Estimating bounds on expected plateau size in maxsat problems

Andrew M. Sutton; Adele E. Howe; L. Darrell Whitley

doi:10.1007/978-3-642-03751-1_3

Estimating bounds on expected plateau size in maxsat problems

Andrew M. Sutton, Adele E. Howe, L. Darrell Whitley

Computer Science (Duluth)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

Stochastic local search algorithms can now successfully solve MAXSAT problems with thousands of variables or more. A key to this success is how effectively the search can navigate and escape plateau regions. Furthermore, the solubility of a problem depends on the size and exit density of plateaus, especially those closest to the optimal solution. In this paper we model the plateau phenomenon as a percolation process on hypercube graphs. We develop two models for estimating bounds on the size of plateaus and prove that one is a lower bound and the other an upper bound on the expected size of plateaus at a given level. The models' accuracy is demonstrated on controlled random hypercube landscapes. We apply the models to MAXSAT through analogy to hypercube graphs and by introducing an approach to estimating, through sampling, a key parameter of the models. Using this approach, we assess the accuracy of our bound estimations on uniform random and structured benchmarks. Surprisingly, we find similar trends in accuracy across random and structured problem instances. Less surprisingly, we find a high accuracy on smaller plateaus with systematic divergence as plateaus increase in size.

Original language	English (US)
Title of host publication	Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings
Pages	31-45
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-642-03751-1_3
State	Published - 2009
Event	2nd International Workshop on Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics, SLS 2009 - Brussels, Belgium Duration: Sep 3 2009 → Sep 4 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5752 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	2nd International Workshop on Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics, SLS 2009
Country/Territory	Belgium
City	Brussels
Period	9/3/09 → 9/4/09

Bibliographical note

Funding Information:
This research was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0422. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

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Sutton, A. M., Howe, A. E., & Whitley, L. D. (2009). Estimating bounds on expected plateau size in maxsat problems. In Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings (pp. 31-45). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5752 LNCS). https://doi.org/10.1007/978-3-642-03751-1_3

Estimating bounds on expected plateau size in maxsat problems. / Sutton, Andrew M.; Howe, Adele E.; Whitley, L. Darrell.
Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. 2009. p. 31-45 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5752 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Sutton, AM, Howe, AE & Whitley, LD 2009, Estimating bounds on expected plateau size in maxsat problems. in Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5752 LNCS, pp. 31-45, 2nd International Workshop on Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics, SLS 2009, Brussels, Belgium, 9/3/09. https://doi.org/10.1007/978-3-642-03751-1_3

Sutton AM, Howe AE, Whitley LD. Estimating bounds on expected plateau size in maxsat problems. In Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. 2009. p. 31-45. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-03751-1_3

Sutton, Andrew M. ; Howe, Adele E. ; Whitley, L. Darrell. / Estimating bounds on expected plateau size in maxsat problems. Engineering Stochastic Local Search Algorithms - Designing, Implementing and Analyzing Effective Heuristics - Second International Workshop, SLS 2009, Proceedings. 2009. pp. 31-45 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Estimating bounds on expected plateau size in maxsat problems

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