In this paper, an exact algorithm is proposed for determining adjustable preference path strategies in multicriteria, stochastic, and time-varying (MSTV) networks. In MSTV networks, multiple arc attributes are associated with each arc, each being a time-varying random variable. Solution paths that seek to minimise the expected value of each of multiple criteria are sought from all origins to a specified destination for all departure times in a period of interest These solution strategies allow a traveler to update a preference for which criterion of multiple criteria is of greatest importance and then adaptively select the best path for the selected criterion at each node in response to knowledge of experienced travel times on the arcs. Such adjustable preference path strategies are particularly useful for providing real-time path-finding assistance.