Controlled Random Search Procedures for Global Optimization

Solving optimization problems arising from engineering and economics, 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 measurable subset of ℝ d $$\mathbb {R}^d$$ and F is a measurable real function defined (at least) on D, one meets often the following situation: (I) One should find the global minimum F ∗ and/or a global minimum point x ∗ of (8.1). Hence, most of the deterministic programming procedures, which are based on local improvements of the objective function F(x), will fail. (II) Concerning the objective function F(x) one has a black-box-situation, i.e. there is only few a priori information A priori information about F especially there is no (complete) knowledge about the direct functional relationship between the control or input vector x ∈ D and its function value y = F(x). Hence, besides the limited a priori information about F, only by evaluating F numerically or by experiments at certain points z 1, z 2, … of ℝ d $$\mathbb {R}^d$$ one gets further information on F.