# An Improved Novel Global Harmony Search Algorithm Based on Selective Acceptance
## 4 Experimental Results and Analysis
### Comparison of Different Harmony Search Algorithms in Ten Benchmark Optimization Problems
** & **Algorithm** & **Min** & **Max** & **Mean** & **Std** \\ \hline  & HS & \(8.7644\times 10^{3}\) & \(1.6480\times 10^{4}\) & \(1.2203\times 10^{4}\) & \(1.5403\times 10^{3}\) & HS & \(2.2313\times 10^{2}\) & \(2.9442\times 10^{2}\) & \(2.5974\times 10^{2}\) & \(2.1788\times 10^{1}\) \\  & HS & \(9.1067\times 10^{1}\) & \(1.4800\times 10^{4}\) & \(1.2428\times 10^{4}\) & \(1.0779\times 10^{4}\) & HS & \(1.9487\times 10^{2}\) & \(2.8706\times 10^{4}\) & \(2.4522\times 10^{2}\) & \(2.0779\times 10^{1}\) \\ F1 & SGHS & \(8.7681\times 10^{2}\) & \(1.6202\times 10^{4}\) & \(1.3666\times 10^{4}\) & \(2.4274\times 10^{-1}\) & F6 & SGHS & \(1.5762\times 10^{4}\) & \(8.5459\times 10^{4}\) & \(4.0935\times 10^{4}\) & \(1.5444\times 10^{4}\) \\  & NCHS & \(4.8032\times 10^{-4}\) & \(1.0576\times 10^{-3}\) & \(7.3694\times 10^{-4}\) & \(1.6006\times 10^{-4}\) & NCHS & \(1.5643\times 10^{-3}\) & \(2.0192\times 10^{4}\) & \(4.7179\times 10^{-1}\) & \(6.1547\times 10^{-1}\) \\  & **SANGHS** & \(\mathbf{5.1238\times 10^{-3}}\) & \(\mathbf{7.0729\times 10^{-15}}\) & \(\mathbf{4.3965\times 10^{-16}}\) & \(\mathbf{1.3365\times 10^{-15}}\) & **SANGHS** & \(\mathbf{0.000\times 10^{0}}\) & \(\mathbf{1.3856\times 10^{-3}}\) & \(\mathbf{6.5133\times 10^{-5}}\) & \(\mathbf{2.4832\times 10^{-14}}\) \\ \hline  & HS & \(5.0156\times 10^{-3}\) & \(7.3431\times 10^{1}\) & \(6.1118\times 10^{4}\) & \(4.9356\times 10^{4}\) & HS & \(4.5600\times 10^{4}\) & \(7.0740\times 10^{4}\) & \(5.5498\times 10^{4}\) & \(5.8842\times 10^{4}\) \\  & HS & \(5.1843\times 10^{4}\) & \(6.8653\times 10^{4}\) & \(6.6208\times 10^{4}\) & \(4.3861\times 10^{4}\) & HS & \(4.4499\times 10^{3}\) & \(5.6993\times 10^{3}\) & \(5.5203\times 10^{3}\) & \(4.9043\times 10^{2}\) \\ F2 & SGHS & \(8.1631\times 10^{-2}\) & \(4.1138\times 10^{-1}\) & \(2.4863\times 10^{-1}\) & \(8.1339\times 10^{-2}\) & F7 & SGHS & \(8.9612\times 10^{4}\) & \(3.0484\times 10^{1}\) & \(1.7210\times 10^{1}\) & \(5.3463\times 10^{-2}\) \\  & NCHS & \(9.9950\times 10^{-3}\) & \(1.6541\times 10^{-3}\) & \(1.3619\times 10^{-2}\) & \(1.5409\times 10^{-3}\) & NCHS & \(3.9466\times 10^{-3}\) & \(1.1539\times 10^{-1}\) & \(1.6436\times 10^{-2}\) & \(2.4948\times 10^{-2}\) \\  & **In addition, to further explore the difference in the performance of the SANGHS algorithm and other four harmony search algorithms, the experiment results were also analyzed through the Wilcoxon rank-sum test [24; 25] as shown in Table 5. In Table 5, the \(p\)-value, which is greater than 0.05, is bold. Based on the \(p\)-value, the SANGHS algorithm is significantly better than the other four HS algorithms in all problems with three different dimensions, except in problem 10 (F10) with D = 10 (6.3886 \(\times\) 10\({}^{-2}\)). Figure 2 shows the typical convergence graphs of five different algorithms for ten problems with D = 30. In Figure 2a-d which are unimodal problems, as the number of iterations increases, the SANGHS algorithm converges faster than other four harmony search algorithms. It means that the SANGHS algorithm has a strong local search ability in unimodal problems. In Figure 2e,f,h,j which are multimodal problems, we can easily observe that the SANGHS algorithm is more effective in escaping from the local optima and have a better convergence ability compared with the other four harmony search algorithms. In other words, the SANGHS algorithm has a better balance between the global search ability and the local search ability in multimodal problems. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**D** & **No.