Admissible heuristics for automated planning by by Patrik Haslum.

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.

Thus hm (s ) hm ((s − add(a)) ∪ pre(a)) + cost(a) ( rather than = since there may be actions with smaller cost applicable to s but not to s) and thus hm ((s −add(a))∪pre(a)) v−cost(a) > v −cost(a) (due to the assumption that v > v and the fact that cost(a) > 0). However, since (s −add(a))∪pre(a) ⊆ (s−add(a))∪pre(a), hm ((s−add(a))∪pre(a)) hm ((s −add(a))∪pre(a)), and thus hm ((s − add(a)) ∪ pre(a)) v − cost(a) > v − cost(a) = hm ((s − add(a)) ∪ pre(a)), contradicting the assumption that v is the smallest value such that hm (s) = v > v = hm (s).

By Chapman (1987), Bylander (1991) and others) the problem model was simplified and the background theories discarded. g. Wilkins, 1983). 2 of PDDL (Edelkamp & Hoffmann 2004). 2 allows so called derived predicates, which are defined by a set of rules evaluated recursively (in PROLOG style), rather than part of the world state. , the transitive closure of a relation to be expressed, but is still compilable into the basic representation (Thiebaux, Hoffmann, & Nebel 2003). The state variable representation (B¨ ackstr¨ om 1992; Sandewall & R¨onnquist 1986) replaces the logical propositions of the STRIPS representation by variables with finite ranges of values, but embodies the same planning model: in fact, it is expressively equivalent with propositional STRIPS (for each variable v and value c, “v = c” is essentially a proposition; a formal proof of equivalence is given by B¨ackstr¨om, 1992).

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