# Crossover Operator Inspired by the Selection Operator
## 3 Experiment and Results Discussion
### Comparative Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crossover Method** & **Cost Definition** & **Mean** & \(\sigma^{2}\) \\ \hline PMX & Euclidean & \(3.07\times 10^{2}\) & \(2.38\times 10^{-2}\) \\ OX & Euclidean & \(3.03\times 10^{2}\) & \(2.91\times 10^{-2}\) \\ Single-Point Crossover & Euclidean & \(2.98\times 10^{2}\) & \(2.18\times 10^{-2}\) \\ SCX & Euclidean & \(3.08\times 10^{2}\) & \(1.88\times 10^{-2}\) \\ New method & Euclidean & \(2.53\times 10^{2}\) & \(1.26\times 10^{-1}\) \\ PMX & Euclidean\({}^{2}\) & \(3.93\times 10^{2}\) & \(7.50\times 10^{-2}\) \\ OX & Euclidean\({}^{2}\) & \(3.84\times 10^{2}\) & \(8.76\times 10^{-2}\) \\ Single-Point Crossover & Euclidean\({}^{2}\) & \(3.76\times 10^{2}\) & \(5.81\times 10^{-2}\) \\ SCX & Euclidean\({}^{2}\) & \(3.93\times 10^{2}\) & \(8.92\times 10^{-2}\) \\ New method & Euclidean\({}^{2}\) & \(2.73\times 10^{2}\) & \(6.99\times 10^{-1}\) \\ PMX & Manhattan & \(8.04\times 10^{2}\) & \(1.56\times 10^{-1}\) \\ OX & Manhattan & \(7.90\times 10^{2}\) & \(2.86\times 10^{-1}\) \\ Single-Point Crossover & Manhattan & \(7.78\times 10^{2}\) & \(2.52\times 10^{-1}\) \\ SCX & Manhattan & \(8.01\times 10^{2}\) & \(1.78\times 10^{-1}\) \\ New method & Manhattan & \(6.34\times 10^{2}\) & \(2.00\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean values and variances of the optimization criterion (total cost) achieved after 1000 generations for the 250-task problem. Figure 13: Effectiveness of the crossover operator for the 1000-task problem. The mean criterion value (three definitions of cost: Euclidean, Euclidean\({}^{2}\), and Manhattan) of the best individual achieved after 1000 generations. \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 & \(1.86\times 10^{-1}\) & \(1.42\times 10^{-14}\) & \(17.43\pm 4.58\%\) \\ OX & Euclidean & \(2.31\times 10^{-1}\) & \(1.25\times 10^{-14}\) & \(16.04\pm 4.31\%\) \\ Single-Point Crossover & Euclidean & \(1.73\times 10^{-1}\) & \(1.78\times 10^{-13}\) & \(15.05\pm 3.95\%\) \\ SCX & Euclidean & \(1.49\times 10^{-1}\) & \(3.57\times 10^{-13}\) & \(17.66\pm 4.64\%\) \\ PMX & Euclidean\({}^{2}\) & \(1.07\times 10^{-1}\) & \(2.56\times 10^{-13}\) & \(30.56\pm 8.03\%\) \\ OX & Euclidean\({}^{2}\) & \(1.25\times 10^{-1}\) & \(3.30\times 10^{-13}\) & \(29.08\pm 7.64\%\) \\ Single-Point Crossover & Euclidean\({}^{2}\) & \(8.31\times 10^{-2}\) & \(2.62\times 10^{-12}\) & \(27.44\pm 7.21\%\) \\ SCX & Euclidean\({}^{2}\) & \(1.28\times 10^{-1}\) & \(1.36\times 10^{-13}\) & \(39.62\pm 8.04\%\) \\ PMX & Manhattan & \(7.78\times 10^{-1}\) & \(1.83\times 10^{-24}\) & \(21.08\pm 5.54\%\) \\ OX & Manhattan & \(1.43\times 10^{0}\) & \(2.38\times 10^{-22}\) & \(19.69\pm 5.17\%\) \\ Single-Point Crossover & Manhattan & \(1.26\times 10^{0}\) & \(2.39\times 10^{-22}\) & \(18.50\pm 4.86\%\) \\ SCX & Manhattan & \(8.87\times 10^{-1}\) & \(2.44\times 10^{-24}\) & \(20.82\pm 5.47\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: 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 250-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.