Incomplete Tree Search using Adaptive Probing

Abstract

When not enough time is available to fully explore a search tree, different algorithms will visit different leaves. Depth-first search and depth-bounded discrepancy search, for example, make opposite assumptions about the distribution of good leaves. Unfortunately, it is rarely clear a priori which algorithm will be most appropriate for a particular problem. Rather than fixing strong assumptions in advance, we propose an approach in which an algorithm attempts to adjust to the distribution of leaf costs in the tree while exploring it. By sacrificing completeness, such flexible algorithms can exploit information gathered during the search using only weak assumptions. As an example, we show how a simple depth-based additive cost model of the tree can be learned on-line. Empirical analysis using a generic tree search problem shows that adaptive probing is competitive with systematic algorithms on a variety of hard trees and outperforms them when the node-ordering heuristic makes many mistakes. Results on boolean satisfiability and two different representations of number partitioning confirm these observations. Adaptive probing combines the flexibility and robustness of local search with the ability to take advantage of constructive heuristics.