Using Reinforcement Learning in a Dynamic Team Orienteering Problem with Electric Batteries

This paper addresses the team orienteering problem (TOP) with vehicles equipped with electric batteries under dynamic travel conditions influenced by weather and traffic, which impact travel times between nodes and hence might have a critical effect on the battery capacity to cover the planned route. The study incorporates a novel approach for solving the dynamic TOP, comparing two solution methodologies: a merging heuristic and a reinforcement learning (RL) algorithm. The heuristic combines routes using calculated savings and a biased-randomized strategy, while the RL model leverages a transformer-based encoder–decoder architecture to sequentially construct solutions. We perform computational experiments on 50 problem instances, each subjected to 200 dynamic conditions, for a total of 10,000 problems solved. The results demonstrate that while the deterministic heuristic provides an upper bound for rewards, the RL model consistently yields robust solutions with lower variability under dynamic conditions. However, the dynamic heuristic, with a 20 s time limit for solving each instance, outperformed the RL model by 3.35% on average. The study highlights the trade-offs between solution quality, computational resources, and time when dealing with dynamic environments in the TOP.