## 1 Introduction  
The team orienteering problem (TOP) is a combinatorial optimization problem that involves selecting a subset of locations, each associated with a specific reward [1, 2, 3]. The goal is to plan routes for a team of agents to maximize the total collected reward while satisfying operational constraints. These constraints may include time limits, agent capacities, and the structure of the route network [4, 5, 6]. The TOP belongs to the class of orienteering problems [7] and has applications in healthcare logistics [8], tourism [9], and resource management, where optimizing the use of limited resources is essential [10]. In the TOP, each agent must determine not only which locations to visit but also the optimal sequence to maximize total reward while adhering to imposed constraints. These characteristics increase the problem's difficulty, as both node selection and visit sequence are crucial for optimization. This study extends the traditional TOP framework by applying it to a fleet of unmanned aerial vehicles (UAVs). In addition to standard constraints, we incorporate environmental factors such as obstacles and wind conditions, which influence UAV performance. To compute routes that avoid obstacles, we employ the A* algorithm, a widely used path-planning method for UAVs [11; 12]. Hence, this paper addresses the scientific problem of solving the TOP under realistic constraints (e.g., physical obstacles and environmental conditions) that are typically ignored in classical approaches. These factors significantly affect the feasibility and efficiency of routes, particularly in applications involving UAVs or autonomous vehicles. The problem is modeled on a two-dimensional grid map, allowing a precise representation of the environment. Using A*, we efficiently determine paths that minimize travel distance while ensuring obstacle avoidance. Once a path is established, the UAV's travel time is estimated based on several factors. The trajectory between two locations is defined as a sequence of two-dimensional coordinates obtained using A*. The total travel distance is computed as the sum of Euclidean distances between successive coordinates, measured in kilometers. The estimated travel time considers: (i) the UAV's speed, assumed to be constant along the trajectory; (ii) the wind's speed and direction, which influence the UAV's effective speed; and (iii) the weight of onboard sensors and equipment required for operations at each location. Figure 1 shows two trajectories: one from node 1 to node 2 and another from node 2 to node 3. These trajectories are located on a \(30\times 30\) km grid. The following factors influence the UAV's trajectory: (i) UAV speed--the UAV maintains a constant speed along the entire trajectory (km/min); (ii) wind speed and direction--wind velocity (km/min) and direction (radians) are considered as environmental factors, which can increase or decrease the UAV's effective speed depending on the trajectory; and (iii) payload weight--the weight (kg) of sensor equipment and other devices mounted on the UAV, which are necessary for performing operations at each location. To predict travel time, we employed a multi-layer fully connected feedforward neural network [13], suitable for regression tasks. The network's input features include (i) UAV speed; (ii) distance between two trajectory coordinates; (iii) angle between successive trajectory vectors; (iv) wind speed and direction; and (v) payload weight. For multi-coordinate trajectories, the network estimates the travel time between each successive coordinate pair,  
Figure 1: Example of trajectories with UAVs avoiding obstacles on a \(30\times 30\) km grid. and the total time is obtained by summing these individual estimates. With this time estimation model, we can solve the TOP by optimizing UAV routes using the A* algorithm.