Predicting optimal solution costs with bidirectional stratified sampling in regular search spaces

Levi H.S. Lelis, Roni Stern, Shahab Jabbari Arfaee, Sandra Zilles, Ariel Felner, Robert C. Holte

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Optimal planning and heuristic search systems solve state-space search problems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for a state-space search problem directly, i.e., without actually finding a solution path of that cost. We present an algorithm, BiSS, which is a hybrid of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost. BiSS is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity. We show empirically that BiSS produces accurate predictions in several domains. In addition, we show that BiSS scales to state spaces much larger than can be solved optimally. In particular, we estimate the average solution cost for the 6×6, 7×7, and 8×8 Sliding-Tile puzzle and provide indirect evidence that these estimates are accurate. As a practical application of BiSS, we show how to use its predictions to reduce the time required by another system to learn strong heuristic functions from days to minutes in the domains tested.

Original languageEnglish
Pages (from-to)51-73
Number of pages23
JournalArtificial Intelligence
StatePublished - 1 Jan 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.


We thank Rong Zhou for providing the optimal solution cost for the instances of the 24-puzzle used in our experiments. This work was supported by the Laboratory for Computational Discovery at the University of Regina, Alberta Innovates – Technology Futures, the Alberta Innovates Centre for Machine Learning, Canada's NSERC , and Brazil's CAPES , FAPEMIG , and Science Without Borders .

FundersFunder number
FAPEMIG , and Science Without Borders
Natural Sciences and Engineering Research Council of Canada
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Alberta Innovates


    • Heuristic search
    • Learning heuristic functions
    • Solution cost prediction
    • Stratified sampling
    • Type systems


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