Opportunistic mobile networks (OMNs) are a class of MANETs where complete endto-end paths rarely exist between sources and destinations; consequently, the end-to-end delays in these networks are much greater than typical MANETs. In this harsh environment networking algorithm actions and decisions are inherently local; the algorithms are mostly greedy, choosing the best solution among the locally ones. In this paper, we study the delivery performance of two classes of gradient utility ascent routing algorithms, deterministic (greedy) and stochastic utility ascent ones, in OMNs. We furthermore discuss the impact of these algorithms on traffic load distribution fairness among the network nodes, since this issue is critical in mobile networking whose nodes typically possess limited resources, e.g. power and storage capacity. Using simulation, driven by real human mobility traces, we investigate the performance of greedy ascent algorithms, Hill Climbing (HC) and Delegation Forwarding (DF), compared with that of stochastic ascent algorithms, Simulated Annealing (SA). The results under the scenario show an advantage of SA over HC and DF in terms of total delivered messages, average delivery delay, and traffic distribution fairness; however, SA negatively impacts the delivery cost performance, i.e. increasing the total message copies beyond those of HC and DF.