Response surface methodology's steepest ascent and step size revisited

Response surface methodology (RSM) searches for the input combination maximizing the output of a real system or its simulation. RSM is a heuristic that locally fits first-order polynomials, and estimates the corresponding steepest ascent (SA) paths. However, SA is scale-dependent; and its step size is selected intuitively. To tackle these two problems, this paper derives novel techniques combining mathematical statistics and mathematical programming. Technique 1, called ‘adapted’ SA (ASA), accounts for the covariances between the components of the estimated local gradient. ASA is scale-independent. The step-size problem is solved tentatively. Technique 2 does follow the SA direction, but with a step size inspired by ASA. Mathematical properties of the two techniques are derived and interpreted; numerical examples illustrate these properties. The search directions of the two techniques are explored in Monte Carlo experiments. These experiments show that, in general, ASA gives a better search direction than SA.