On the convergence of parallel simulated annealing

We consider a parallel simulated annealing algorithm that is closely related to the so-called parallel chain algorithm. Periodically a new state from states is chosen as the initial state for simulated annealing Markov chains running independent of each other. We use selection strategies such as best-wins or worst-wins and show that the algorithm in the case of best-wins does not in general converge to the set of global minima. Indeed the period length and the number have to be large enough. In the case of worst-wins the convergence result is true. The phenomenon of the superiority of worst-wins over best-wins already occurs in finite-time simulations.