Neutrality in fitness landscapes
Applied Mathematics and Computation
Stochastic Local Search: Foundations & Applications
Stochastic Local Search: Foundations & Applications
An empirical analysis of search in GSAT
Journal of Artificial Intelligence Research
SATzilla: portfolio-based algorithm selection for SAT
Journal of Artificial Intelligence Research
When gravity fails: local search topology
Journal of Artificial Intelligence Research
A portfolio approach to algorithm select
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
Elementary bit string mutation landscapes
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Search based software engineering: techniques, taxonomy, tutorial
Empirical Software Engineering and Verification
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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.