# A Sim-Learnheuristic for the Team Orienteering Problem: Applications to Unmanned Aerial Vehicles
## 6 Results and Discussion  
Table 2 shows the experimental results for each instance. The first column identifies the instances, while the remaining columns show the obtained results under the four considered scenarios. The first section of the table reports the best-known solutions for the deterministic variant of the problem obtained from the literature (\(BKS\)), our best-found solutions for the deterministic version of the problem (\(OBD\)), and the percentage gaps when both solutions are compared. The second section of the table reports the obtained results for the stochastic scenario. First, the best-found solutions for the deterministic scenario when evaluated in a stochastic environment are reported (\(OBD\)-\(S\)). To compute this solution, an intensive simulation process has been applied to the \(OBD\). The main idea behind this process is to assess the best-found deterministic solutions under stochastic uncertainty. Next, the best-found stochastic solutions obtained using our sim-leanheuristic approach are reported (\(OBS\)). This approach considers the stochastic elements during the search for a high-quality solution. The next section of the table shows the obtained results for the dynamic scenario. First, the best-found solutions for the deterministic version when evaluated under a dynamic environment are shown (\(OBD\)-\(Dy\)). Similarly, the best-found solutions for the dynamic scenario are reported (\(OBDy\)). Lastly, the results for the hybrid scenario are reported. First, the best-found solutions for the deterministic version when evaluated in a hybrid scenario are shown (\(OBD\)-\(H\)). Next, the best-found solutions for the hybrid scenario are reported (\(OBH\)). It is noteworthy that for each instance, the best-found solutions obtained by our sim-learnheuristic approach are consistently closer to the \(BKS\) when compared with the best-found deterministic solutions simulated under the corresponding types of uncertainty. In other words, our best-found solutions for the deterministic version of the problem are sub-optimal for the different stochastic, dynamic, and hybrid scenarios. For instance, considering the dynamic scenario, when simulating the \(OBD\), solutions often exhibit significant fluctuations. This is exemplified by the \(p5.3.z\) instance, as exemplified by p5.3.z, where \(OBD\)-\(Dy\) yields an expected reward of 2.34 and \(OBDy\) yields an expected reward of 1525.00. This difference can be attributed to the way our sim-learnheuristic approach explores the search space for solutions. Specifically, our novel methodology considers this uncertainty throughout the search for high-quality solutions. In other words, incorporating uncertainty elements in the search process leads to superior results compared to solely solving a deterministic version of the problem and then applying the solution in a real-life scenario with dynamic uncertainty. This fundamental difference serves as the key factor behind the substantial disparities observed between the best-found solutions obtained using our sim-learnheuristic method and the results obtained simulating the best-found deterministic solutions under the different uncertainty scenarios. Moreover, if we compare the computed averages for the different scenarios, we observe that we can classify the four different scenarios based on their uncertainty levels. Firstly, the deterministic scenario can be considered a reference scenario with perfect information (i.e., without uncertainty) for the expected reward under different uncertainty conditions. Conversely, in the stochastic scenario, we observe a lower uncertainty level, resulting in an average expected reward of 221.87 and 243.02 for the _OBD-S_ and _OBS_, respectively. This can be attributed to half of the edges' travel times being stochastic in nature, while the other half being deterministic. Similarly, for the hybrid scenario, we can observe a medium level of uncertainty which results in an average expected reward of 209.73 and 233.10 for the _OBD-H_ and _OBH_, respectively.