A Reinforcement Learning Approach to the Orienteering Problem with Time Windows

The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial optimization has recently shown promising results in dealing with similar problems, like the Travelling Salesman Problem. A neural network allows learning solutions using reinforcement learning or supervised learning, depending on the available data. After the learning stage, it can be generalized and quickly fine-tuned to further improve performance and personalization. The advantages are evident since, for real-world applications, solution quality, personalization, and execution times are all important factors that should be taken into account. This study explores the use of Pointer Network models trained using reinforcement learning to solve the OPTW problem. We propose a modified architecture that leverages Pointer Networks to better address problems related with dynamic time-dependent constraints. Among its various applications, the OPTW can be used to model the Tourist Trip Design Problem (TTDP). We train the Pointer Network with the TTDP problem in mind, by sampling variables that can change across tourists visiting a particular instance-region: starting position, starting time, available time, and the scores given to each point of interest. Once a model-region is trained, it can infer a solution for a particular tourist using beam search. We based the assessment of our approach on several existing benchmark OPTW instances. We show that it generalizes across different tourists that visit each region and that it generally outperforms the most commonly used heuristic, while computing the solution in realistic times.