# Optimizing Aircraft Routes in Dynamic Conditions Utilizing Multi-Criteria Parameters
## 3 Materials and Methods
\begin{table}
\begin{tabular}{c c c c} \hline
**Area for Improvement** & **Suggestions** & **Connection with Classical Algorithms** & **Expected Result** \\ \hline \multirow{4}{*}{Integration of external factors} & Developing universal models that simultaneously take into account weather conditions, fuel consumption, topography, air traffic, and other critical factors. & The A*, B*, and Dijkstra algorithms can be modified to consider external factors by introducing weighting factors. & Increase the efficiency of routes through a comprehensive analysis of conditions, reducing risks and costs. \\ \hline \multirow{4}{*}{Adaptive algorithms} & Implementation of algorithms that can dynamically adjust routes in real time, factoring in changing weather conditions and other operational data. & D* and its variations are already adapted to dynamic conditions; further improvements may include real integration of variable factors. & Ensure route flexibility, improve flight safety, and reduce operating costs. \\ \hline \multirow{4}{*}{Economic optimization} & Integrate economic analysis into route planning processes, including estimating maintenance costs, aircraft depreciation, and time costs. & The A* and Dijkstra algorithms can be improved to take into account not only fuel costs but also other economic parameters in the cost function. & Optimization of not only fuel consumption but also overall economic performance of the flight, increasing profitability. \\ \hline \multirow{4}{*}{Scalability of solutions} & Development of high-performance and scalable algorithms capable of efficiently processing large amounts of data in global aviation systems. & The B* and Dijkstra algorithms can be parallelized or optimized for scalable systems with large amounts of data. & Application of solutions in large aviation systems, increasing productivity and the efficiency of route planning. \\ \hline \multirow{4}{*}{Standardization and integration} & Introduce standards for route planning that take into account external factors and integrate these standards into global aviation systems. & The use of common standards for modifying A*, D*, and other algorithms will allow for universal approaches to routing. & Improving the consistency and efficiency of route planning, facilitating cooperation between different aviation systems. \\ \hline \end{tabular}
\end{table} 
Table 3: Possible options for further improvement of algorithms for constructing optimal aircraft routes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm Name** & **Description** & \begin{tabular}{c} **Application in** \\ **Aviation** \\ \end{tabular} & **Advantages** & **Disadvantages** \\ \hline B* & \begin{tabular}{c} An improved version of A* \\ with balancing \\ optimization: \\ \(f(n)=g(n)+\epsilon\cdot h(n)\), where \\ \(\epsilon\)—coefficient for heuristic \\ correction. \\ \end{tabular} & \begin{tabular}{c} Limited memory \\ resources. \\ \end{tabular} & \begin{tabular}{c} There may be \\ trade-offs between \\ the speed of \\ computation and its \\ accuracy. \\ \end{tabular} \\ \hline B\_Lite* & \begin{tabular}{c} Reducing memory by \\ reducing the number of \\ stored nodes: \\ \(f(n)=g(n)+h(n)\), \\ but with data structure \\ optimization. \\ \end{tabular} & \begin{tabular}{c} Limited memory \\ resources. \\ \end{tabular} & Resource saving. & It may lose accuracy. \\ \hline Enhanced B* & \begin{tabular}{c} Optimization for \\ large spaces: \\ \(f(n)=g(n)+h(n)\) \\ with additional adaptation \\ of the heuristic to \\ large spaces. \\ \end{tabular} & \
\begin{tabular}{c} Large data spaces \\ or long routes. \\ \end{tabular} &
\begin{tabular}{c} Fast work in \\ large spaces. \\ difficult conditions. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis of modern improvements of the B* algorithm. Table 6 shows the results of the analysis of modern improvements to the D* algorithm.