# HyperDE: An Adaptive Hyper-Heuristic for Global Optimization
## 6 Results
\begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Problem** & **Method** & **Best** & **Mean** & **Std. Dev** \\ \hline F1 & HyperDE & 300.0 & 300.0 & \(3.11\times 10^{-14}\) \\  & SHADE & \(300.000000106882\) & \(300.0000004073815\) & \(2.43\times 10^{-7}\) \\  & LSHADE & \(300.0000001404671\) & \(300.00000041613555\) & \(2.21\times 10^{-7}\) \\  & DE & \(1235.4661553234967\) & \(4130.32659367826\) & \(1205.22\) \\ \hline F2 & HyperDE & \(400.000006692489313\) & \(405.7762007938934\) & \(3.18\) \\  & SHADE & \(400.3938197535978\) & \(407.5481893148344\) & \(2.13\) \\  & LSHADE & \(400.3851128433223\) & \(408.0876491551797\) & \(1.55\) \\  & DE & \(410.80352316352435\) & \(417.77563978207604\) & \(3.27\) \\ \hline F3 & HyperDE & 600.0 & 600.0 & \(2.08\times 10^{-14}\) \\  & SHADE & 600.0 & 600.0 & \(0.0\) \\  & LSHADE & 600.0 & 600.0 & \(0.0\) \\  & DE & \(600.00000112734627\) & \(600.00000363216427\) & \(1.05\times 10^{-5}\) \\ \hline F4 & HyperDE & 800.0971590987756 & \(800.29929127267\) & \(0.19\) \\  & SHADE & 800.2721523050697 & \(800.4602925668243\) & \(0.09\) \\  & LSHADE & 800.2506108454668 & \(800.397114829017\) & \(0.08\) \\  & DE & \(800.2004337865635\) & \(800.4850824190988\) & \(0.09\) \\ \hline F5 & HyperDE & 900.0 & 900.0436061309064 & \(0.11\) \\  & SHADE & 900.000000000498 & \(900.00000000002758\) & \(1.74\times 10^{-10}\) \\  & LSHADE & 900.0000000000752 & \(900.0000000001007\) & \(5.35\times 10^{-12}\) \\  & DE & \(900.0308300706507\) & \(900.2115266993348\) & \(0.04\) \\ \hline F6 & HyperDE & 1800.550008569961 & \(2349.376836704244\) & \(1611.13\) \\  & SHADE & \(2527.2166249124543\) & \(3318.210953638849\) & \(515.35\) \\  & LSHADE & \(2448.651779056926\) & \(3156.2346074618913\) & \(433.08\) \\  & DE & \(18,245.220034908845\) & \(55,938.99918382257\) & \(23,898.85\) \\ \hline F7 & HyperDE & 2001.494972244204 & \(2020.428895032187\) & \(8.00\) \\  & SHADE & \(2023.69169017458\) & \(2028.6419318989665\) & \(1.74\) \\  & LSHADE & \(2014.5645721366564\) & \(2027.7440931323101\) & \(2.78\) \\  & DE & \(2024.5036568238922\) & \(2028.4449058504215\) & \(1.99\) \\ \hline F8 & HyperDE & 2200.226924720861 & \(2218.3297256215615\) & \(6.73\) \\  & SHADE & \(2209.5886930417746\) & \(2218.297973263973\) & \(4.32\) \\  & LSHADE & \(2208.325106401539\) & \(2217.383152114902\) & \(4.02\) \\  & DE & \(2230.0941806086953\) & \(2245.28243788769\) & \(9.28\) \\ \hline F9 & HyperDE & 2300.0 & 2437.838567116613 & \(174.83\) \\  & SHADE & \(2300.0001089307398\) & \(2300.0048868578\) & \(0.03\) \\  & LSHADE & \(2300.0001212533975\) & \(2300.0061751439484\) & \(0.03\) \\  & DE & \(2396.4069384108525\) & \(2646.9062600644074\) & \(60.17\) \\ \hline F10 & HyperDE & 2598.545516771906 & \(2605.156197642855\) & \(25.86\) \\  & SHADE & \(2598.5468912550587\) & \(2598.5620204350707\) & \(0.07\) \\  & LSHADE & \(2598.5468210921954\) & \(2598.551948117506\) & \(0.00\) \\  & DE & \(2608.799360629708\) & \(2614.908013661977\) & \(3.19\) \\ \hline F11 & HyperDE & 2600.0 & 2601.8934468491198 & \(6.28\) \\  & SHADE & \(2600.00000050187055\) & \(2600.0000090069157\) & \(2.17\times 10^{-6}\) \\  & LSHADE & \(2600.00000049464516\) & \(2600.0000009874206\) & \(2.98\times 10^{-6}\) \\  & DE & \(2607.8865627810346\) & \(2624.76104595252\) & \(4.06\) \\ \hline F12 & HyperDE & 2863.76941226926 & \(2865.838163178578\) & \(1.26\) \\  & SHADE & \(2821.118856642622\) & \(2864.1391105809807\) & \(5.62\) \\  & LSHADE & \(2864.224719298684\) & \(2864.904468801826\) & \(0.50\) \\  & DE & \(2866.84004856121\) & \(2867.9027213119152\) & \(0.50\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Method comparison for multiple problems. Table 5 gives the results of the Wilcoxon signed-rank test. They show a statistically significant difference of HyperDE from the other methods on F1, as indicated by the extremely low p-values (approximately \(1.63\times 10^{-11}\)).