## 4 Solution Method
### Overview of Our Approach  
Our approach starts with an initialization phase that has two main parts (Figure 3). First, the 'Initial Setup' creates the environment for UAV route planning by configuring a grid-based operational area and placing obstacles. It also sets the drone's speed and payload capacity and defines environmental conditions like wind speed and direction. After setting up the environment, the system trains a neural network with random data to create an initial predictive model. This model estimates travel times based on factors like UAV speed, distance, wind conditions, and payload weight. Using synthetic data for various scenarios, it establishes a foundation for accurate predictions before actual route planning. The travel time estimates will be refined through feedback as more operational data are collected. After initialization, the system loads instance data from input files detailing problem specifications. Each file includes parameters like the number of nodes (UAV points), fleet size (number of UAVs), and maximum route duration. The system extracts node locations and rewards, ensuring they do not conflict with obstacles. This converts raw  
Figure 3: General overview of our approach. descriptions into structured data for route planning algorithms, defining the optimization challenge. At the core of our methodology lies an iterative optimization and learning process. Each iteration executes our simheuristic algorithm to generate two solutions: OBD (our best deterministic solution) and OBS (our best stochastic solution). The system then extracts operational data from the OBS to retrain the neural network model, improving travel time prediction accuracy. This feedback loop between optimization and learning represents a key innovation--the system progressively learns from its own results, creating increasingly reliable UAV routing solutions with each iteration. Rather than treating travel time estimation as static, we continuously refine it throughout the solution process, enhancing route quality as the neural network adapts to operational realities. The simheuristic algorithm follows a two-stage approach to solve the dynamic team-orienteering problem with obstacles. The process begins with an initialization phase that creates an initial solution by setting the alpha value for enhanced savings calculations and generating an initial efficiency list. This solution is established as our initial best deterministic solution (OBD) and serves as the first entry in our list of candidate solutions. Stage 1 focuses on building a collection of high-quality candidate solutions through an iterative time-constrained process (Figure 4). During this stage, the algorithm repeatedly generates new solutions using a merging process with biased randomization. Each promising solution (one that exceeds the current best reward) is designated as the new OBD and undergoes Monte Carlo simulation with 100 runs to evaluate its performance under stochastic conditions. These promising solutions are added to the list of candidate stochastic solutions (list\({}_{\text{O}}BS\)). This stage efficiently explores the solution space to identify diverse high-quality route configurations that perform well under varying conditions. Figure 4: A schema of Stage 1. As shown in Figure 5, Stage 2 refines the most promising stochastic solutions to determine our best stochastic solution (OBS). First, the algorithm sorts all candidate solutions in list\({}_{0}BS\) by their simulated reward values and selects the top-\(k\) solutions, where \(k\) is the minimum between a predefined maximum (5) and the total number of candidates. Each of these elite solutions undergoes a more intensive Monte Carlo simulation with 1000 runs to more accurately assess its performance under uncertainty. The solution that demonstrates the highest reward after this intensive simulation becomes the final OBS.