A comparative runtime analysis of heuristic algorithms for satisfiability problems.

Artificial Intelligence
Yuren ZhouQing Nie

Abstract

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, (1+1) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT(k >/= 3) is O((k - 1)(n)), and presents a k-SAT instance that has Theta((k - 1)(n)) expected runtime bound.

References

Mar 26, 2002·Evolutionary Computation·Jens GottliebClaudio Rossi
Jul 13, 2006·Evolutionary Computation·Frédéric LardeuxJin-Kao Hao
May 13, 1983·Science·S KirkpatrickM P Vecchi

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Citations

Sep 15, 2015·Computational Intelligence and Neuroscience·Yushan Zhang, Guiwu Hu
Dec 14, 2016·Evolutionary Computation·Xinsheng LaiQingfu Zhang
Jun 20, 2019·International Journal of Environmental Research and Public Health·Longlong LengChunmiao Zhang
Apr 10, 2015·PloS One·Ariel José BerensteinAriel Chernomoretz
Sep 29, 2017·Neural Computation·Yan-Shuo ChangHeng Huang

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