Complex search and second-order response surface analysis

This paper describes a two-phase approach to systems optimization via computer simulation experimentation. In the first phase, Box's Complex Search is employed to search from some initial set of simulation trials X₁..., X_K to an estimated optimum solution X*. Then a second-order response surface is fitted to these K points, or to some subset thereof, and analyzed through classical optimization procedures to gain yet another estimate X**. If y(X*) and y(X**) are sufficiently close, and X* and X** are close together, then the superior solution can be chosen. If either y(X*) is not close to y(X**), or X* is not close to X**, additional simulation trials in the neighborhood of X* and X** should be conducted to seek improved solutions.