Abstract
The memory requirements of best-first graph search algorithms such as A* often prevent them from solving large problems. The best-known approach for coping with this issue is iterative deepening, which performs a series of bounded depth-first searches. Unfortunately, iterative deepening only performs well when successive cost bounds visit a geometrically increasing number of nodes. While it happens to work acceptably for the classic sliding tile puzzle, IDA* fails for many other domains. In this paper, we present an algorithm that adaptively chooses appropriate cost bounds on-line during search. During each iteration, it learns a model of the search tree that helps it to predict the bound to use next. Our search tree model has three main benefits over previous approaches: (1) it will work in domains with real-valued heuristic estimates, (2) it can be trained on-line, and (3) it is able to make more accurate predictions with only a small number of training examples. We demonstrate the power of our improved model by using it to control an iterative-deepening A* search on-line. While our technique has more overhead than previous methods for controlling iterative-deepening A*, it can give more robust performance by using its experience to accurately double the amount of search effort between iterations.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Arbelaez, A., Hamadi, Y., Sebag, M.: Continuous search in constraint programming. In: 22nd IEEE International Conference on Tools with Artificial Intelligence (ICTAI-10), vol. 1, pp. 53–60 (2010)
Battiti, R., Brunato, M., Mascia, F.: Reactive Search and Intelligent Optimization, vol. 45. Springer (2008)
Culberson, J.C., Schaeffer, J.: Pattern databases. Comput. Intell. 14(3), 318–334 (1998)
Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley (1998)
Hamadi, Y., Monfroy, E., Saubion, F.: What is autonomous search? In: van Hentenryck, P., Milano, M. (eds.) Hybrid Optimization. Springer Optimization and Its Applications, vol. 45, pp. 357–391. Springer, New York (2011)
Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)
Haslum, P., Botea, A., Helmert, M., Bonte, B., Koenig, S.: Domain-independent construction of pattern database heuristics for cost-optimal planning. In: Proceedings of the 22nd Conference on Artificial Intelligence (AAAI-07) (2007)
Korf, R.E.: Iterative-deepening-A*: An optimal admissible tree search. In: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI-85), pp. 1034–1036 (1985)
Korf, R.E., Reid, M., Edelkamp, S.: Time complexity of iterative-deepening-A*. Artif. Intell. 129, 199–218 (2001)
Korf, R.E., Zhang, W., Thayer, I., Hohwald, H.: Frontier search. Journal of the ACM 52(5), 715–748 (2005)
Lelis, L., Stern, R., Jabbari Arfaee, S.: Predicting solution cost with conditional probabilities. In: Proceedings of the 4th Annual Symposium on Combinatorial Search (SoCS-11) (2011)
Malitsky, Y.: Instance-Specific Algorithm Configuration. Ph.D. Thesis, Brown University (2012)
Méro, L.: A heuristic search algorithm with modifiable estimate. Artif. Intell. 23(1), 13–27 (1984)
Nilsson, N.J.: Principles of Artificial Intelligence. Tioga Publishing Co (1980)
Pearl, J.: Heuristics: Intelligent Search Strategies for Computer Problem Solving. Addison-Wesley (1984)
Rose, K., Burns, E., Ruml, W.: Best-first search for bounded-depth trees. In: Proceedings of the 4th Annual Symposium on Combinatorial Search (SoCS-11) (2011)
Ruml, W.: Adaptive Tree Search. Ph.D. Thesis, Harvard University (2002)
Sarkar, U., Chakrabarti, P., Ghose, S., Sarkar, S.D.: Reducing reexpansions in iterative-deepening search by controlling cutoff bounds. Artif. Intell. 50, 207–221 (1991)
Thayer, J., Ruml, W.: Using distance estimates in heuristic search. In: Proceedings of the 19th International Conference on Automated Planning and Scheduling (ICAPS-09) (2009)
Vempaty, N.R., Kumar, V., Korf, R.E.: Depth-first vs best-first search. In: Proceedings of AAAI-91, pp. 434–440 (1991)
Wah, B.W., Shang, Y.: Comparison and evaluation of a class of IDA* algorithms. Int. J. Artif. Intell. Tools 3(4), 493–523 (1995)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. 32(1), 565–606 (2008)
Zahavi, U., Felner, A., Burch, N., Holte, R.C.: Predicting the performance of IDA* using conditional distributions. J. Artif. Intell. Res. 37, 41–83 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Burns, E., Ruml, W. Iterative-deepening search with on-line tree size prediction. Ann Math Artif Intell 69, 183–205 (2013). https://doi.org/10.1007/s10472-013-9347-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-013-9347-9