Random Search Procedures for Global Optimization

Solving optimization problems from engineering, as, e.g., parameter—or process—optimization problems min F ( x ) s.t. x ∈ D , $$\displaystyle \min F (x) \mbox{ s.t. } x \in D, $$ where D is a subset of ℝ n $$\mathbb {R}^n$$ , one meets often the following situation: (a) One should find the global optimum in (6.1), hence most of the deterministic programming procedures, which are based on local improvements of the performance index F(x), will fail. (b) Concerning the objective function F one has a blackbox—situation, i.e. there is only few a priori information A priori information about the structure of F, especially there is no knowledge about the direct functional relationship between the control or input vector x ∈ D and its index of performance F(x); hence—besides the more or less detailed a priori information about F—the only way of getting objective information about the structure of F is via evaluations of its values F(x) by experiments or by means of a numerical procedure simulating the technical plant.