Hybrid Search Strategies for Heterogeneous Search Spaces

Recently, there has been much interest in enhancing purely combinatorial formalisms with numerical information. For example, planning formalisms can be enriched by taking resource constraints and probabilistic information into account. The Mixed Integer Programming (MIP) paradigm from operations research provides a natural tool for solving optimization problems that combine such numeric and non-numeric information. The MIP approach relies heavily on linear program relaxations and branch-and-bound search. This is in contrast with depth-first or iterative deepening strategies generally used in artificial intelligence. We provide a detailed characterization of the structure of the underlying search spaces as explored by these search strategies. Our analysis shows that much can be gained by combining different search strategies for solving hard MIP problems, thereby leveraging each strategy's strength in terms of the combinatorial and numeric information.

[1]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[2]  Henry A. Kautz,et al.  State-space Planning by Integer Optimization , 1999, AAAI/IAAI.

[3]  Martin W. P. Savelsbergh,et al.  An Updated Mixed Integer Programming Library: MIPLIB 3.0 , 1998 .

[4]  Tom Bylander.  A Linear Programming Heuristic for Optimal Planning , 1997, AAAI/IAAI.

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

[6]  Robert H. Smith.  Integer Programming Models in AI Planning : Preliminary Experimental Results , 1998 .

[7]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

[8]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

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

[10]  竹中 茂夫.  G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance , 1996 .

[11]  Bart Selman,et al.  Algorithm Portfolio Design: Theory vs. Practice , 1997, UAI.

[12]  Tad Hogg,et al.  An Economics Approach to Hard Computational Problems , 1997, Science.

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

[14]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[15]  Irina Rish,et al.  Summarizing CSP Hardness with Continuous Probability Distributions , 1997, AAAI/IAAI.