The problem of constrained workflow scheduling on heterogeneous computing systems has been of major interest in the recent years. The user requirements are described by defining constraints on the workflow makespan and/or its execution cost. The uncertainty in the activity execution path and the dynamicity in the resource workload may cause some run-time changes of the makespan or cost. To prohibit runtime constraint violation, the system needs robust schedules. In this paper, probability of violation (POV) of constraints is proposed as a criterion for the schedule robustness. An ant colony system is then used to minimize an aggregation of violation of constraints and the POV. Simulation results on real world workflows show the effectiveness of the proposed method in finding feasible schedules. The results also indicate that the proposed method decreases the POV, as well as the expected penalty at run-time.