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Scholars who view organizational, social, and technological systems as sets of interdependent decisions have increasingly used simulation models from the biological and physical sciences to examine system behavior. These models shed light on an enduring managerial question: How much exploration is necessary to discover a good configuration of decisions? The models suggest that, as interactions across decisions intensify and local optima proliferate, broader exploration is required. The models typically assume, however, that the interactions among decisions are distributed randomly. Contrary to this assumption, recent empirical studies of real organizational, social, and technological systems show that interactions among decisions are highly patterned. Patterns such as centralization, small-world connections, power-law distributions, hierarchy, and preferential attachment are common. We embed such patterns into an NK simulation model and obtain dramatic results: Holding fixed the total number of interactions among decisions, a shift in the pattern of interaction can alter the number of local optima by more than an order of magnitude. Thus, the long-run value of broader exploration is significantly greater in the face of some interaction patterns than in the face of others. We develop simple, intuitive rules of thumb that allow a decision maker to examine two interaction patterns and determine which warrants greater investment in broad exploration. We also find that, holding fixed the interaction pattern, an increase in the number of interactions raises the number of local optima regardless of the pattern. This validates prior comparative static results with respect to the number of interactions, but highlights an important implicit assumption in earlier work—that the underlying interaction pattern remains constant as interactions become more numerous.