# Optimizing Aircraft Routes in Dynamic Conditions Utilizing Multi-Criteria Parameters
## 3 Materials and Methods
The analysis of the key areas of optimal air routes for aircraft in the table shows the need to improve universal models that would simultaneously take into account weather conditions, fuel consumption, and other factors, as well as adapt to changing conditions in real time. In addition, there is a need to consider cost-effectiveness, including maintenance costs, and to develop scalable solutions that can handle large amounts of data. It is also important to introduce standards and guidelines to ensure the versatility and effectiveness of models for modern aviation logistics. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Achievements of Scientists** & **Disadvantages and Limitations** \\ \hline Route-building algorithms & Using the classic A*, B*, D*, and Dijkstra algorithms with modifications to take into account external factors such as weather conditions and fuel consumption. & Most works focus on a theoretical basis with limited practical application in real-world conditions. Lack of standardized approaches to taking all factors into account. \\ \hline Consideration of weather conditions & Mathematical models have been developed to assess the impact of weather conditions on routing. Penalty functions and weighting coefficients are used to model weather conditions. & Lack of a universal model for different climatic conditions. Some works do not take into account variable weather conditions in real time. \\ \hline Accounting for fuel consumption & Models for calculating fuel consumption are proposed that consider the length of the route, speed, and external factors such as weather conditions and topography. & Insufficient attention is paid to integrating fuel consumption with other factors, such as delivery time or route reliability. \\ \hline Optimization for real-world conditions & Some researchers propose algorithms that can adapt to changing conditions (e.g., the D* algorithm), which allows for quick real-time route adjustments when weather or traffic conditions change. & Significant computational costs when implemented in real time, which limits the scalability of such solutions for large systems. \\ \hline Practical application & Some studies demonstrate the effectiveness of the proposed models in specific conditions, such as autonomous vehicles or logistics systems. & Lack of widespread use in various industries, which results in limited availability of off-the-shelf solutions for aviation logistics. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analysis of key scientific achievements in the field of building optimal aircraft routes. Table 3 shows possible options for further improvement of algorithms for constructing optimal air routes for aircraft. It also shows that classical algorithms can be adapted and improved to meet modern challenges in building optimal flight routes for aircraft by integrating them with new technologies and expanding their capabilities in aviation logistics. Table 4 shows the results of the analysis of modern modifications of the A* algorithm. The following notations are introduced: \(f(n)\)--total cost estimate of the path (which includes the real cost of the path, from the starting point to the current point, and the estimated cost from the current point to the target point); \(g(n)\)--actual cost of the path from the starting point to the current point \(n\) (reflects the part of the path that has already been traveled); \(h(n)\)--heuristic estimate of the cost of the path from the current point \(n\) to the target point (projected costs to complete the route); \(\theta(n)\)--the angle at which the algorithm takes into account the possibility of moving diagonally, which allows for shortening the path; \(i\)--an index indicating a single agent in a multi-agent system (for example, several aircraft coordinating their actions); and _bound_--a boundary value that determines the maximum possible cost for the current iterative search.