Solving SAT Problems with TA Algorithms Using Constant and Dynamic Markov Chains Length

• Published in: Algorithmic Applications in Management pp. 281 - 290
• Main Authors: Sanvicente–Sánchez, Héctor, Frausto–Solís, Juan, Imperial–Valenzuela, Froilán
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Combinatorial Optimization; Computer science; control theory; systems; Cooling Scheme; Dynamic Markov Chains; Exact sciences and technology; Heuristic Optimization; Mathematical programming; Operational research and scientific management; Operational research. Management science; SAT problem; Simulated Annealing; Theoretical computing; Threshold Accepting; Combinatorial problem; Chain length; Optimization method; Algorithmics; Constraint satisfaction; Processing time; Combinatorial optimization; Markov chain; Propositional logic; Combinatorial method; Quality; Simulated annealing; Problem solving; Satisfiability problem; Mathematical programming; Threshold
• ISBN: 3540262245; 9783540262244
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11496199_31

Since the apparition of Simulated Annealing algorithm (SA) it has shown to be an efficient method to solve combinatorial optimization problems. Due to this, new algorithms based on two looped cycles (temperatures and Markov chain) have emerged, one of them have been called Threshold Accepting (TA). Classical algorithms based on TA usually use the same Markov chain length for each temperature cycle, these methods spend a lot of time at high temperatures where the Markov chain length is supposed to be small. In this paper we propose a method based on the neighborhood structure to get the Markov chain length in a dynamic way for each temperature cycle. We implemented two TA algorithms (classical or TACM and proposed or TADM) for SAT. Experimentation shows that the proposed method is more efficient than the classical one since it obtain the same quality of the final solution with less processing time.