods led to the conclusion that when using a range between 0.7 and 1 in each of the parameters, and moving them dynamically using a fuzzy system, better results are achieved with the original method and the other existing methods in the literature applied, in this case, to six mathematical functions benchmarks. However, more variations with the rules of the FHS3 are needed to obtain a significant advantage in all function benchmarks. In the future, when the method is applied to more complex math functions and more dimensions, it is expected to achieve good results in the same number of iterations. Future work includes testing the proposed fuzzy harmony search with other functions and real world applications. In addition, type-2 fuzzy logic could be used instead of type-1, as is done in this paper.  
We would like to express our gratitude to CONACYT, Tijuana Institute of Technology for the facilities and resources granted for the development of this research.  
[PERSON] and [PERSON] reviewed the state of the art; [PERSON] and [PERSON] contributed to the discussion and analysis of the results; [PERSON] analyzed of the original method and applied fuzzy logic for parameter adaptation, and contributed to the simulations and wrote the paper.  
The authors declare no conflict of interest.