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Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT

Author

Listed:
  • M. Yagiura

    (Kyoto University)

  • T. Ibaraki

    (Kyoto University)

Abstract

For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most effective approaches. Most of the local search algorithms are based on the 1-flip neighborhood, which is the set of solutions obtainable by flipping the truth assignment of one variable. In this paper, we consider r-flip neighborhoods for r ≥ 2, and propose, for r = 2, 3, new implementations that reduce the number of candidates in the neighborhood without sacrificing the solution quality. For 2-flip (resp., 3-flip) neighborhood, we show that its expected size is O(n + m) (resp., O(m + t2n)), which is usually much smaller than the original size O(n2) (resp., O(n3)), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance.

Suggested Citation

  • M. Yagiura & T. Ibaraki, 1999. "Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 95-114, July.
    • Handle: RePEc:spr:jcomop:v:3:y:1999:i:1:d:10.1023_a:1009873324187
    DOI: 10.1023/A:1009873324187
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    Cited by:

    1. Hideki Hashimoto & Mutsunori Yagiura & Shinji Imahori & Toshihide Ibaraki, 2013. "Recent progress of local search in handling the time window constraints of the vehicle routing problem," Annals of Operations Research, Springer, vol. 204(1), pages 171-187, April.
    2. Michael Drexl, 2021. "On efficient testing of capacity constraints in pickup-and-delivery problems with trailers," 4OR, Springer, vol. 19(2), pages 289-307, June.

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