# A Stigmergy-Based Differential Evolution
## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Final Fitness \(\mu(\sigma)\)**} & \multicolumn{3}{c}{**Final Iterations \(\mu(\sigma)\)**} \\ \hline
**Function** & **SDE** & **DE** & **SDE** & **DE** \\ \hline F1: Sphere & **0.0099 (6.0612 \(\times\) 10\({}^{-5}\))** & 27.3649 (1.4603) & **3685.16 (30.18)** & 20,000.00 (0) \\ F2: Step & **0.0 (0)** & 10.338 \(\times\) 10\({}^{4}\) (696.03) & **3311.96 (107.64)** & 20,000.00 (0) \\ F3: Sum Powers & 0.0077 (0.0017) & **0.0075 (0.0019)** & 68.86 (13.06) & **62.63 (13.32)** \\ F4: Sum Squares & **0.0099 (1.0435 \(\times\) 10\({}^{-4}\))** & \(1.9638\times\) 10\({}^{4}\) (1214.0749) & **5884.63 (30.66)** & 20,000.00 (0) \\ F5: Dixon and Price & **1186.7 (455.0704)** & 1.1704 \(\times\) 10\({}^{4}\) (2084.0) & 20,000.00 (0) & 20,000.00 (0) \\ F6: [PERSON] & **2266.0 (683.9547)** & 3656.1 (212.327) & 20,000.00 (0) & 20,000.00 (0) \\ F7: [PERSON] 2.22 & **0.0099 (4.9013 \(\times\) 10\({}^{-5}\))** & 202.258 (8.5413) & **5181.37 (27.57)** & 20,000.00 (0) \\ F8: [PERSON] & **1.4072 \(\times\) 10\({}^{10}\)**(1.775 \(\times\) 1\({}^{11}\))** & 1.8198 \(\times\) 10\({}^{11}\) & 20,000.00 (0) & 20,000.00 (0) \\ F9: [PERSON] & **3109.1 (348.8842)** & 4175.8 (112.1416) & 20,000.00 (0) & 20,000.00 (0) \\ F10: [PERSON] & **0.0099 (3.4051 \(\times\) 10\({}^{-5}\))** & 7.0142 (0.1369) & **5229.16 (45.38)** & 20,000.00 (0) \\ F11: [PERSON] & **1567.246 (388.10)** & 4909.5538 (47.224) & 20,000.00 (0) & 20,000.00 (0) \\ F12: [PERSON] & **4.0269 \(\times\) 10\({}^{4}\)** & 1.7120 \(\times\) 10\({}^{5}\) (760.9840) & 20,000.00 (0) & 20,000.00 (0) \\ F13: [PERSON] & **(2.107 \(\times\) 10\({}^{4}\))** & 94.8377 (5.1547) & **4964.13 (42.25)** & 20,000.00 (0) \\ F14: [PERSON] & **0.0099 (8.3354 \(\times\) 10\({}^{-5}\))** & 96.7644 (6.7583) & **4355.60 (48.12)** & 20,000.00 (0) \\ F15: Treccani & 0.0061 (0.0024) & **0.0049 (0.0032)** & 33.16 (13.69) & **4.1 (2.23)** \\ F16: Beale & 0.0063 (0.0032) & **0.0044 (0.0025)** & 69.66 (31.39) & **7.4 (3.59)** \\ F17: [PERSON] & 0.0075 (0.0026) & **0.0056 (0.0029)** & 87.63 (63.26) & **16.56 (9.58)** \\ F18: Brent & 0.0075 (0.0024) & **0.0048 (0.0029)** & 65.4 (19.48) & **14.23 (4.27)** \\ F19: [PERSON] & **0.0058 (0.0037)** & 0.0059 (0.0030) & 252.03 (168.68) & **26.67 (11.38)** \\ F20: [PERSON] & **0.00370 (0.0034)** & 0.0067 (0.0015) & 571.11 (133.95) & **149.2 (12.54)** \\ F21: [PERSON] & 0.0049 (0.0032) & **0.0035 (0.0028)** & 47 (16.06) & 2.13 (16.63) \\ F22: [PERSON] & **0.0051 (0.0031)** & 0.0055 (0.0031) & 218.36 (168.65) & **14.96 (7.87)** \\ F23: [PERSON] & 0.0072 (0.0027) & **0.0043 (0.0032)** & 92.13 (27.13) & 32.63 (6.32) \\ F24: Egg Crate & 0.0063 (0.0027) & **0.0050 (0.0031)** & 53.67 (17.51) & 13.4 (3.63) \\ F25: Bohachevsky2 & 0.0058 (0.0034) & **0.0043 (0.0031)** & 120.43 (52.24) & **31.83 (6.90)** \\ F26: Bohachevsky3 & 0.0073 (0.0027) & **0.0050 (0.0032)** & 140.73 (64.64) & 30.9 (5.54) \\ F27: Three-Hump & 0.0062 (0.0028) & **0.0051 (0.0030)** & 49.9 (19.74) & **4.93 (3.31)** \\ Camel & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Mean and averaged final fitness and iterations of DE and SDE (\(N_{p}=512\); \(D=500\)). Even if the iterations are insufficient to find the global optimum, SDE performs better than DE, so it can be a good alternative for solving multiple engineering optimization problems. As mentioned in [59], applications can be in industrial engineering for the job-shop scheduling problem [60, 61], in image processing to perform a multilevel thresholding process on a 2D histogram to segment images [62, 63], in path planning to solve robotics challenges [64], or to solve area coverage problems for wireless sensor networks (WSNs) [65], to mention a few.