Search Strategies for an Anytime Usage of the Branch and Prune Algorithm

But this premature paving is not very useful if the searchtree is explored depth-first (DFS) or breadth-first (BFS): DFS When applied to numerical CSPs, the branch and quickly converges to ɛ-boxes that are too close to one another prune algorithm (BPA) computes a sharp covering to be representative of the solution set (see the left part of of the solution set. The BPA is therefore impractical Figure 1); BFS computes a homogeneous paving but finds no when the solution set is large, typically when ɛ-box at all if stopped too early (see the center graphic of Figure it has a dimension larger than four or five which is 1; note that such a sharp paving cannot be computed for often met in underconstrained problems. The purpose larger solution sets, making BFS useless in such cases). of this paper is to present a new search tree The search strategy used in an anytime BPA should quickly exploration strategy for BPA that hybridizes depthfirst find ɛ-boxes that are representative of the solution set: ɛ- and breadth-first searches. This search strategy boxes should be discovered uniformly on a continuous connected allows the BPA discovering potential solutions component in the solution set, while every connected in different areas of the search space in early stages components should be reached by some ɛ-boxes in early of the exploration, hence allowing an anytime usage stages of the search. Two such strategies are introduced in of the BPA. The merits of the proposed search the present paper. The most distant-first strategy (MDFS) strategy are experimentally evaluated.