# A Stigmergy-Based Differential Evolution
## 4 Experimental Results
### Convergence Speed
In fact, DE no longer reaches the optimum in 20,000 iterations for the Sum Squares, Schwefel 2.22, Ackley, Griewank and Levy functions, whereas SDE has no problems achieving the optimum for these functions. Another important detail is that with a larger number of individuals (\(Np=512\)), SDE finds the optimum in slightly fewer iterations than when the population is smaller (see Tables 9 and 10). This highlights the advantage of using the stigmergy concept for the indirect communication among the population. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Final Fitness \(\boldsymbol{\mu}(\boldsymbol{\sigma})\)**} & \multicolumn{2}{c}{**Final Iterations \(\boldsymbol{\mu}(\boldsymbol{\sigma})\)**} \\ \hline
**Function** & **SDE** & **DE** & **SDE** & **DE** \\ \hline F1: Sphere & 0.0096 (\(3.1580\times 10^{-4}\)) & **0.0095(\(4.3491\times 10^{-4}\))** & **861.00 (20.67)** & 4344.16 (114.73) \\ F2: Step & 0.0 (0) & 0.0 (0) & **828.56 (24.44)** & 5486.53 (193.96) \\ F3: Sum Powers & 0.0077 (0.0020) & **0.0070** (0.0023) & 530.0 (8.47) & **26.86 (6.14)** \\ F4: Sum Squares & 0.0097 (\(2.0231\times 10^{-4}\)) & **0.0095 (\(4.1157\times 10^{-4}\))** & **126.32 (17.43)** & 6216.26 (113.12) \\ F5: Dixon and Price & 36.3413 (16.9494) & **0.6667 (\(1.8257\times 10^{-7}\))** & 20,000.00 (0) & 20,000.00 (0) \\ F6: Rosenbrock & 348.7744 (127.6737) & **90.7098 (\(0.1733\))** & 20,000.00 (0) & 20,000.00 (0) \\ F7: Schwefel 2.22 & 0.0098 (\(1.3374\times 10^{-4}\)) & 0.0098 (\(2.0745\times 10^{-4}\)) & **1227.43 (17.91)** & 6962.76 (111.36) \\ F8: Trid & \(7.746\times 10^{6}\) (\(6.448\times 10^{6}\)) & \(\left(8.365\times 10^{5}\right)\) & 20,000.00 (0) & 20,000.00 (0) \\ F9: [PERSON] & **0.2058 (0.0850)** & 257.4497 (14.3462) & 20,000.00 (0) & 20,000.00 (0) \\ F10: [PERSON] & 0.0098 (\(2.0868\times 10^{-4}\)) & \(\left(2.2258\times 10^{-4}\right)\) & **1373.53 (\(211.39\))** & 7410.03 (159.97) \\ F11: [PERSON] & 0.4355 (\(0.6197\)) & 600.0198 (\(10.0965\)) & **9035.56 (\(846.8\))** & 20,000.00 (0) \\ F12: [PERSON] & **52.4709 (\(65.0721\))** & 5852.3797 (\(5544.0\)) & **1981.50 (\(32.62\))** & 20,000.00 (0) \\ F13: [PERSON] & 0.0097 (\(2.8136\times 10^{-4}\)) & **0.0095 (\(3.6761\times 10^{-4}\))** & **1303.60 (\(22.27\))** & 6690.20 (152.02) \\ F14: Levy & 0.0097 (\(2.1518\times 10^{-4}\)) & **0.0096 (\(2.4228\times 10^{-4}\))** & **989.70 (\(25.23\))** & 7744.56 (209.23) \\ F15: Treccani & 0.0059 (\(0.0031\)) & **0.009 (\(0.0028\))** & 33.5 (\(14.83\)) & **3.8 (\(3.14\))** \\ F16: Beale & 0.0066 (\(0.0032\)) & **0.0048 (\(0.0031\))** & 76.16 (\(36.74\)) & **4.73 (\(2.99\))** \\ F17: [PERSON] & 0.0068 (\(0.0025\)) & **0.0051 (\(0.0031\))** & 82.66 (\(34.35\)) & 15.86 (\(6.83\)) \\ F18: [PERSON] & 0.0068 (\(0.0025\)) & **0.0044 (\(0.0026\))** & 61.4 (\(21.82\)) & **13.63 (\(4.77\))** \\ F19: [PERSON] & 0.0051 (\(0.0040\)) & **0.0048 (\(0.0028\))** & 329.83 (\(205.35\)) & **27.47 (\(11.98\))** \\ F20: [PERSON] & **0.0038 (\(0.0346\))** & 0.0055 (\(0.0017\)) & 587.36 (\(99.63\)) & 149.76 (\(9.49\)) \\ F21: Matyas & 0.0059 (\(0.0035\)) & **0.0038 (\(0.0026\))** & 48.13 (\(23.34\)) & **2.1 (\(1.56\))** \\ F22: [PERSON] & 0.0048 (\(0.0033\)) & 0.0048 (\(0.0027\)) & 258.21 (\(14.02\)) & 16.56 (\(8.22\)) \\ F23: Boahchevsky1 & 0.0070 (\(0.0028\)) & **0.0055 (\(0.0031\))** & 88.13 (\(24.36\)) & **33.8 (\(5.88\))** \\ F24: Egg Crate & 0.0067 (\(0.0029\)) & **0.0053 (\(0.0028\))** & 45.67 (\(15.39\)) & **13.23 (\(4.78\))** \\ F25: Boahchevsky2 & 0.0053 (\(0.0033\)) & 0.0049 (\(0.0029\)) & 108.23 (\(61.14\)) & **36.1 (\(4.79\))** \\ F26: Boahchevsky3 & 0.0059 (\(0.0032\)) & **0.0039 (\(0.0026\))** & 102.3 (\(34.34\)) & 30.86 (\(3.88\)) \\ F27: Three-Hump & & **0.0053 (\(0.0033\))** & 0.0070 (\(0.0023\)) & 53.00 (\(8.47\)) & **26.86 (\(6.14\))** \\ Camel & **0.0053 (\(0.0033\))** & 0.0070 (\(0.0023\)) & 5 Figure 3: Comparison between the number of SDE and DE iterations.