## 3 Proposed Approach  
### Algorithm for the Objective Function Calculation  
It is worth considering the algorithm for calculating the objective function in detail. Therefore, for each target request, one needs to create a special list of routes. We use the following notation:  
* \(L_{i}\) is the number of routes in the \(i\)-target request;* \(q_{ij}\) is the traffic intensity transmitted along the corresponding route;
* \(\omega_{ij}\) is the weight in proportion to which \(Q_{i}\), for a fixed \(i\), divided among all \(m_{ij}\), where \(m_{ij}\) is the sequence of nodes in the \(j\)th route for the \(i\)th target request (e.g., \(m_{23}=[1,4,3]\) means that the third route in the list for the second target request consists of three nodes and two edges, respectively);
* \(m_{ij}[t]\) is the \(t\)th node located on the corresponding route (e.g., \(m_{23}[2]=4\));
* \(l_{ij}\) is the number of elements of vector \(m_{ij}\). For \(m_{23}\) discussed above, the value \(l_{23}=3\). For each target request, \(Q_{i}\), the traffic intensity, \(q_{ij}\), is not optimized in terms of the proportions or weights in which the total information flow, \(Q_{i}\), is distributed among \(m_{ij}\) routes. The quantities discussed above are related to each other in the following way:  
\[q_{ij}=\frac{\omega_{ij}}{\sum_{k=1}^{L_{i}}\omega_{ik}}Q_{i}. \tag{4}\]  
One should note that Equation (4) allows one to transmit from traffic intensity, \(q_{ij}\), to weights, \(\omega_{ij}\) and, accordingly, not to meet the conditions of the normalization (5):  
\[\sum_{j=1}^{L_{i}}q_{ij}=Q_{i}. \tag{5}\]  
Since it is not known in advance whether it is possible to transmit all the information over the network, the parameter \(K\) is introduced. It is defined as part of the transmitted information, e.g., if \(K=0.5\), the algorithm considers the network state in which only half of all the information is transmitted. An algorithm for calculating the objective function of the information loss rate is given below. This algorithm resembles the method of simple iteration relating to variables \(x_{ij}\) and \(p_{ij}\). However, it proves its convergence on the problems being solved, if a solution exists. Target requests can have such values that the network is physically unable to transmit the entire amount of arriving information. In this case, it is necessary to know the maximum value of parameter \(K\) at which information can be delivered by the routes under consideration, as well as the corresponding network state. The amount of transmitted information, \(K\), can be found using a binary search (Algorithm 1). It takes only up to eight iterations of Algorithm 2 (\(Calculate\_Traffic\)) and allows the determination of this parameter with sufficient accuracy. One should specify that such accuracy of calculation is important only for small values of parameter \(K\); otherwise, calculations can be performed with a smaller number of iterations. If function \(Calculate\_Traffic\) (Algorithm 2) uses \(K^{3}\) instead of \(K\) (see step \(5d\) and step \(5e\)), the number of iterations of Algorithm 2 is reduced to five. Then, the grid of found values is \(K_{rez}=\{0.02\%;0.20\%;0.76\%;1.56\%;3.05\%;5.27\%;8.37\%;12.50\%;17.80 \%;24.41\%;32.50\%;42.19\%;53.64\%;66.99\%;82.40\%\}\). Since calculation of the \(Calculate\_Traffic\) function is a time-consuming process, the algorithm for finding the maximum amount of transmitted information significantly affects the algorithm operating time, and therefore such a step is justified. Thereby, the problem in a specified objective function has been solved. Algorithm 1 can reduce the optimization problem without using equality constraints. Moreover, the algorithm converges for any function \(p(x,\mu,N)\) monotonically increasing in \(x\), which makes it possible for it to be used for loss probability functions in an arbitrary way. ```
1. Assign \(K=1\). // amount of information
2. Assign \(dK=0.5\). // varying step \(K\)
3. Call \(Calculate\_Traffic(K)\). 4.