# 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 & \(6.16\times 10^{2}\) & \(1.11\times 10^{-2}\) \\ OX & Euclidean & \(6.08\times 10^{2}\) & \(9.64\times 10^{-3}\) \\ Single-Point Crossover & Euclidean & \(6.08\times 10^{2}\) & \(1.50\times 10^{-2}\) \\ SCX & Euclidean & \(6.14\times 10^{2}\) & \(1.29\times 10^{-2}\) \\ New method & Euclidean\({}^{2}\) & \(5.24\times 10^{2}\) & \(6.05\times 10^{-2}\) \\ PMX & Euclidean\({}^{2}\) & \(7.89\times 10^{2}\) & \(9.84\times 10^{-2}\) \\ OX & Euclidean\({}^{2}\) & \(7.74\times 10^{2}\) & \(3.03\times 10^{-2}\) \\ Single-Point Crossover & Euclidean\({}^{2}\) & \(7.66\times 10^{2}\) & \(1.18\times 10^{-1}\) \\ SCX & Euclidean\({}^{2}\) & \(7.90\times 10^{2}\) & \(3.68\times 10^{-2}\) \\ New method & Euclidean\({}^{2}\) & \(5.74\times 10^{2}\) & \(2.83\times 10^{-1}\) \\ PMX & Manhattan & \(1.61\times 10^{3}\) & \(6.26\times 10^{-2}\) \\ OX & Manhattan & \(1.59\times 10^{3}\) & \(1.27\times 10^{-1}\) \\ Single-Point Crossover & Manhattan & \(1.58\times 10^{3}\) & \(1.81\times 10^{-1}\) \\ SCX & Manhattan & \(1.61\times 10^{3}\) & \(4.05\times 10^{-2}\) \\ New method & Manhattan & \(1.33\times 10^{3}\) & \(4.43\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean values and variances of the optimization criterion (total cost) achieved after 1000 generations for the 50-task problem. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crossover Method** & **Cost Definition** & **Mean** & \(\sigma^{2}\) \\ \hline PMX & Euclidean & \(1.24\times 10^{3}\) & \(3.66\times 10^{-3}\) \\ OX & Euclidean & \(1.24\times 10^{3}\) & \(9.36\times 10^{3}\) \\ Single-Point Crossover & Euclidean & \(1.23\times 10^{3}\) & \(2.39\times 10^{-2}\) \\ SCX & Euclidean & \(1.24\times 10^{3}\) & \(1.12\times 10^{-2}\) \\ New method & Euclidean & \(1.08\times 10^{3}\) & \(6.48\times 10^{-2}\) \\ PMX & Euclidean\({}^{2}\) & \(1.60\times 10^{3}\) & \(3.45\times 10^{-2}\) \\ OX & Euclidean\({}^{2}\) & \(1.59\times 10^{3}\) & \(5.06\times 10^{-2}\) \\ Single-Point Crossover & Euclidean\({}^{2}\) & \(1.57\times 10^{3}\) & \(8.57\times 10^{-2}\) \\ SCX & Euclidean\({}^{2}\) & \(1.60\times 10^{3}\) & \(1.77\times 10^{-2}\) \\ New method & Euclidean\({}^{2}\) & \(1.24\times 10^{3}\) & \(4.72\times 10^{-1}\) \\ PMX & Manhattan & \(3.25\times 10^{3}\) & \(7.48\times 10^{-2}\) \\ OX & Manhattan & \(3.23\times 10^{3}\) & \(6.31\times 10^{-2}\) \\ Single-Point Crossover & Manhattan & \(3.22\times 10^{3}\) & \(4.49\times 10^{-2}\) \\ SCX & Manhattan & \(3.26\times 10^{3}\) & \(2.56\times 10^{-2}\) \\ New method & Manhattan & \(2.78\times 10^{3}\) & \(5.73\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean values and variances of the optimization criterion (total cost) achieved after 1000 generations for the 100-task problem. Table 4-6 also present the percentage reductions in the criterion values obtained in comparison with the previous crossover methods, together with the confidence intervals. Reducing the cost of executing a series of tasks by at least 9% (taking into account the obtained confidence intervals) compared with evolutionary algorithms based on previous crossover methods makes the solution attractive in practical applications. Reducing the time of executing a series of production tasks as a result of shortening the time of device changeovers (increasing efficiency) or/and reducing the cost of executing such a series of tasks as a result of reducing the costs of, for example, changeovers, device cleaning, and raw material waste after the previous task without the need for new equipment are already attractive to companies, even for much smaller reductions. The validation of the new crossover method was based on synthetic data. Of course, this does not reflect the complexity of real problems, e.g., sequencing of industrial tasks.