Abstract
In this paper, we propose a method to encode Constraint Satisfaction Problems (CSP) and Constraint Optimization Problems (COP) with integer linear constraints into Boolean Satisfiability Testing Problems (SAT) . The encoding method is basically the same with the one used to encode Job-Shop Scheduling Problems by Crawford and Baker. Comparison x ≤a is encoded by a different Boolean variable for each integer variable x and integer value a. To evaluate the effectiveness of this approach, we applied the method to Open-Shop Scheduling Problems (OSS) . All 192 instances in three OSS benchmark sets are examined, and our program found and proved the optimal results for all instances including three previously undecided problems.
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Tamura, N., Taga, A., Kitagawa, S., Banbara, M. (2006). Compiling Finite Linear CSP into SAT. In: Benhamou, F. (eds) Principles and Practice of Constraint Programming - CP 2006. CP 2006. Lecture Notes in Computer Science, vol 4204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889205_42
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DOI: https://doi.org/10.1007/11889205_42
Publisher Name: Springer, Berlin, Heidelberg
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