An Hybrid Simulated Annealing Threshold Accepting Algorithm for Satisfiability Problems using Dynamically Cooling Schemes

For Satisfiability (SAT) Problem there is not a deterministic algorithm able to solve it in a polynomial time. Simulated Annealing (SA) and similar algorithms like Threshold Accepting (TA) are able to find very good solutions of SAT instances only if their control parameters are correctly tuned. Classical TA’s algorithms usually use the same Markov chain length for each temperature cycle but they spend a lot of time. In this paper a new hybrid algorithm is presented. This algorithm is in fact a TA algorithm which is hybridized with SA in a certain way. For this TA algorithm, the Markov chain length (L) is obtained in a dynamical way for each temperature. Besides, it is known that TA and SA obtain very good results whether their parameters are correctly tuned. Experimental tuning methods expend a lot of time before a TA algorithm can correctly be executed; in other hand, analytical tuning methods for TA were only completely developed for the geometrical cooling function. This paper also shows how TA can be tuned for three common cooling functions with an analytical model. Experimentation presented in the paper shows that the new TA algorithm is more efficient than the classical one. Key-Words: Simulated Annealing, Threshold Accepting, Cooling function, Dynamic Markov Chains, SAT problem