# A Stigmergy-Based Differential Evolution
## 4 Experimental Results
### Benchmark Used in the Experiments
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Execution Time \(\mu(\sigma)\) for 256 Individuals**} & \multicolumn{2}{c}{**Execution Time \(\mu(\sigma)\) for 512 Individuals**} \\ \hline
**Function** & **DE** & **SDE** & **Speedup** & **DE** & **SDE** & **Speedup** \\ \hline F1: Sphere & 45.1006 (0.1674) & **43.5942 (0.1625)** & **1.03** & 47.8527 (0.0200) & **46.3508 (0.0062)** & **1.03** \\ F2 Step & 55.7603 (0.0492) & **55.1497 (0.1864)** & **1.01** & 59.7023 (0.0347) & **57.5648 (0.2401)** & **1.04** \\ F3: Sum Powers & 47.3895 (0.1270) & **44.0992 (0.2072)** & **1.07** & 51.0338 (0.0389) & **47.4896 (0.0307)** & **1.07** \\ F4: Sum Squares & 45.0150 (0.1787) & **43.3325 (0.1482)** & **1.04** & 48.2126 (0.0252) & **46.6274 (0.0068)** & **1.03** \\ F5: Dixon and Price & 70.2937 (0.2209) & **70.2279** (0.1731) & **1.00** & 74.9822 (0.0298) & **71.0612 (0.0428)** & **1.06** \\ F6: [PERSON] & 95.6219 (0.2426) & **94.9924** (0.1544) & **1.01** & 101.3959 (0.036) & **95.4034 (0.0300)** & **1.06** \\ F7: [PERSON] 2.22 & 31.7049 (0.0719) & **30.0035** (0.1929) & **1.06** & 33.6836 (0.2565) & **31.4718** (0.1376) & **1.07** \\ F8: [PERSON] & 47.2107 (0.1703) & **43.6624 (0.1782)** & **1.08** & 50.2172 (0.0326) & **43.7325 (0.0232)** & **1.03** \\ F9: [PERSON] & 46.9736 (0.1404) & **45.1113** (0.1838) & **1.04** & 50.1629 (0.0517) & **47.0111** (0.0762)** & **1.07** \\ F10: [PERSON] & 92.2495 (0.1712) & **56.5934** (0.1743) & **1.05** & 62.5976 (0.1638) & **60.1282 (0.0707)** & **1.04** \\ F11: [PERSON] & 58.9961 (0.0955) & **56.4700** (0.1942) & **1.04** & 62.2493 (0.0507) & **59.5437 (0.3830)** & **1.05** \\ F12: [PERSON] & 39.6069 (0.1385) & **39.0363** (0.1085) & **1.01** & 41.7337 (0.0551) & **40.8717** (0.0721)** & **1.02** \\ F13: [PERSON] & **67.4986** (**0.14888) & **71.4827** (0.1742) & 0.94 & **71.7673 (**0.0992)** & **75.6721** (0.0595) & 0.95 \\ F14: [PERSON] & 88.1310 (0.1206) & **83.0872** (0.1613) & **1.06** & 93.9297 (0.1430) & **89.1134** (0.0781) & **1.05** \\ F15: Treccani & 23.8224 (0.6603) & **21.2687** (**0.2196) & **1.12** & 25.3578 (0.6672) & **22.4922** (**0.2129) & **1.13** \\ F16: Beale & 23.5141 (0.0369) & **23.1105** (0.3537) & **1.02** & 25.1768 (0.0694) & **24.5135** (**0.0285) & **1.03** \\ F17: Booth & 23.2668 (0.0490) & **23.0368** (**0.2329) & **1.01** & 24.8573 (0.0480) & **24.4406** (**0.1686) & **1.02** \\ F18: Brent & **23.1873 (0.0809)** & 23.8490 (0.1661) & 0.97 & **24.7574 (0.0653)** & **25.2045** (0.1205) & 0.98 \\ F19: Cube & 23.6192 (0.0523) & **21.1600** (**0.2700) & **1.12** & 25.1667 (0.0651) & **22.5187** (**0.2063) & **1.12** \\ F20: [PERSON] & 24.6654 (0.0647) & **21.3285** (0.2838) & **1.16** & 26.2479 (0.0403) & **22.7148** (**0.1962) & **1.16** \\ F21: Matyas & 25.3824 (0.0144) & **21.4355** (**0.1936) & **1.20** & 27.0852 (0.0140) & **22.3725** (**0.0781) & **1.21** \\ F22: [PERSON] & 23.3038 (0.0899) & **21.3305** (**0.1633) & **1.09** & 24.9515 (0.0555) & **22.7985** (**0.2195) & **1.09** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean and averaged execution times in seconds of DE and SDE (\(D=500\)).