# A Hybrid IVFF-AHP and Deep Reinforcement Learning Framework for an ATM Location and Routing Problem
## 4 A Real Case Study
### ATM Routing Network
The proposed approach provides a practical solution suitable for logistics, urban distribution systems, and transportation planning where dynamic routing optimization is necessary to enhance operational efficiency. NetworkX was utilized to compute the shortest paths between these locations, forming a distance matrix as the foundation for routing optimization. A traffic-adjusted distance  
Figure 7: ATM routing network with selected nodes and road connectivity in the selected region. matrix was generated based on historical traffic data corresponding to the ATM vehicle's operational period. By keeping this matrix fixed during training, the model was able to incorporate realistic travel constraints while avoiding the computational overhead associated with real-time updates. During the training phase, the model was not restricted to ATM locations alone but was trained on all 30 central locations, with each location (except for the starting point) assigned an artificial demand. This approach ensured that the model effectively learned the complete road network topology, allowing it to navigate to any designated ATM location during deployment efficiently. This also enabled it to adapt to changes in the network, such as the addition or removal of ATM sites, without requiring re-training and handle unexpected routing modifications, such as last-minute ATM insertions or removals, thereby increasing the model's flexibility and robustness in real-world applications. The proposed DDQN-RL model was extensively evaluated to measure its performance, adaptability, and robustness under various ATM deployment scenarios. Following a training phase of 10,000 episodes, the model underwent a series of 100-episode test runs to assess the efficiency of the optimized routing policy. To enhance adaptability, the RL agent was trained on all 30 central locations, rather than restricting learning to pre-selected ATM sites. By assigning artificial demand levels to these locations during training, the agent effectively internalized the entire network structure, enabling it to generalize efficiently to any ATM configuration. This means that when new ATMs are introduced or existing ones are removed, the model can adjust without requiring re-training. Additionally, the learned policy supports real-time modifications, allowing mid-route updates such as last-minute ATM additions or cancellations to be incorporated seamlessly. The reward convergence curve, shown in Figure 8, indicates that the model rapidly stabilized after the early episodes and maintained consistent performance throughout. Following the training phase, seven different test scenarios were constructed to simulate practical variations in ATM network configurations, including node additions and removals. For each scenario, 100 independent test runs were performed. Remarkably, all test runs yielded identical outputs for each scenario, indicating that the trained model exhibits highly stable behavior and robust generalization performance. Additionally, in each test case, the trained model generated a near-optimized routing solution in under 3 s without any additional set-up, showcasing its suitability for real-time or near-real-time deployment in operational environments. During training, the distance matrix remained fixed, reflecting the traffic-adjusted travel costs for the designated operational period. The model was trained for 10,000 episodes, ensuring robust convergence of the Q-values. The epsilon-greedy strategy was used to balance exploration and exploitation, with an initial exploration rate of \(\epsilon=0.7\) that gradually decayed to \(\epsilon=0.01\). The final trained model successfully demonstrated optimal ATM servicing strategies, effectively minimizing total travel distance, maximizing vehicle utilization, and dynamically responding to operational changes in real-world deployment scenarios. The designated ATM locations in the first experimental setup were set to nodes 127, 228, 110, and 911, respectively.