This work details theory in which selection favors generalists in a more variable environment. Specifically, in a two-host-one-parasitoid model, temporal variation in host abundances alters the optimal searching strategy and leads to the evolution of more generalist parasitoid strategies. Consistent with empirical observations, parasitoids learn host/plant odors, and use them as a cue to search for oviposition sites. The amount of unsuccessful search time required before a parasitoid alters its searching cues (the ''giving-up time'') is modeled in order to understand the evolutionarily optimal giving-up times under a variety of conditions. When host abundances vary across time, a generalist parasitoid strategy evolves with short giving-up times as it is likely that the host initially favored by a parasitoid will now have a low abundance. In contrast, when populations reach stable dynamics across time, giving-up times typically evolve to longer times, i.e. parasitoids remain specialized longer. The effect of temporal fluctuations is consistent across variation caused by endogenous population interactions and, to some degree, by environmental stochasticity. The conclusions are robust in that there is a strong degree of concordance between the results of a stochastic, individual-based model and a deterministic, numerical model. As an extension, spatial variation in hosts that leads to unequal tradeoffs between generalist parasitoids and specialist parasitoids may also result in the evolution of reduced giving-up times.