Tuned Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Maxsat Problem

In this paper, a hybrid Simulated Annealing algorithm using Boltzmann and Bose-Einstein Distributions (SABBE) is proposed. SABBE was designed for solving satisfiability (SAT) instances, and it has three phases: i) BP (Boltzmann Phase), ii) BEP (Bose-Einstein Phase), and iii) DEP (Dynamical Equilibrium Phase). BP and BEP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions respectively. BP ranges from high to low temperature values, while BEP goes from low to very low temperatures. Another simulated annealing search procedure, DEP, is applied at the final temperature of the second phase. However, DEP uses a particular heuristic for detection of stochastic equilibrium by employing a least squares method during its execution. Finally, SABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of SAT instances.