Abstract
The time required for a backtracking search procedure to solve a problem can be minimized by employing randomized restart procedures. To date, researchers designing restart policies have relied on the simplifying assumption that runs are probabilistically independent from one another. We relax the assumption of independence among runs and address the challenge of identifying an optimal restart policy for the dependent case. We show how offline dynamic programming can be used to generate an ideal restart policy, and how the policy can be used in conjunction with real-time observations to control the timing of restarts. We present results of experiments on applying the methods to create ideal restart policies for several challenging search problems using two different solvers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dimitris Achlioptas, Carla P. Gomes, Henry A. Kautz, and Bart Selman. Generating satisfiable problem instances. In AAAI/IAAI, pages 256–261, 2000.
D.P. Bertsekas and J. N. Tsitsiklis. Neuro-Dynamic Programming. Athena Scientific, 1996.
Hubie Chen, Carla Gomes, and Bart Selman. Formal models of heavy-tailed behavior in combinatorial search. Lecture Notes in Computer Science, 2239:408ff, 2001.
David Maxwell Chickering, David Heckerman, and Christopher Meek. A Bayesian approach to learning Bayesian networks with local structure. In Proceedings of the Thirteenth Conference On Uncertainty in Artificial Intelligence (UAI-97), pages 80–89, Providence, RI, 1997. Morgan Kaufman Publishers.
Joseph C. Culberson and Feng Luo. Exploring the k-colorable landscape with iterated greedy. In David S. Johnson and Michael A. Trick, editors, Dimacs Series in Discrete Mathematics and Theoretical Computer Science, Vol. 36, pages 245–284, 1996.
I. Gent and T. Walsh. Easy Problems are Sometimes Hard. Artificial Intelligence, 70:335–345, 1993.
Carla P. Gomes and Bart Selman. Problem Structure in the Presence of Perturbations. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97), pages 221–227, New Providence, RI, 1997. AAAI Press.
Carla P. Gomes, Bart Selman, and Nuno Crato. Heavy-tailed Distributions in Combinatorial Search. In Gert Smolka, editor, Principles and practice of Constraint Programming (CP97) Lecture Notes in Computer Science, pages 121–135, Linz, Austria., 1997. Springer-Verlag.
Carla P. Gomes, Bart Selman, Nuno Crato, and Henry Kautz. Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. of Automated Reasoning, 24(1-2):67–100, 2000.
Carla P. Gomes, Bart Selman, and Henry Kautz. Boosting Combinatorial Search Through Randomization. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98), pages 431–438, New Providence, RI, 1998. AAAI Press.
Carla P. Gomes, Bart Selman, and Henry A. Kautz. Boosting combinatorial search through randomization. In AAAI/IAAI, pages 431–437, 1998.
Aaai-2000 workshop on leveraging probability and uncertainty in computation, 2000.
T. Hogg, B. Huberman, and C. Williams (Eds.). Phase Transitions and Complexity (Special Issue). Artificial Intelligence, 81(1–2), 1996.
Eric Horvitz, Yongshao Ruan, Carla Gomes, Henry Kautz, Bart Selman, and Max Chickering. A Bayesian approach to tackling hard computational problems. In Proceedings the 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), pages 235–244, Seattle, USA, 2001.
R. A. Howard. Dynamic Programming and Markov Processes. MIT Press, 1960.
H. Kautz and B. Selman. Pushing the envelope: planning, propositional logic, and stochastic search. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), pages 1188–1194, Portland, OR, 1996. AAAI Press.
Henry Kautz, Eric Horvitz, Yongshao Ruan, Bart Selman, and Carla Gomes. Dynamic randomized restarts: Optimal restart policies with observation. To appear in AAAI, 2002.
Henry Kautz, Yongshao Ruan, D. Achlioptas, Carla P. Gomes, Bart Selman, and Mark Stickel. Balance and filtering in structured satisfiable problems. In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI-01), pages 351–358, 2001.
S. Kirkpatrick and B. Selman. Critical behavior in the satisfiability of random Boolean expressions. Science, 264:1297–1301, 1994.
Chu Min Li and Anbulagan. Heuristics based on unit propagation for satisfiability problems. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 366–371. AAAI Pess, 1997.
M. Luby, A. Sinclair, and D. Zuckerman. Optimal speedup of las vegas algorithms. Information Process. Letters, pages 173–180, 1993.
Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. Chaff: Engineering an efficient SAT solver. In Design Automation Conference, pages 530–535, 2001.
B. Selman, H. Kautz, and B. Cohen. Local search strategies for satisfiability testing. In D. Johnson and M. Trick, editors, Dimacs Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26, pages 521–532. AMS, 1993.
T. Walsh. Search in a Small World. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1172–1177, Stockholm, Sweden, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ruan, Y., Horvitz, E., Kautz, H. (2002). Restart Policies with Dependence among Runs: A Dynamic Programming Approach. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_38
Download citation
DOI: https://doi.org/10.1007/3-540-46135-3_38
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44120-5
Online ISBN: 978-3-540-46135-7
eBook Packages: Springer Book Archive