Abstract
The fundamental topic addressed in this paper concerns stochastic optimization problems. More specifically, our problem of interest is the determination of a ground state of a Hamiltonian function of an Ising model through the application of a simulated annealing algorithm based on parallel dynamics. Some theoretical aspects which were already mathematically proven by the same authors are presented in order to justify the application of simulated annealing for a particular class of probabilistic cellular automata. After that, it is demonstrated via simulations that for some class of examples its performance is higher than the performance of a well-stablished simulated annealing algorithm based on a single spin-flip dynamics, the so-called Glauber dynamics. In the end, we propose a derivation of the method presented initially in this paper and show through simulations that its accuracy in obtaining ground states is significantly higher within all studied cases. The observations in this paper support the need of further investigations of simulated annealing based on parallel dynamics from a rigorous perspective aiming at determining the limitations of such methods and finding clear directions to solve real-world combinatorial problems in an optimal way.
