SAT Solving for Optimization

Question

Suppose you have a CNF formula with some variables marked special.
Is there a way to make a SAT Solver (say, minisat) find a solution maximizing the number of special variables assigned to true?

You could create a cardinality constraint (cf. http://www.carstensinz.de/papers/CP-2005.pdf) to enforce the lower bound of special variables set to true. This is not a true optimization, but you delimit the search space. By increasing the cardinality threshold until UNSAT, you get your maximum "by hand". — Axel Kemper, Jan 31 '13 at 22:47

score 3 · Accepted Answer · answered Jan 31 '13 at 22:45

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What you (I) want is called Partial Max Sat. There is a solver called qmaxsat, which seems to work well enough.

answered Jan 31 '13 at 22:45

Joseph Victor

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score 0 · Answer 2 · answered Feb 07 '13 at 12:44

Not sure if all of these can handle the indication of special variables, but at least wikipedia gives some direction for the search:

There are several solvers submitted to the last Max-SAT Evaluations:

Branch and Bound based: Clone, MaxSatz (based on Satz), IncMaxSatz, IUT_MaxSatz, WBO.

Satisfiability based: SAT4J, QMaxSat.

Unsatisfiability based: msuncore, WPM1, PM2.

Checking the description for all of them should be managable.

score 0 · Answer 3 · answered Feb 26 '14 at 12:48

You can use a PBC solver such as minisat+ http://minisat.se/MiniSat+.html They solve regular CNF files with additional constraints called pseudo Boolean constraints Minisat+ also supports optimization of such constraints and from my understanding it solves your problem

Let x1, .... xn be the variables you want to maximize the number o truth assignments Then you can define the constraints maximize +1 x1 ..... +1 xn minisat+ solves such optimization problems

SAT Solving for Optimization

3 Answers3