A mobile wireless network experiences random variations due to node mobility, which may potentially be exploited for more cost-effective communications. The pioneering work by Grossglauser and Tse (2001) first demonstrated that a network under sufficient amount of (random) mobility could provide a larger scaling rate of throughput capacity than a static network, at the cost of significant and potentially unbounded end-to-end delay. Subsequent works have addressed the issue of the capacity gain under bounded delay. In this paper, we take a rather different approach in that we explore node mobility in the search for the optimal packet delivery routes subject to the QoS criteria such as delay and energy consumption. This is obtained by adopting a deterministic model in a non-interfering mobile ad hoc network (MANET). We present polynomial time algorithms for finding these optimal routes. Specifically, in a system without power control capability, where the transmission range of each node is fixed, we seek optimal routes with minimal end-to-end delivery time or lowest total power consumption along the path, respectively. For both formulations, we propose hop-expansion based algorithms that carry out the computations inductively over the number of hops. In a system with power control, we seek the minimum energy route, subject to certain end-to-end delay constraint. For this optimization, we propose a layered algorithm that performs the computations inductively over the discrete time periods.