# A Sim-Learnheuristic for the Team Orienteering Problem: Applications to Unmanned Aerial Vehicles
## 5 Computational Experiments
This means that instead of relying on fixed or predefined travel times, the travel times between nodes are now estimated based on the real-time or dynamic information available at the time of planning the routes. This multiple regression model takes into account external factors such as weather and congestion conditions to calculate the dynamic cost. The weather adversity level \(w\) and congestion adversity level \(c\), ranging from 0 (low) to 1 (high), serve as input variables for the regression model. These two parameters are generated from a uniform distribution, which indicates that extreme weather and traffic conditions are as likely to occur as more standard ones. This generation matches the dynamic nature of the system, as every condition is likely to occur at any point in time. Thus, the dynamic travel times are calculated with Equation (10) as follows:  
\[\hat{t}_{ij}=b_{e}\cdot t_{ij}+(b_{1}w+b_{2}c+e) \tag{10}\]  
where \(t_{ij}\) represents the deterministic time of the edge connecting nodes \(i\) and \(j\), \(b_{e}\) is a coefficient for edge standard time, \(b_{1}\) represents the coefficient for the weather, and \(b_{2}\) represents the coefficient of the congestion. In addition, the term \(e\) represents the independent error term, assumed to be 0 to maintain the deterministic travel time value when the conditions are ideal (\(w\) and \(c\) parameters are 0). For our analysis, we have employed the values \(b_{e}=1\), \(b_{1}=0.005\), and \(b_{2}=0.0075\), which was designed so the dynamic travel time varies between the deterministic travel time and 1.125 times the deterministic travel time. In addition, the edges are categorized into two parts for the dynamic scenario following these conditions. If the node index is even, we classify the corresponding edge as dynamic. Otherwise, we classify the edge as deterministic. In the hybrid scenario, we combine three distinct edge types: deterministic, stochastic, and dynamic edges. In determining the type of edge, we implement these specific conditions. If the node index is even, we classify the corresponding edge as stochastic. Otherwise, if the node index is divisible by three, we classify the edge as dynamic. If neither of these conditions is met, we assign the edge as a deterministic edge. This systematic approach ensures the accurate classification of edges within our model. Due to the uncertain nature of travel times, there is a possibility of route failure when a UAV is unable to reach the destination depot within the designated time limit. Therefore, the reward collected by a particular UAV, \(r_{d}\), is defined as follows:  
\[r_{d}=\left\{ \begin{aligned} &\sum_{(i,j)\in A}u_{i}\cdot x_{ij}^{d}& \text{if}\quad\sum_{(i,j)\in A_{det}}t_{ij}x_{ij}^{d}+\sum_{(i,j)\in A_{ affine}}\hat{t}_{ij}x_{ij}^{d}+\sum_{(i,j)\in A_{stch}}T_{ij}x_{ij}^{d}\leq T_{max}\\ & 0&\text{otherwise}\end{aligned} \right. \tag{11}\]  
Hence, when a UAV embarks on a route, it faces uncertainty in the time it takes to travel between nodes due to the probabilistic nature of the travel times. If the UAV fails to complete the planned route within the limited time, it forfeits all the rewards it accumulated during its journey. It is important to note that any partial rewards obtained are considered valid solely if the UAV manages to reach the destination node before the end of its travel time.