# Enhancing Backtracking Search Algorithm using Reflection Mutation Strategy Based on Sine Cosine
## 5 Experimental Results
### Compared with State-of-the-Art Algorithms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Benchmark** & **Function** & **PSO** & **ABC** & **DE** & **CA** & **BSA** & **RSCBSA** \\ \hline \multirow{4}{*}{F1} & best & \(2.6078\times 10^{-21}\) & \(5.3796\times 10^{-16}\) & \(2.5816\times 10^{-46}\) & \(2.5562\times 10^{2}\) & \(1.4976\times 10^{-17}\) & \(0.0000\times 10^{0}\) \\  & mean & \(3.9736\times 10^{-7}\) & \(7.5685\times 10^{-16}\) & \(5.4588\times 10^{-45}\) & \(1.6712\times 10^{3}\) & \(2.4454\times 10^{-15}\) & \(0.0000\times 10^{0}\) \\  & worst & \(3.6505\times 10^{-6}\) & \(5.4117\times 10^{-15}\) & \(2.4629\times 10^{-44}\) & \(4.1270\times 10^{3}\) & \(2.8521\times 10^{-14}\) & \(0.0000\times 10^{0}\) \\  & std & \(1.3868\times 10^{-12}\) & \(6.8910\times 10^{-31}\) & \(2.6423\times 10^{-89}\) & \(9.5577\times 10^{5}\) & \(3.0966\times 10^{-29}\) & \(0.0000\times 10^{0}\) \\ \hline \multirow{4}{*}{F2} & best & \(5.4694\times 10^{-28}\) & \(1.6002\times 10^{-15}\) & \(4.1335\times 10^{-28}\) & \(5.8462\times 10^{0}\) & \(5.0408\times 10^{-10}\) & \(4.3459\times 10^{-218}\) \\  & mean & \(1.3657\times 10^{-12}\) & \(1.8228\times 10^{-15}\) & \(2.0667\times 10^{-27}\) & \(2.2100\times 10^{1}\) & \(3.2572\times 10^{-3}\) & \(3.9314\times 10^{-214}\) \\  & worst & \(1.5274\times 10^{-11}\) & \(3.3803\times 10^{-15}\) & \(5.6259\times 10^{-27}\) & \(6.9183\times 10^{1}\) & \(1.0338\times 10^{-38}\) & \(3.1240\times 10^{-213}\) \\  & std & \(1.5008\times 10^{-23}\) & \(1.6937\times 10^{-31}\) & \(1.2307\times 10^{-54}\) & \(2.3890\times 10^{2}\) & \(5.5714\times 10^{-18}\) & \(0.0000\times 10^{0}\) \\ \hline \multirow{4}{*}{F3} & best & \(3.9653\times 10^{-103}\) & \(3.5792\times 10^{3}\) & \(7.3893\times 10^{3}\) & \(8.3334\times 10^{3}\) & \(3.0345\times 10^{1}\) & \(8.1950\times 10^{-204}\) \\  & mean & \(6.4404\times 10^{-93}\) & \(5.9449\times 10^{3}\) & \(1.11857\times 10^{4}\) & \(2.0627\times 10^{4}\) & \(1.7266\times 10^{2}\) & \(7.7379\times 10^{-188}\) \\  & worst & \(1.5655\times 10^{-91}\) & \(1.1140\times 10^{4}\) & \(1.9801\times 10^{4}\) & \(4.0887\times 10^{4}\) & \(3.7642\times 10^{2}\) & \(2.3203\times 10^{-186}\) \\  & std & \(8.1160\times 10^{-184}\) & \(3.2828\times 10^{6}\) & \(6.0971\times 10^{6}\) & \(7.8083\times 10^{7}\) & \(6.6997\times 10^{3}\) & \(0.0000\times 10^{0}\) \\ \hline \multirow{4}{*}{F4} & best & \(7.8193\times 10^{-83}\) & \(2.8317\times 10^{1}\) & \(5.1221\times 10^{-4}\) & \(3.0161\times 10^{1}\) & \(9.0018\times 10^{-1}\) & \(8.1338\times 10^{-152}\) \\  & mean & \(1.5871\times 10^{-72}\) & \(3.9440\times 10^{1}\) & \(1.0355\times 10^{-3}\) & \(4.6255\times 10^{1}\) & \(2.1297\times 10^{6}\) & \(4.7338\times 10^{-144}\) \\  & worst & \(2.4649\times 10^{-71}\) & \(5.0921\times 10^{1}\) & \(2.2349\times 10^{-3}\) & \(7.9715\times 10^{1}\) & \(3.9292\times 10^{0}\) & \(8.8191\times 10^{-143}\) \\  & std & \(2.1488\times 10^{-143}\) & \(3.7018\times 10^{1}\) & \(1.5905\times 10^{-7}\) & \(1.4438\times 10^{2}\) & \(4.0870\times 10^{-1}\) & \(2.6901\times 10^{-286}\) \\ \hline \multirow{4}{*}{F5} & best & \(7.9093\times 10^{-2}\) & \(8.6115\times 10^{-3}\) & \(2.3793\times 10^{1}\) & \(1.0168\times 10^{5}\) & \(8.6456\times 10^{-1}\) & \(2.3440\times 10^{1}\) \\  & mean & \(2.2878\times 10^{0}\) & \(5.3359\times 10^{-1}\) & \(3.3665\times 10^{1}\) & \(1.2073\times 10^{6}\) & \(5.5375\times 10^{1}\) & \(2.4658\times 10^{1}\) \\  & worst & \(7.0303\times 10^{0}\) & \(1.8079\times 10^{1}\) & \(8.8254\times 10^{1}\) & \(4.4121\times 10^{6}\) & \(8.6258\times 10^{1}\) & \(2.6975\times 10^{1}\) \\  & std & \(3.1431\times 10^{0}\) & \(1.3289\times 10^{1}\) & \(4.0340\times 10^{2}\) & \(1.0354\times 10^{12}\) & \(9.4312\times 10^{2}\) & \(6.2485\times 10^{1}\) \\ \hline \multirow{4}{*}{F6} & best & \(0.0000\times 10^{0}\) & \(5.5033\times 10^{-16}\) & \(0.0000\times 10^{0}\) & \(4.3707\times 10^{2}\) & \(2.2988\times 10^{-17}\) & \(8.6469\times 10^{-7}\) \\  & mean & \(1.9105\times 10^{-32}\) & \(7.4696\times 10^{-16}\) & \(0.0000\times 10^{0}\) & \(1.8850\times 10^{3}\) & \(4.8673\times 10^{16}\) & \(1.4989\times 10^{-1}\) \\  & worst & \(1.1093 Fixed-dimension multimodal benchmark functions (_F_14-_F_23): For the category of benchmark function, the proposed RSCBSA can obtain the best performance on 7 test functions (_F_14, \(F\)16-_F_19 and \(F\)21-_F_22) from Table 5. BSA can perform the best than other competitors on the all test functions.