## 4 Simulation Results
### Evaluation of 23 Additional Benchmark Models
 } & \multirow{2}{*}{**LOW**} & \multirow{2}{*}{**UP**} & \multirow{2}{*}{**Dim**} & \multicolumn{6}{c}{**Proposed IMGO**} & \multicolumn{6}{c}{**Standard MGO**} \\ \cline{4-14}  & & & & & **Best** & & **Mean** & **Worst** & **STD** & **Best** & **Mean** & **Worst** & **STD** \\ \hline F1-Sphere & \(-100\) & \(100\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.003\) & \(0.010\) & \(0.003\) \\ \hline F2-Schwefel 2.22 & \(-10\) & \(10\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.010\) & \(0.890\) & \(4.439\) & \(1.007\) \\ \hline F3-Schwefel 1.2 & \(-100\) & \(100\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(1.396\) & \(35.286\) & \(6.428\) \\ \hline F4-Schwefel 2.21 & \(-100\) & \(100\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.038\) & \(3.864\) & \(10.840\) & \(2.993\) \\ \hline F5-Rosenbrock & \(-50\) & \(50\) & \(30\) & \(0.000\) & \(0.000\) & \(0.002\) & \(0.000\) & \(0.008\) & \(85.748\) & \(417.316\) & \(97.143\) \\ \hline F6-Step & \(-100\) & \(100\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.005\) & \(0.011\) & \(0.002\) \\ \hline F7-Quadrtic & \(-1.28\) & \(1.28\) & \(30\) & \(0.039\) & \(0.474\) & \(0.951\) & \(0.311\) & \(0.025\) & \(0.476\) & \(0.998\) & \(0.264\) \\ \hline F8-Schwefel & \(-500\) & \(500\) & \(30\) & \(-12.569.5\) & \(-11.302.9\) & \(-10.338.9\) & \(694.4\) & \(-12.569.5\) & \(-9984.5\) & \(-7301.8\) & \(1143.7\) \\ \hline F9-Rastrigin & \(-5.12\) & \(5.12\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(13.715\) & \(29.869\) & \(11.400\) \\ \hline F10-Ackley & \(-32\) & \(32\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(1.503\) & \(2.894\) & \(0.894\) \\ \hline F11-Griewank & \(-600\) & \(600\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.022\) & \(0.096\) & \(0.025\) \\ \hline F12-Penalized & \(-50\) & \(50\) & \(30\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(0.000\) & \(3.259\) & \(10.426\) & \(3.111\) \\ \hline F13-Penalized2 & \(-50\) & \(50\) & \(30\) & \(0.000\) & \(0.006\) & \(0.099\) & \(0.018\) & \(0.001\) & \(0.011\) & \(0.043\) & \(0.011\) \\ \hline F14-Foxholes & \(-65.536\) & \(65.536\) & \(2\) & \(0.998\) & \(2.165\) & \(12.671\) & \(3.562\) & \(0.998\) & \(1.295\) & \(5.929\) & \(0.940\) \\ \hline F15-Kowalik & \(-5\) & \(5\) & \(4\) & \(0.000\) & \(0.000\) & \(0.001\) & \(0.000\) & \(0.000\) & \(0.001\) & \(0.020\) & \(0.004\) \\ \hline F16-Six Hump Camel & \(-5\) & \(5\) & \(2\) & \(-1.032\) & \(-1.032\) & \(-1.032\) & \(0.000\) & \(-1.032\) & \(-1.032\) & \(-1.032\) & \(0.000\) \\ \hline F17-Branin & \([-5;0]\) & \([10,15]\) & \(2\) & \(0.398\) & \(0.398\) & \(0.398\) & \(0.000\) & \(0.398\) & \(0.398\) & \(0.000\) \\ \hline F18-GoldStein-Price & \(-2\) & \(2\) & \(2\) & \(3.000\) & \(3.000\) & \(3.000\) & \(0.000\) & \(3.000\) & \(3.000\) & \(3.000\) & \(0.000\) \\ \hline F19-Hartman 3 & \(0\) & \(1\) & \(3\) & \(-3.863\) & \(-3.863\) & \(-3.863\) & \(0.00\) & \(-3.863\) & \(-3.863\) & \(-3.863\) & \(0.000\) \\ \hline F20-Hartman 6 & \(0\) & \(1\) & \(6\) & \(-3.322\) & \(-3.298\) & \(-3.203\) & \(0.048\) & \(-3.322\) & \(-3.270\) & \(-3.195\) & \(0.061\) \\ \hline F21-Shekel 5 & \(0\) & \(10\) & \(4\) & \(-10.153\) & \(-8.659\) & \(-2.683\) & \(3.039\) & \(-10.153\) & \(-7.163\) & \(-2.630\) & \(3.724\) \\ \hline F22-Shekel 7 & \(0\) & \(1 In contrast, IMGO demonstrates worse performance than MGO in a limited number of instances. Specifically, higher fitness values are observed in 1 function for the best, 2 for the mean, 3 for the worst, and 4 for the STD. These account for poorer performance in only 4.35%, 8.70%, 13.04%, and 17.39% of the functions, respectively. Despite these occasional setbacks, the overall results confirm that IMGO excels in most cases, delivering enhanced accuracy, consistency, and resilience against suboptimal solutions. These findings highlight the effectiveness of IMGO as a robust optimization method.