Simulated Annealing Algorithms for Continuous Global Optimization

In this chapter we will consider Simulated Annealing algorithms for continuous global optimization. After a description of the generic Simulated Annealing algorithm, its four main components (the distribution of the next candidate point, the acceptance function, the cooling schedule and the stopping criterion) will be analyzed in greater detail and some key ideas will be presented. In view of the strict connection with Simulated Annealing algorithms, we will also discuss the Langevin equation and its discretized version. The theoretical issue of convergence in probability to the set of global optima of the sequences of iterates and candidates will be explored. We will also give some insight into the properties of the objective functions for which a successful application of Simulated Annealing algorithms can be expected. Finally, some other issues such as applications, computational tests and parallelization of these algorithms will be discussed.