## 1 Introduction
Such interest in this area of communication systems is associated with the significant shortcomings of existing routing algorithms used in traditional IP networks, which researchers are trying to eliminate, for example:  
* inefficient use of network resources [19; 20; 21];
* lack of prompt response to overloads when generating traffic and changing the network topology in existing satellite routing protocols [1; 22; 23; 24; 25; 26; 27; 28; 29; 30];
* inability to work with different types of traffic [19; 31];
* focusing on a single criteria when solving optimization problems with multiple objectives [19; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. In addition to various problem settings for finding optimal routes, there are various methods to find them: heuristic algorithms [19; 28; 29], greedy algorithms [21], gradient methods [31], reinforcement learning [20], and neural networks [23]. In [3], the authors discuss the importance of global adaptive routing in large-scale systems with a large coverage area. For global adaptive routing, the choice of optimal routes is usually based on local information, such as line occupancy and approximate overload of information. However, existing heuristic-based adaptive routing algorithms often rely solely on local information, which can lead to inefficient solutions of the routing problem. Many recent papers are devoted to local routing, i.e., the route is determined for a single flow, without considering its influence on others. Hybrid algorithms that combine heuristic approaches with local search are also widely used for location problems [24; 25; 26], including location on networks, and the application of similar algorithmic combinations for traffic routing seems to be promising. However, correct local actions do not always provide a proper solution from a global point of view. Approaches to global routing were proposed in [3; 14; 17]. However, these methods have several disadvantages. Since some of them are not sufficiently adapted for satellite networks [3; 14], significant attention is paid to the probability of failures and delay time. Other authors [14; 17] assume that there is a certain list of pre-defined routes for information delivery. However, determining this list is not a trivial task and, in general, it is difficult to specify in advance which routes will be used, and the total number of routes is growing so quickly that it is difficult to use all of them. Some researchers believe that the optimum of the unconstrained optimization problem is close to the optimum of the conditional optimization problem [17], which is not always true. One of the main problems in finding optimal routes is the computational complexity that increases with the number of nodes used in the network. Furthermore, existing telecommunication networks often have a heterogeneous structure, which also complicates the process of route optimization. Ref. [32] provides an overview of a large list of protocols used in wireless ad-hoc networks, and we can use them to solve the routing problem, since each of these protocols would enable us to find a set of information transmission routes; based on these, it would be possible to estimate the intensity of information loss. We set a different goal for developing an optimization algorithm: finding routes that minimize losses, rather than using a routing protocol and then estimating the resulting losses. Such a problem in global traffic routing in telecommunication systems, and especially in satellite systems, had not yet been solved. Therefore, the development and application of effective algorithms for optimal routes while minimizing losses is an important issue. In this paper, we present a greedy-gradient algorithmic combination for solving such a problem and investigate the efficiency of the new approach by computational experiment. The rest of this paper is organized as follows. In Section 2, we formulate the problem statement in a general form, and overview known methods of dynamic routing in the telecommunication networks.