Hardness-Aware Restart Policies

Recent work has demonstrated that it is possible to boost the efficiency of combinatorial search procedures via the use of principled restart policies. We present a coupling of machine learning and dynamic programming that extends prior efforts by endowing restart policies with knowledge of the hardness of the specific instance being solved. This ability allows a restart policy to take into consideration an updated probability distribution over hardness as a previously unseen instance is being solved. We discuss the methods, highlighting their importance for real-world applications of combinatorial search. Finally, we present the empirical results.

[1]  Bart Selman,et al.  Balance and Filtering in Structured Satisfiable Problems , 2001, IJCAI.

[2]  S Kirkpatrick,et al.  Critical Behavior in the Satisfiability of Random Boolean Expressions , 1994, Science.

[3]  Bart Selman,et al.  Heavy-Tailed Distributions in Combinatorial Search , 1997, CP.

[4]  Solomon Kullback,et al.  Information Theory and Statistics , 1970, The Mathematical Gazette.

[5]  Bart Selman,et al.  Generating Satisfiable Problem Instances , 2000, AAAI/IAAI.

[6]  Feng Luo,et al.  Exploring the k-colorable landscape with Iterated Greedy , 1993, Cliques, Coloring, and Satisfiability.

[7]  Toby Walsh,et al.  Easy Problems are Sometimes Hard , 1994, Artif. Intell..

[8]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[9]  Bart Selman,et al.  Pushing the Envelope: Planning, Propositional Logic and Stochastic Search , 1996, AAAI/IAAI, Vol. 2.

[10]  Yoav Shoham,et al.  Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions , 2002, CP.

[11]  David Zuckerman,et al.  Optimal speedup of Las Vegas algorithms , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[12]  Eric Horvitz,et al.  Dynamic restart policies , 2002, AAAI/IAAI.

[13]  Bart Selman,et al.  Problem Structure in the Presence of Perturbations , 1997, AAAI/IAAI.

[14]  Eric Horvitz,et al.  Restart Policies with Dependence among Runs: A Dynamic Programming Approach , 2002, CP.

[15]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[16]  Bart Selman,et al.  Boosting Combinatorial Search Through Randomization , 1998, AAAI/IAAI.

[17]  Bart Selman,et al.  Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems , 2000, Journal of Automated Reasoning.

[18]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[19]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[20]  David Maxwell Chickering,et al.  A Bayesian Approach to Tackling Hard Computational Problems (Preliminary Report) , 2001, Electron. Notes Discret. Math..