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The Orienteering Problem with Time Windows (OPTW) is a combinatorialoptimization problem where the goal is to maximize the total score collectedfrom different visited locations. The application of neural network models tocombinatorial optimization has recently shown promising results in dealing withsimilar problems, like the Travelling Salesman Problem. A neural network allowslearning solutions using reinforcement learning or supervised learning,depending on the available data. After the learning stage, it can begeneralized and quickly fine-tuned to further improve performance andpersonalization. The advantages are evident since, for real-world applications,solution quality, personalization, and execution times are all importantfactors that should be taken into account.  This study explores the use of Pointer Network models trained usingreinforcement learning to solve the OPTW problem. We propose a modifiedarchitecture that leverages Pointer Networks to better address problems relatedwith dynamic time-dependent constraints. Among its various applications, theOPTW can be used to model the Tourist Trip Design Problem (TTDP). We train thePointer Network with the TTDP problem in mind, by sampling variables that canchange across tourists visiting a particular instance-region: startingposition, starting time, available time, and the scores given to each point ofinterest. Once a model-region is trained, it can infer a solution for aparticular tourist using beam search. We based the assessment of our approachon several existing benchmark OPTW instances. We show that it generalizesacross different tourists that visit each region and that it generallyoutperforms the most commonly used heuristic, while computing the solution inrealistic times.

A Reinforcement Learning Approach to the Orienteering Problem with Time Windows