The design of admissible (or nearly admissible) heuristics which are both effective (close to actual completion costs) and also efficient to compute is a difficult, open problem in most domains.
most work on search has focused on non-optimal methods, such as beam search or pruning based on approximate models (Collins, 1999), though in certain cases admissible heuristics are known (Och and Ney, 2000;Zhang and Gildea, 2006).