Abstract. Given a nite state machine denoting the specication of a system, nding some short interaction sequences capable to reach some/all states or transitions of this machine is a typical goal in testing methods. If these sequences are applied to an implementation under test, then equivalent states or transitions would be reached and observed in the implementation provided that the implementation were actually dened as the specication. We study the problem of nding such sequences in the case where congurations previously traversed can be saved and restored (at some cost). In general, this feature enables sequences to reach the required parts of the machine in less time, because some repetitions can be avoided. However, we show that nding optimal sequences for this case is an NP-hard problem. We propose an heuristic method to approximately solve this problem based on an evolutionary computation approach, in particular river formation dynamics. Besides, some experimental res...