Searching Without a Heuristic: Efficient Use of Abstraction

Abstract

In problem domains where an informative heuristic evaluation function is not known or not easily computed, abstraction can be used to derive admissible heuristic values. Optimal path lengths in the abstracted problem are consistent heuristic estimates for the original problem. Pattern databases are the traditional method of creating such heuristics, but they exhaustively compute costs for all abstract states and are thus usually appropriate only when all instances share the same single goal state. Hierarchical heuristic search algorithms address these shortcomings by searching for paths in the abstract space on an as-needed basis. However, existing hierarchical algorithms search less efficiently than pattern database constructors: abstract nodes may be expanded many times during the course of a base-level search. We present a novel hierarchical heuristic search algorithm, called Switchback, that uses an alternating direction of search to avoid abstract node re-expansions. This algorithm is simple to implement and demonstrates superior performance to existing hierarchical heuristic search algorithms on several standard benchmarks.

Faster Optimal and Suboptimal Hierarchical Search

“…In order to gain a better understanding of the performance of Short Circuit, we modified the original Switchback code from Larsen et al (2010) and compared the two algorithms on the four domains used in their work. Each instance was tested on a dual quad-core Xeon running at 2.66 GHz with 48 GB of RAM.…”

“…Switchback Switchback (Larsen et al 2010) is a hierarchical search algorithm that changes the direction of search at every level of the hierarchy. This technique is used to prevent node re-expansion.…”

“…This tile cannot be moved during the entire search process. The 100 instances reported by Larsen et al (2010) were used for the experiment. The median solution length is 51.…”

“…Switchback (Larsen et al 2010) is a state-of-the-art hierarchical search algorithm. We propose a simple modification to the Switchback algorithm, called Short Circuit, that reduces the number of node expansions required at each abstract level search.…”

Potential Search: A Bounded-Cost Search Algorithm

“…Many years of research in the field of heuristic search have produced powerful methods for creating sophisticated heuristics, such as abstractions (Larsen et al 2010), constraint relaxation and memory based heuristics (Felner, Korf, and Hanan 2004;Sturtevant et al 2009) as well as heuristics for planning domains (Katz and Domshlak 2010). Next, we show how it is possible to use any given heuristic and still choose to expand the node with the highest potential even without explicitly calculating it.…”