## 4 Computational Experiments
### Comparative Results  
Let us compare the results of the developed optimization algorithm with those of the coordinate descent algorithm. Therefore, in both cases two test problems with arbitrary input parameters are used. Test task #1, initial data:  
Figure 5: Histogram of the distribution of objective function values. Figure 6: Distribution of matching route parts. * number of nodes: 12;
* number of target requests: 1000. The value of the objective function obtained by the developed optimization algorithm is 37,606; the value of the objective function obtained by coordinate descent is 37,342, i.e., the difference is 0.702%. Test task #2, initial data:  
* number of nodes: 40;
* number of target requests: 2000. The value of the objective function obtained by the developed optimization algorithm is 81,191; the value of the objective function obtained by coordinate descent is 80,768, i.e., the difference is 0.52%. Since in the solutions obtained by the proposed optimization algorithm, the length of the optimal routes, did not exceed three nodes, all the routes with a length of no more than 4 nodes were used in the search space for the coordinate descent optimization algorithm. Therefore, the solutions obtained are quite close to optimal in terms in the value of the objective function, since additional optimization does not allow improvement of the value of the objective function by more than 1%. As coordinate descent frequently requires more calculations of the objective function, further complication of the optimization algorithm is of no use. For low-dimensional problems (up to four nodes), the following algorithms were compared: the modified Gallagher's method [20] and the greedy-gradient algorithm. The research results are presented in Table 1.  
When comparing the modified Gallagher's method and the greedy-gradient algorithm, the network structure was unchanged, whereas the values of the target queries varied. The results obtained by these two algorithms either coincide with each other or differ significantly, which is explained by the multi-extremal nature of the objective function. At the same time, solving high-dimensional tasks using the modified Gallagher's method is impractical, as the traditional optimization methods are not fast. When solving large-dimensional problems (more than ten nodes), the following algorithms were compared: the greedy-gradient algorithm and the coordinate descent algorithm in a new search space. The results obtained using these two algorithms differ by no more than 1%. For low-dimensional problems, with the use of the modified Gallagher's method implemented in MATLAB, the calculation time does not exceed one minute on a commodity single-processor system. For the greedy-gradient algorithm implemented in the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Task No.** & **Number of Nodes** &
\begin{tabular}{c} **Number of Targeted** \\ **Requests** \\ \end{tabular} & \multicolumn{2}{c}{**Loss of Information**} \\ \hline  & & & & & **The Coordinate** \\  & & & **Modified** & **Greedy-Gradient** & **Descent Algorithm** \\  & & & **Gallagher’s Method** & **Algorithm** & **in a New** \\  & & & & & **Search Space** \\ \hline
1 & 4 & 12 & 6.85 & 6.84 & - \\
2 & 4 & 12 & 308 & 308 & - \\
3 & 4 & 12 & 11,762 & 9520 & - \\
4 & 4 & 12 & 3 233 & 3237 & - \\
5 & 4 & 12 & 23.08 & 23.08 & - \\
6 & 4 & 12 & 9206 & 8154 & - \\
7 & 12 & 1000 & - & 37,606 & 37,342 \\
8 & 40 & 2000 & - & 81,191 & 80,768 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative results of optimization algorithms. C++ programming language, the calculation time does not exceed 0.1 s using the same computer capability. For high-dimensional problems, the calculation time of the greedy-gradient algorithm implemented in the same programming language, and with the same computer capability, does not exceed 10 s. For the coordinate descent algorithm in the new search space, implemented in the C++ programming language, using the same computer capability, the calculation time is does not exceed 30 h.