Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT
Mutsunori Yagiura and Toshihide Ibaraki
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 $r \geq 2$,
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 $O(n+m)$
which is usually much smaller than the original size $O(n^2)$
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.
MAX SAT, SAT, local search, neighborhood
Journal of Combinatorial Optimization, Vol. 3, No. 1, pp. 95-114, July 1999.
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