Stochastic global optimization

Stochastic global optimization methods are methods for solving a global optimization prob-lem incorporating probabilistic (stochastic) elements, either in the problem data (the objective function, the constraints, etc.), or in the algorithm itself, or in both. Global optimization is a very important part of applied mathematics and computer science. The importance of global optimization is primarily related to the applied areas such as engi-neering, computational chemistry, finance and medicine amongst many other fields. For the state of the art in the theory and methodology of global optimization we refer to the ‘Journal of Global Optimization ’ and two volumes of the ‘Handbook of Global Optimization ’ [1,2]. If the objective function is given as a ‘black box ’ computer code, the optimization problem is es-pecially difficult. Stochastic approaches can often deal with problems of this kind much easier and more efficiently than the deterministic algorithms. The problem of global minimization. Consider a general minimization problem f(x)→minx∈X with objective function f(·) and feasible region X. Let x ∗ be a global minimizer of f(·); that is, x ∗ is a point in X such that f(x∗) = f ∗ where f ∗ = minx∈Xf(x). Global optimization problems are usually formulated so that the structure of the feasible region X is relatively simple; thi