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    <p>You might want to look into constraint optimization, specifically soft-arc consistency, and constraint satisfaction, specifically arc-consistency, or other types of consistency such as i-consistency. Here's some references about constraint optimization:</p> <p>[1] Thomas Schiex. Soft constraint Processing. <a href="http://www.inra.fr/mia/T/schiex/Export/Ecole.pdf" rel="nofollow">http://www.inra.fr/mia/T/schiex/Export/Ecole.pdf</a></p> <p>[2] Dechter, Rina. Constraint Processing, 1st ed. Morgan Kaufmann, San Francisco, CA 94104-3205, 2003.</p> <p>[3] Kask, K., and Dechter, R. Mini-Bucket Heuristics for Improved Search. In Proc. UAI-1999 (San Francisco, CA, 1999), Morgan Kaufmann, pp. 314–323.</p> <p>[3] might be especially interesting because it deals with combining A* with a heuristic of the type you seem to be interested in. </p> <p>I'm not sure whether this helps you. Here's how I got the idea that it might:</p> <p>Constraint optimization is a generalization of SAT towards optimization and variables with more than two values. A set of soft-constraints, i.e. partial cost functions, and a set of discrete variables define your problem. Typically a branch-and-bound algorithm is used to traverse the search tree that this problem implies. Soft-arc consistency refers to a set of heuristics that use local soft-constraints to compute the approximate distance to the goal node in that search tree, from your current position. These heuristics are used within the branch-and-bound search, much like heuristics are used within A* search.</p> <p>Branch-and-bound relates to A* over trees much the same way that depth-first search relates to breadth-first search. So, apart from the fact that a DFS-like algorithm (branch-and-bound) is used in this case, and that it is a tree instead of a graph, it looks like (soft)-arc consistency or other types of consistency is what you are looking for. </p> <p>Unfortunately, while you can in principle use A* in place of branch-and-bound, it is not clear yet (as far as I know) how in general you could combine A* with soft-arc consistency. Going from a tree to a graph might further complicate things, but I don't know that.</p> <p>So, no final answer, just some stuff to look at as a starter, maybe :).</p>
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