The TSP, VRP and OP problems with time constraints have one common sub-problem – the task of finding the minimum route duration for a given order of customers. While much work has been done on routing and scheduling problems with time windows, to this date only few articles considered problems with multiple time windows. Moreover, since the assumption of constant travel time between two locations at all times is very unrealistic, problems with time-dependent travel were introduced and studied. Finally, it is also possible to imagine some situations, in which the service time changes during the day. Again, both issues have been investigated only in conjunction with single time windows. In this paper we propose a novel algorithm for computing minimum route duration in traveling salesman problem with multiple time windows and time-dependent travel and service time. The algorithm can be applied to wide range of problems in which a traveler has to visit a set of customers or locations within specified time windows taking into account the traffic and variable service/visit time. Furthermore, we compare three metaheuristics for computing a one-day schedule for this problem, and show that it can be solved very efficiently.