We propose an Adaptive Variable Neighbourhood Search (AVNS) metaheuristic for dynamic optimisation of tourist itineraries at destination for use in an interactive online tourist route recommender. The recommendation must use up-to-date information and be able to adapt the recommendation according to changes in the circumstances of the touristic activities or to specific requirements of the tourist user. Instead of using an algorithm to get the new recommendation from scratch after the changes, we propose to apply AVNS from the previous proposal. The adaptive mechanism takes into account previous performance to tune the parameters to the change that occurred. We test the proposal using real data from the tourist island of Tenerife in the Canary Islands. The results show that our proposal provides better results in less computational time.