# An Innovative Hybrid Approach Producing Trial Solutions for Global Optimization
## 3 Experiments
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**FUNCTION** & **GEN** & **PSO** & **IPSO** & **DE** & **GWO** & **WOA** & **MEWOA** & **PROPOSED** & **KMEANS** \\ \hline RASTRING & 4106 & 3539 & 2211 & 6216 & 9043 & 8116 & 5523 & 3672 & 2364 \\ ROSENBROCK4 & 3679 & 5858 & 2025 & 8452 & 8078 & 10,759 & 7750 & 5642 & 3641 \\ \hline ROSENBROCK8 & 5269 & 7843 & 2085 & 11,530 & 11,167 & 14,094 & 9469 & 7926 & 6119 \\ \hline ROSENBROCK16 & 8509 & 11,450 & 2432 & 17,432 & 15,590 & 23,544 & 13,554 & 11,285 & 7490 \\ \hline SCHWFEL & 1880 & 2178 & 1504 & 3437 & 4564 & 4158 & 3005 & 2208 & 1572 \\ \hline SCHWFEL221 & 2666 & 2529 & 1875 & 3909 & 71,847 & 8519 & 3815 & 2867 & 2256 \\ \hline SCHWFEL222 & 33,724 & 42,897 & 28,965 & 86,861 & 101,960 & 11,4161 & 65,835 & 78,734 & 18,058 \\ \hline SHEKEL5 & 3325 & 3886 & 2018 & 6662 & 10,043 & 17,010 & 5359 & 5322 & 2657 \\ \hline SHEKEL7 & 3360 & 4009 & 1994 & 6967 & 10,079 & 17,873 & 5344 & 5503 & 2648 \\ \hline SHEKEL10 & 2488 & 3985 & 1914 & 6757 & 10,055 & 15,524 & 5321 & 4784 & 2901 \\ \hline SINU4 & 2990 & 3409 & 1961 & 5953 & 8132 & 10,150 & 4874 & 3446 & 2254 \\ \hline SINU8 & 3441 & 3995 & 1853 & 6973 & 10,481 & 20,782 & 5886 & 4371 & 3359 \\ \hline SINU16 & 4320 & 4680 & 2251 & 6979 & 15,356 & 34,409 & 7274 & 6450 & 5992 \\ \hline TEST2N4 & 3330 & 3390 & 1930 & 6396 & 8093 & 11,876 & 4930 & 3569 & 2204 \\ \hline TEST2N5 & 4000 & 3604 & 1982 & 6271 & 8812 & 16,256 & 5045 & 3877 & 2575 \\ \hline TEST2N7 & 4775 & 4020 & 2157 & 7074 & 10,124 & 25,005 & 6363 & 4285 & 2831 \\ \hline TEST30N3 & 3210 & 4018 & 2432 & 6178 & 7647 & 8163 & 5311 & 4215 & 4389 \\ \hline TEST30N4 & 3678 & 4504 & 3354 & 7006 & 10,656 & 13,596 & 7069 & 5013 & 2901 \\ \hline
**TOTAL** & **261,106** & **317,168** & **145,908** & **506,409** & **802,608** & **916,996** & **419,939** & **361,454** & **230,033** \\ \hline MAX & **33,724** & **42,897** & **28,965** & **86,861** & **101,960** & **11,4161** & **65,835** & **78,734** & **26,615** \\ \hline MIN & **1630** & **1998** & **1376** & **2814** & **4564** & **3153** & **2117** & **2208** & **1335** \\ \hline STDEV & **5517** & **7735** & **5.58** & **4121** & **63** & **13,674** & **61** & **18,893** & **71** & **19,622** & **90** & **10,608** & **0.07** & **11,562** & **7.76** & **5885** \\ \hline
**AVERAGE** & **5466** & **6613** & **330** & **3047** & **10,665** & **14** & **16,791** & **13** & **19,219** & **6.3** & **8853** & **4.3** & **7495** & **353** & **5316** \\ \hline MEDIAN & **3678** & **3886** & **1982** & **6781** & **9415** & **11,717** & 5359 & **4406** & **2921** \\ \hline SKEW & **3.54** & **3.35** & **5.55** & **4.32** & **2.89** & **2.9** & **4.02** & **5.3** & **2.53** \\ \hline KURT & **14.75** & **12.05** & **34.01** & **21.19** & **9.12** & **10.87** & **18.43** & **31.3** & **5.77** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._evaluations to achieve a result, making it the most efficient algorithm. The DE algorithm, with 506,409 evaluations, performs worse compared to IPSO and other algorithms. For difficult functions, such as DIFFPOWER10, with 46,914 calls, and SCHWEFEL222, with 86,861 calls, it requires significantly more evaluations, indicating difficulties in optimizing efficiently. GWO has the largest number of total evaluations (802,608), showing its reduced efficiency. It encounters particular difficulties in hard problems, such as DIFFPOWER10, with 54,442 calls, and SCHWEFEL222, with 101,960 calls. The WOA, with 916,996 evaluations, is even less efficient than GWO. It faces serious issues with demanding functions such as DIFFPOWER10 (56,381 calls) and SCHWEFEL222 (114,161 calls), indicating a poor performance. The MEWOA (Modified WOA) has 419,939 total evaluations, showing some improvement over WOA, but is still less efficient than IPSO and PROPOSED+KMEANS. Despite the improvement, it continues to require many calls in difficult problems, such as DIFFPOWER10 (38,559 calls) and SCHWEFEL222 (65,835 calls).