The nonlinear optimization problem and statistical design problem can both be formulated as a region search problem. In this paper, we present a stochastic optimization process, suitable for optimizing functions of a certain measure over generalized regions inR^n. Conditions for an optimal process are discussed, and examples of a wide range of different optimization problems are given. These include the optimization of constrained, discontinuous and random functions in both discrete and continuous variable space. Design centering and tolerancing of large size systems subject to environmental disturbances are also treated.