Using Transformers and Reinforcement Learning for the Team Orienteering Problem Under Dynamic Conditions

This paper presents a reinforcement learning (RL) approach for solving the team orienteering problem under both deterministic and dynamic travel time conditions. The proposed method builds on the transformer architecture and is trained to construct routes that adapt to real-time variations, such as traffic and environmental changes. A key contribution of this work is the model’s ability to generalize across problem instances with varying numbers of nodes and vehicles, eliminating the need for retraining when problem size changes. To assess performance, a comprehensive set of experiments involving 27,000 synthetic instances is conducted, comparing the RL model with a variable neighborhood search metaheuristic. The results indicate that the RL model achieves competitive solution quality while requiring significantly less computational time. Moreover, the RL approach consistently produces feasible solutions across all dynamic instances, demonstrating strong robustness in meeting time constraints. These findings suggest that learning-based methods can offer efficient, scalable, and adaptable solutions for routing problems in dynamic and uncertain environments.