By by Patrik Haslum.
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3: Calculation of (a) the h1 value and (b) the h2 value for the goal of the “tower construction” Blocksworld problem. The “critical tree” is indicated by bold arrows in each. or generalized shortest path algorithm. A variation of the generalized Bellman-Ford algorithm is presented below (see Liu et al (2002) for some alternative methods). The parameter m offers a trade-off between the accuracy of the heuristic and its computational cost. As m increases, the relaxation (last clause of equation (6)) plays a lesser role and the heuristic function more and more resembles the optimal cost function.
U) to distinguish when the UAV is in the air from when it is on the ground. u p42) true near the end of the action (say within the last 10 seconds). Preconditions of the action are associated with time intervals during which they are required to hold, rather than with time points. u along the path between points p0 and p42: (a) the control modes and continuous evolution of the world state (heading, altitude, velocity) during and surrounding the action; (b) abstracted view of the action (incomplete).
At the same time, however, the computation of a complete hm solution is polynomial in the number of atoms but exponential in m (since the number of subsets of size m or less grows exponentially with m). Also, the heuristic resulting from a complete solution to the hm equation exhibits for many planning problems a “diminishing marginal gain”: once m goes over a certain threshold (typically, m = 2) the improvement brought by the use of hm+1 over hm becomes smaller for increasing m. This combines to make this method of computing the heuristic cost effective, in the sense that the heuristic reduces search time more than the time required to compute it, only for small values of m (typically m 2; Zhou & Hansen (2004) report also using h3 ).
Admissible heuristics for automated planning by by Patrik Haslum.