This article explores how machine learning can be applied in efficiently solving a variation of the Travelling Salesman Problem (TSP) in the context of air travel tourism. Large number of cities create too many trip route combinations to be efficiently evaluated in real time. The method proposed uses a feedforward neural network to narrow down the number of trip route combinations, while a more traditional algorithm based on dynamic programming is then able to select the best trip offers. It was shown that the method could be applied in practice to achieve almost real-time generation of best possible trip offers while evaluating a large amount of real-world flight data.