We aim at constructing a timetable that minimizes average perceived passenger travel time, which, in addition to the in-train and transfer times, includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. Besides considering safety restrictions (i.e., headway times, overtaking and crossing constraints), passenger routing, based on origin- destination demand pairs, must be taken into account when building the timetable. This problem can be modelled as an extension of a Periodic Event Scheduling Problem (PESP) formulation, but cannot be directly solved by a general-purpose solver for our real-size instances. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a simplified timetabling model, and determine an ideal timetable that minimizes the average perceived passenger travel time but neglects safety restrictions. Then, a Lagrangian-based heuristic makes the timetable feasible by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting average perceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting safety constraints. We have tested the proposed iterative heuristic approach on real-life instances of Netherlands Railways, showing that it converges to a feasible timetable very close to the ideal one.