We develop an approach for solving rooted orienteering problems with category constraints as found in tourist trip planning and logistics. It is based on expanding partial solutions in a systematic way, prioritizing promising ones, which reduces the search space we have to traverse during the search. The category constraints help in reducing the space we have to explore even further. We implement an algorithm that computes the optimal solution and also illustrate how our approach can be turned into an approximation algorithm, yielding much faster run times and guaranteeing lower bounds on the quality of the solution found. We demonstrate the effectiveness of our algorithms by comparing them to the state-of-the-art approach and an optimal algorithm based on dynamic programming, showing that our technique clearly outperforms these methods.