We present a partial Max-SAT solver QMaxSAT which uses CNF encoding of Boolean cardinality constraints. The old version 0.1 was obtained by adapting a CDCL based SAT solver MiniSat to manage cardinality constraints. It was placed first in the industrial subcategory and second in the crafted subcategory of partial Max-SAT category of the 2010 Max-SAT Evaluation. The new version 0.2 is obtained by modifying version 0.1 to decrease the number of clauses for the cardinality encoding. We compare the two versions by solving Max-SAT instances taken from the 2010 Max-SAT Evaluation.

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SUMMARYThis paper tries to solve open Job-Shop Scheduling Problems (JSSP) by translating them into Boolean Satisfiability Testing Problems (SAT). The encoding method is essentially the same as the one proposed by Crawford and Baker. The open problems are ABZ8, ABZ9, YN1, YN2, YN3, and YN4. We proved that the best known upper bounds 678 of ABZ9 and 884 of YN1 are indeed optimal. We also improved the upper bound of YN2 and lower bounds of ABZ8, YN2, YN3 and YN4.