Weighted [formula omitted] search – unifying view and application

Abstract

The A ∗ algorithm is a well-known heuristic best-first search method. Several performance-accelerated extensions of the exact A ∗ approach are known. Interesting examples are approximate algorithms where the heuristic function used is inflated by a weight (often referred to as weighted A ∗ ). These methods guarantee a bounded suboptimality. As a technical contribution, this paper presents the previous results related to weighted A ∗ from authors like Pohl, Pearl, Kim, Likhachev and others in a more condensed and unifying form. With this unified view, a novel general bound on suboptimality of the result is derived. In the case of avoiding any reopening of expanded states, for ϵ > 0 , this bound is ( 1 + ϵ ) ⌊ N 2 ⌋ where N is an upper bound on an optimal solution length. Binary Decision Diagrams (BDDs) are well-known to AI, e.g. from set-based exploration of sparse-memory and symbolic manipulation of state spaces. The problem of exact or approximate BDD minimization is introduced as a possible new challenge for heuristic search. Like many classical AI domains, this problem is motivated by real-world applications. Several variants of weighted A ∗ search are applied to problems of BDD minimization and the more classical domains like blocksworld and sliding-tile puzzles. For BDD minimization, the comparison of the evaluated methods also includes previous heuristic and simulation-based methods such as Rudell's hill-climbing based sifting algorithm, Simulated Annealing and Evolutionary Algorithms. A discussion of the results obtained in the different problem domains gives our experiences with weighted A ∗ , which is of value for the AI practitioner.