# A Stigmergy-Based Differential Evolution
## 4 Experimental Results
### Convergence Speed
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Final Fitness \(\mu(\sigma)\)**} & \multicolumn{2}{c}{**Final Iterations \(\mu(\sigma)\)**} \\ \hline
**Function** & **SDE** & **DE** & **SDE** & **DE** \\ \hline F1: Sphere & **0.0099**(7.1685 \(\times\) 10\({}^{-5}\)) & 1.5596 (0.1287) & **3915.83** (37.75) & 20,000.00 (0) \\ F2: Step & **0.000**(0) & 648.46 (49.02) & **3796.33** (**208.28) & 20,000.00 (0) \\ F3: Sum Powers & 0.0073 (0.0018) & **0.0070** (**0.0022**) & 68.66 (14.84) & **65.60 (15.11)** \\ F4: Sum Squares & **0.0099** (6.1043 \(\times\) 10\({}^{-5}\)) & 1114.1061 (97.5739) & **6257.00** (**48.87**) & 20,000.00 (0) \\ F5: Dixon and Price & **1116.7** (411.7089) & 1.1704 \(\times\) 10\({}^{4}\) (2084.0) & 20,000.00 (0) & 20,000.00 (0) \\ F6: Rosenbrock & 2015.3 (675.7089) & 3656.1 (321.2327) & 20,000.00 (0) & 20,000.00 (0) \\ F7 Schwefel 2.22 & **0.0099** (5.7235 \(\times\) 10\({}^{-5}\)) & 39.2896 (2.1531) & **5416.53** (**37.09**) & 20,000.00 (0) \\ F8: [PERSON] & **1.4111** \(\times\) 10\({}^{40}\) & 3.6207 \(\times\) 10\({}^{10}\) & 20,000.00 (0) & 20,000.00 (0) \\ F9: [PERSON] & **3137.0** (397.5563) & 4175.8 (112.141) & 20,000.00 (0) & 20,000.00 (0) \\ F10: [PERSON] & **0.0099** (4.3961 \(\times\) 10\({}^{-5}\)) & 3.1094 (0.0798) & **5680.50** (**117.0**) & 20,000.00 (0) \\ F11: [PERSON] & **1568.87** (252.57) & 4620.047 (101.5107) & 20,000.00 (0) & 20,000.00 (0) \\ F12: [PERSON] & **5.0077** \(\times\) 10\({}^{4}\) & \(1.7129\times\) 10\({}^{5}\) (776.5318) & 20,000.00 (0) & 20,000.00 (0) \\ F13: Griewank & **(1.9810 \(\times\) 10\({}^{4}\))** & & & \\ F14: Levy & **0.0099** (7.9325 \(\times\) 10\({}^{-5}\)) & 6.3713 (0.5136) & **5270.16** (**42.23**) & 20,000.00 (0) \\ F15: Treccani & 0.0049 (0.0034) & **0.0039** (**0.0026**) & 33.13 (7.89) & **6.86 (3.77)** \\ F16: Beale & 0.0057 (0.0032) & **0.0052** (**0.0029**) & 67.76 (35.51) & 8.26 (**4.40**) \\ F17: [PERSON] & 0.0064 (0.0036) & **0.0051** (**0.0030**) & 80.5 (41.65) & **21.63 (**10.99**) \\ F18: Brent & 0.0074 (0.0021) & **0.0049** (**0.0029**) & 63.8 (17.98) & 14.43 (**5.87**) \\ F19: Cube & 0.0049 (0.0038) & **0.0048** (**0.0031**) & 271.63 (117.09) & 38.03 (15.18) \\ F20: [PERSON] & 0.0069 (0.0033) & **0.0065** (**0.0018**) & 584.75 (133.71) & 154.3 (**9.18**) \\ F21: [PERSON] & 0.0064 (0.0027) & **0.0047** (**0.0028**) & 41.63 (19.11) & **4 (**3.36**) \\ F22: [PERSON] & 0.0047 (0.0029) & 0.0047 (0.0031) & 214.08 (107.21) & **21.7 (**11.65**) \\ F23: [PERSON] & 0.0074 (0.0025) & **0.0047** (**0.0028**) & 94.2 (22.08) & 35.93 (**5.19**) \\ F24: Egg Crate & **0.0057** (**0.0026**) & 0.0060 (0.0027) & 48.23 (13.61) & 16.36 (3.92) \\ F25: [PERSON] & 0.0047 (0.0034) & **0.0045** (**0.0027**) & 145.2 (68.44) & 37.3 (5.75) \\ F26: [PERSON] & 0.0061 (0.0031) & **0.0048** (**0.0026**) & 123.07 (42.16) & 34.3 (**4.06**) \\ F27: Three-Hump & 0.0070 (0.0026) & **0.0042** (**0.0026**) & 41.03 (21.40) & 7.4 (4.61) \\ Camel & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Mean and averaged final fitness and iterations of DE and SDE (\(N_{p}=256;\)\(D=500\)).