# Crossover Operator Inspired by the Selection Operator
## 3 Experiment and Results Discussion
### Comparative Analysis
In order to somewhat approach these issues, the studies were supplemented with distributions of task parameters that differ from the basic uniform distribution and that may occur in industrial conditions. In the first test, it was checked whether the use of a continuous normal distribution of task parameters (which occurs more often in real problems than the continuous uniform distribution) will affect the degree of superiority of our method. Figure 14 shows a comparison of results for such a distribution of parameters of the analyzed crossover methods. As can be seen, the level of superiority of our method has \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Crossover Method** & **Cost Definition** & **F-Test (p)** & \(t\)**-Test (p)** & **Reduction** \\ \hline PMX & Euclidean & \(5.64\times 10^{-2}\) & \(1.63\times 10^{-14}\) & \(12.87\pm 3.38\%\) \\ OX & Euclidean & \(1.44\times 10^{-1}\) & \(8.80\times 10^{-16}\) & \(12.48\pm 3.28\%\) \\ Single-Point Crossover & Euclidean & \(3.69\times 10^{-1}\) & \(2.87\times 10^{-18}\) & \(12.11\pm 3.18\%\) \\ SCX & Euclidean & \(1.73\times 10^{-1}\) & \(2.00\times 10^{-16}\) & \(12.96\pm 3.40\%\) \\ PMX & Euclidean\({}^{2}\) & \(7.32\times 10^{-2}\) & \(5.53\times 10^{-14}\) & \(22.45\pm 5.90\%\) \\ OX & Euclidean\({}^{2}\) & \(1.07\times 10^{-1}\) & \(2.49\times 10^{-14}\) & \(21.81\pm 5.73\%\) \\ Single-Point Crossover & Euclidean\({}^{2}\) & \(1.82\times 10^{-1}\) & \(3.45\times 10^{-15}\) & \(21.27\pm 5.59\%\) \\ SCX & Euclidean\({}^{2}\) & \(3.76\times 10^{-2}\) & \(1.89\times 10^{-13}\) & \(22.60\pm 5.94\%\) \\ PMX & Manhattan & \(7.48\times 10^{-2}\) & \(1.00\times 10^{-15}\) & \(14.55\pm 3.82\%\) \\ OX & Manhattan & \(6.31\times 10^{0}\) & \(3.52\times 10^{-15}\) & \(13.99\pm 3.67\%\) \\ Single-Point Crossover & Manhattan & \(4.49\times 10^{-2}\) & \(1.46\times 10^{-14}\) & \(13.71\pm 3.60\%\) \\ SCX & Manhattan & \(2.56\times 10^{-2}\) & \(2.51\times 10^{-14}\) & \(14.66\pm 3.85\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: F-test and \(t\)-test confirming a statistically significant reduction in the mean value of the optimization criterion (total cost) achieved after 1000 generations for the 100-task problem and the percentage value of the criterion reduction for the new crossover compared with the previous methods with confidence intervals for a confidence level of 0.99. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Crossover Method** & **Cost Definition** & **F-Test (p)** & \(t\)**-Test (p)** & **Reduction** \\ \hline PMX & Euclidean & \(1.84\times 10^{-1}\) & \(1.29\times 10^{-15}\) & \(14.87\pm 3.91\%\) \\ OX & Euclidean & \(1.59\times 10^{-1}\) & \(7.62\times 10^{-15}\) & \(13.80\pm 3.63\%\) \\ Single-Point Crossover & Euclidean & \(2.48\times 10^{-1}\) & \(6.84\times 10^{-16}\) & \(13.78\pm 3.62\%\) \\ SCX & Euclidean & \(2.14\times 10^{-1}\) & \(6.17\times 10^{-16}\) & \(14.72\pm 3.87\%\) \\ PMX & Euclidean\({}^{2}\) & \(3.48\times 10^{-1}\) & \(6.50\times 10^{-18}\) & \(27.22\pm 7.15\%\) \\ OX & Euclidean\({}^{2}\) & \(1.07\times 10^{-1}\) & \(1.36\times 10^{-14}\) & \(25.89\pm 6.80\%\) \\ Single-Point Crossover & Euclidean\({}^{2}\) & \(4.16\times 10^{-1}\) & \(1.02\times 10^{-17}\) & \(25.03\pm 6.57\%\) \\ SCX & Euclidean\({}^{2}\) & \(1.30\times 10^{-1}\) & \(2.74\times 10^{-15}\) & \(27.31\pm 7.17\%\) \\ PMX & Manhattan & \(1.41\times 10^{-1}\) & \(1.09\times 10^{-15}\) & \(17.55\pm 4.61\%\) \\ OX & Manhattan & \(2.87\times 10^{-1}\) & \(3.48\times 10^{-17}\) & \(16.54\pm 4.35\%\) \\ Single-Point Crossover & Manhattan & \(4.09\times 10^{-1}\) & \(5.82\times 10^{-18}\) & \(15.87\pm 4.17\%\) \\ SCX & Manhattan & \(9.14\times 10^{-2}\) & \(6.14\times 10^{-15}\) & \(17.65\pm 4.63\%\) \\ \hline \hline \end{tabular}
\end{table}