## 3 Proposed MISAO
### Results Comparisons and Analysis of CEC2017 Benchmark Functions
#### 3.4.1 Effectiveness Validation of Different Components

Table 1: _Cont._  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **F1** & & **F2** & & **F3** & \\ \hline  & AVG & STD & AVG & STD & AVG & STD \\ \hline SAO & \(1.4356\times 10^{10}\) & \(4.1652\times 10^{9}\) & \(1.9597\times 10^{37}\) & \(7.4719\times 10^{37}\) & \(6.2312\times 10^{4}\) & \(8.7433\times 10^{3}\) \\ MISAO-1 & \(3.0675\times 10^{6}\) & \(1.2035\times 10^{6}\) & \(3.6374\times 10^{32}\) & \(1.5265\times 10^{33}\) & \(1.6754\times 10^{5}\) & \(2.9168\times 10^{4}\) \\ MISAO-2 & \(2.1009\times 10^{9}\) & \(1.1516\times 10^{9}\) & \(9.5503\times 10^{29}\) & \(5.2109\times 10^{30}\) & \(6.7376\times 10^{4}\) & \(1.4574\times 10^{4}\) \\ MISAO-3 & \(1.3708\times 10^{7}\) & \(5.7049\times 10^{7}\) & \(1.7082\times 10^{33}\) & \(7.0088\times 10^{33}\) & \(5.9686\times 10^{4}\) & \(2.5339\times 10^{4}\) \\ MISAO-4 & \(1.0374\times 10^{9}\) & \(2.7584\times 10^{8}\) & \(6.8887\times 10^{30}\) & \(3.7723\times 10^{31}\) & \(1.2342\times 10^{5}\) & \(2.9425\times 10^{4}\) \\ MISAO-5 & \(1.1051\times 10^{6}\) & \(6.1015\times 10^{5}\) & \(\mathbf{5.9048\times 10^{12}}\) & \(\mathbf{6.8204\times 10^{12}}\) & \(\mathbf{4.0549\times 10^{4}}\) & \(1.2012\times 10^{4}\) \\ MISAO-6 & \(4.0262\times 10^{6}\) & \(1.3219\times 10^{6}\) & \(7.0249\times 10^{16}\) & \(9.5988\times 10^{16}\) & \(5.0456\times 10^{4}\) & \(1.9200\times 10^{4}\) \\ MISAO & \(\mathbf{2.1933\times 10^{4}}\) & \(\mathbf{2.2253\times 10^{4}}\) & \(2.4396\times 10^{21}\) & \(9.2127\times 10^{21}\) & \(6.1219\times 10^{4}\) & \(\mathbf{3.5196\times 10^{5}}\) \\ \hline  & F4 & & F5 & & F6 & \\ \hline SAO & \(2.5458\times 10^{3}\) & \(9.4491\times 10^{2}\) & \(8.3048\times 10^{2}\) & \(3.9304\times 10^{1}\) & \(6.6958\times 10^{2}\) & \(1.3766\times 10^{1}\) \\ MISAO-1 & \(\mathbf{4.7403\times 10^{2}}\) & \(3.1313\times 10^{1}\) & \(6.8997\times 10^{2}\) & \(3.2949\times 10^{1}\) & \(6.4940\times 10^{2}\) & \(8.1975\times 10^{0}\) \\ MISAO-2 & \(7.8114\times 10^{2}\) & \(2.5851\times 10^{2}\) & \(7.0181\times 10^{2}\) & \(2.6274\times 10^{1}\) & \(6.3143\times 10^{2}\) & \(8.8476\times 10^{0}\) \\ MISAO-3 & \(5.4624\times 10^{2}\) & \(4.5613\times 10^{1}\) & \(6.7147\times 10^{2}\) & \(4.0756\times 10^{1}\) & \(6.4119\times 10^{2}\) & \(8.7626\times 10^{0}\) \\ MISAO-4 & \(6.1316\times 10^{2}\) & \(8.4760\times 10^{1}\) & \(6.3167\times 10^{2}\) & \(4.4956\times 10^{1}\) & \(6.1396\times 10^{2}\) & \(4.5371\times 10^{0}\) \\ MISAO-5 & \(5.1841\times 10^{2}\) & \(1.8175\times 10^{1}\) & \(6.8840\times 10^{2}\) & \(2.1006\times 10^{1}\) & \(\mathbf{6.0017\times 10^{2}}\) & \(\mathbf{3.4353\times 10^{-2}}\) \\ MISAO-6 & \(5.2706\times 10^{2}\) & \(3.2561\times 10^{1}\) & \(6.0968\times 10^{2}\) & \(2.9046\times 10^{1}\) & \(6.1498\times 10^{2}\) & \(6.1363\times 10^{0}\) \\ MISAO & \(5.0148\times 10^{2}\) & \(\mathbf{1.5002\times 10^{1}}\) & \(\mathbf{5.8517\times 10^{2}}\) & \(\mathbf{1.2773\times 10^{1}}\) & \(6.0116\times 10^{2}\) & \(8.1538\times 10^{-1}\) \\ \hline  & F7 & & F8 & & F9 & \\ \hline  & AVG & STD & AVG & STD & AVG & STD \\ \hline SAO & \(1.1424\times 10^{3}\) & \(6.4035\times 10^{1}\) & \(1.0909\times 10^{3}\) & \(4.1032\times 10^{1}\) & \(7.6505\times 10^{3}\) & \(2.0115\times 10^{3}\) \\ MISAO-1 & \(9.1294\times 10^{2}\) & \(4.6527\times 10^{1}\) & \(9.3927\times 10^{2}\) & \(2.6927\times 10^{1}\) & \(6.8644\times 10^{3}\) & \(1.5740\times 10^{3}\) \\ MISAO-2 & \(1.1618\times 10^{3}\) & \(7.0989\times 10^{1}\) & \(9.7827\times 10^{2}\) & \(3.6054\times 10^{1}\) & \(4.3277\times 10^{3}\) & \(1.3862\times 10^{3}\) \\ MISAO-3 & \(1.1352\times 10^{3}\) & \(1.1395\times 10^{2}\) & \(9.3225\times 10^{2}\) & \(2.8250\times 10^{1}\) & \(4.0505\times 10^{3}\) & \(1.2546\times 10^{3}\) \\ MISAO-4 & \(9.6689\times 10^{2}\) & \(2.0132\times 10^{1}\) & \(9.0470\times 10^{2}\) & \(3.4856\times 10^{1}\) & \(2.3933\times 10^{3}\) & \(1.0566\times 10^{3}\) \\ MISAO-5 & \(9.2969\times 10^{2}\) & \(\mathbf{1.5678\times 10^{1}}\) & \(9.9259\times 10^{2}\) & \(2.2065\times 10^{1}\) & \(2.2256\times 10^{3}\) & \(\mathbf{4.0278\times 10^{2}}\) \\ MISAO-6 & \(\mathbf{8.6983\times 10^{2}}\) & \(3.9362\times 10^{1}\) & \(9.9552\times 10^{2}\) & \(2.9839\times 10^{1}\) & \(3.0513\times 10^{3}\) & \(1.1130\times 10^{3}\) \\ MISAO & \(9.1464\times 10^{2}\) & \(2.0630\times 10^{1}\) & \(\mathbf{8.8206\times 10^{2}}\) & \(\mathbf{1.1588\times 10^{1}}\) & \(\mathbf{1.1370\times 10^{3}}\) & \(4.9427\times 10^{2}\) \\  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & F16 & & F17 & & F18 & \\ \hline  & AVG & STD & AVG & STD & AVG & STD \\ \hline SAO & \(4.0919\times 10^{3}\) & \(2.2891\times 10^{2}\) & \(2.8521\times 10^{3}\) & \(2.0374\times 10^{2}\) & \(6.0175\times 10^{6}\) & \(7.8567\times 10^{6}\) \\ MISAO-1 & \(2.8586\times 10^{3}\) & \(3.2794\times 10^{2}\) & \(2.3739\times 10^{3}\) & \(2.6183\times 10^{2}\) & \(3.3062\times 10^{6}\) & \(1.3364\times 10^{6}\) \\ MISAO-2 & \(3.4653\times 10^{3}\) & \(2.8507\times 10^{2}\) & \(2.2694\times 10^{3}\) & \(1.4860\times 10^{2}\) & \(\mathbf{3.2023\times 10^{5}}\) & \(\mathbf{3.0023\times 10^{5}}\) \\ MISAO-3 & \(2.9941\times 10^{3}\) & \(4.0675\times 10^{2}\) & \(2.4128\times 10^{3}\) & \(3.2043\times 10^{2}\) & \(1.5622\times 10^{6}\) & \(1.5784\times 10^{6}\) \\ MISAO-4 & \(2.5897\times 10^{3}\) & \(2.9668\times 10^{2}\) & \(2.1976\times 10^{3}\) & \(2.2014\times 10^{2}\) & \(1.6698\times 10^{6}\) & \(2.2653\times 10^{6}\) \\ MISAO-5 & \(3.0026\times 10^{3}\) & \(\mathbf{1.6919\times 10^{2}}\) & \(2.1945\times 10^{3}\) & \(\mathbf{1.0216\times 10^{2}}\) & \(1.2447\times 10^{6}\) & \(1.8219\times 10^{6}\) \\ MISAO-6 & \(2.8338\times 10^{3}\) & \(2.9254\times 10^{2}\) & \(2.2222\times 10^{3}\) & \(2.1668\times 10^{2}\) & \(3.6235\times 10^{5}\) & \(1.2828\times 10^{6}\) \\ MISAO & \(\mathbf{2.4310\times 10^{3}}\) & \(2.7776\times 10^{2}\) & \(\mathbf{2.0723\times 10^{3}}\) & \(2.1126\times 10^{2}\) & \(1.4183\times 10^{6}\) & \(4.3452\times 10^{5}\) \\ \hline  & F19 & & F20 & & F21 & \\ \hline SAO & \(\mathbf{\alpha}\) & STD & AVG & STD & AVG & STD \\ \hline SAO & \(7.2239\times 10^{6}\) & \(5.5667\times 10^{6}\) & \(3.1064\times 10^{3}\) & \(\mathbf{1.3302\times 10^{2}}\) & \(2.5980\times 10^{3}\) & \(3.4620\times 10^{1}\) \\ MISAO-1 & \(3.7651\times 10^{4}\) & \(5.1006\times 10^{4}\) & \(2.6207\times 10^{3}\) & \(1.6306\times 10^{2}\) & \(2.4898\times 10^{3}\) & \(3.3569\times 10^{1}\) \\ MISAO-2 & \(1.4293\times 10^{4}\) & \(1.2085\times 10^{4}\) & \(2.6935\times 10^{3}\) & \(1.4011\times 10^{2}\) & \(2.4696\times 10^{3}\) & \(2.6380\times 10^{1}\) \\ MISAO-3 & \(1.9362\times 10^{4}\) & \(1.7485\times 10^{4}\) & \(2.7057\times 10^{3}\) & \(2.1425\times 10^{2}\) & \(2.4446\times 10^{3}\) & \(3.4623\times 10^{1}\) \\ MISAO-4 & \(8.1096\times 10^{3}\) & \(9.2642\times 10^{3}\) & \(2.4366\times 10^{3}\) & \(1.9564\times 10^{2}\) & \(2.4170\times 10^{3}\) & \(3.6339\times 10^{1}\) \\ MISAO-5 & \(5.6148\times 10^{5}\) & \(4.3506\times 10^{5}\) & \(2.5305\times 10^{3}\) & \(1.5118\times 10^{2}\) & \(2.4906\times 10^{3}\) & \(\mathbf{2.1467\times 10^{1}}\) \\ MISAO-6 & \(1.1439\times 10^{4}\) & \(8.9838\times 10^{3}\) & \(2.5444\times 10^{3}\) & \(1.7995\times 10^{2}\) & \(2.4301\times 10^{3}\) & \(3.6692\times 10^{1}\) \\ MISAO & \(\mathbf{7.6499\times 10^{3}}\) & \(\mathbf{6.5555\times 10^{3}}\) & \(\mathbf{2.4066\times 10^{3}}\) & \(1.4461\times 10^{2}\) & \(\mathbf{2.3775\times 10^{3}}\) & \(2.4169\times 10^{1}\) \\ \hline  & F22 & & F23 & & F24 & \\ \hline  & AVG & STD & AVG & STD & AVG & STD \\ \hline SAO & \(4.2848\times 10^{3}\) & \(7.7451\times 10^{2}\) & \(3.1781\times 10^{3}\) & \(8.6918\times 10^{1}\) & \(3.2481\times 10^{3}\) & \(7.5466\times 10^{1}\) \\ MISAO-1 & \(5.1942\times 10^{3}\) & \(1.9892\times 10^{3}\) & \(3.1338\times 10^{3}\) & \(1.1503\times 10^{2}\) & \(3.2335\times 10^{3}\) & \(9.4918\times 10^{1}\) \\ MISAO-2 & \(\mathbf{2.7830\times 10^{3}}\) & \(\mathbf{3.1781\times 10^{2}}\) & \(2.9072\times 10^{3}\) & \(4.3431\times 10^{1}\) & \(3.1070\times 10^{3}\) & \(6.4303\times 10^{1}\) \\ MISAO-3 & \(5.2942\times 10^{3}\) & \(1.8909\times 10^{3}\) & \(2.9089\times 10^{3}\) & \(8.2676\times 10^{1}\) & \(3.0764\times 10^{3}\) & \(8.0174\times 10^{1}\) \\ MISAO-4 & \(3.6568\times 10^{3}\) & \(1.8248\times 10^{3}\) & \(2.7834\times 10^{3}\) & \(4.5567\times 10^{1}\) & \(2.9711\times 10^{3}\) & \(5.0791\times 10^{1}\) \\ MISAO-5 & \(6.4097\times 10^{3}\) & \(1.9746\times 10^{3}\) & \(2.8367\times 10^{3}\) & \(\mathbf{1.4110\times 10^{1}}\) & \(3.0393\times 10^{3}\) & \(\mathbf{1.6466\times 10^{1}}\) \\ MISAO-6 & \(5.4154\times 10^{3}\) & \(1.3964\times 10^{3}\) & \(2.7923\times 10^{3}\) & \(4.9717\times 10^{1}\) & \(2.9508\times 10^{3}\) & \(3.3197\times 10^{1}\) \\ MISAO & \(3.9161\times 10^{3}\) & \(6.8382\times 10^{2}\) & \(\mathbf{2.7165\times 10^{3}}\) & \(1.7152\times 10^{1}\) & \(\mathbf{2.8943\times 10^{3}}\) & \Table 3 demonstrates that the mature MISAO significantly outperformed the other comparison approaches by utilizing three strategies.