# Optimizing Aircraft Routes in Dynamic Conditions Utilizing Multi-Criteria Parameters
## 2 Related Works  
**Analysis of recent research and publications. ** The theoretical analysis of professional sources has shown that classical algorithms such as the A*, B*, D*, and Dijkstra's algorithms are effective for finding optimal paths in a two-dimensional plane. However, they have a number of drawbacks when applied to problems in three dimensions. Paper [3] presents the results of a practical and experimental flight path construction using the A* algorithm and taking into account restricted areas and wind direction. This solution provides examples of optimization by trajectory length, considering deviations from the optimal flight path based on SNS positioning data. The disadvantage of this solution in modern conditions is that the influence of weather conditions and the characteristics of aircraft fuel consumption at different altitudes have not been studied. In general, according to the authors of this paper, despite the fact that the A* algorithm always finds the optimal route under certain conditions, its effectiveness is significantly reduced in 3D space due to the need to take into account a large number of nodes and branches, which increases memory requirements and computation time. Paper [5] provides a fairly detailed description of the study of the effects of various natural disturbances on flight duration and fuel consumption. The authors also analyze the results of flight path optimization and present a geometric algorithm as an alternative to the A* and Dijkstra algorithms. The authors investigate how various natural factors, such as wind, rain, and snow, affect flight time and fuel consumption, making their research highly relevant to real-world aviation tasks where weather conditions are crucial. It is worth noting that this is a rather innovative approach to solving flight path optimization problems that can be useful in specific cases, for example, for quick route estimation under certain conditions. Also, as noted above, the authors of this paper point out the importance of optimizing flight paths with respect to wind effects, which is an important feature for reducing fuel consumption and improving flight efficiency. However, the above approach has a significant drawback: in this solution, the search problem is reduced to a two-dimensional plane, and the main optimization criterion is only the duration of the flight, not fuel consumption or safety. Nevertheless, this study is extremely useful in the case of overlaying the downwind flight path optimization procedure. In particular, according to this work, the B* algorithm, similarly to the A* algorithm, depends on the efficiency of the passage through the structure of the decision tree used to find the optimal route. However, this algorithm has a rather significant drawback in its practical application, namely, the urgent need to store data on the nodes passed, which becomes problematic given the large number of possible flight paths in 3D space. Study [6] presents the results of analyzing the impact of wind when searching for the optimal route, taking into account the fuel burned. The paper also analyzes the peculiarities of fuel consumption at different altitudes and provides examples of finding the optimal flight path, considering the following factors: flight duration and the amount of fuel burned, taking into account the vertical profiles of the aircraft. According to this work, the D* algorithm is suitable for dynamic environments, but at the same time, it has limitations when working with large amounts of data in 3D space, which may affect its performance. Like the A* algorithm, it has node weights in two-dimensional space and requires increased memory resources to store data on the third dimension and the distance between nodes, taking the third coordinate plane into account. In terms of practical application, the refinements highlighted in this paper indicate the importance of considering altitude profiles and the impact of dynamic conditions on the effectiveness of algorithms in three-dimensional space.