Multicriteria steepest ascent

Abstract

A simple multiresponse steepest ascent procedure has been developed by combining the standard steepest ascent method with multicriteria decision making. The steepest ascent method is one of the older methods in response surface methodology. It can be applied in optimization where the operability region is so large that a very complex function would be needed to fit an empirical function. With steepest ascent, local designs and local models in a part of the operability region are used to find a .direction where the response is improved most. Experiments performed along a line in that direction will reveal the region of interest. There the response may be fitted with a second degree equation. The problem of multiresponse steepest ascent is that directions of improvement have to be combined into one direction. In general, the directions of improvement indicated by the individual responses are different and they may even be opposite. In this paper, steepest ascent has been adapted to the use of more responses by combination of the directions of steepest ascent to a simultaneous direction of interest. The combination is made by consideration of the obtainable improvements of the responses in the response space. These improvements can be calculated from the centre point (of the local design) response values and the response values at a fixed distance of the centre point. As an example, the method has been applied to a tablet optimization. This optimization problem had two responses and two independent variables.

Steepest Ascent for Multiple-Response Applications

“…Duineveld et al (1994) illustrated this for a particular case and showed how a search direction can be PO for some step sizes but not for others. Although many of the methods proposed herein depend on the simplicity of the first-order model, the concept of "paths of improvement" regions does not.…”

“…In Section 3 we formally define PO treatment combinations and show which points are PO for the first-order model. Duineveld et al (1994) presented examples of PO points lying a fixed distance from the design center for both first-order and more complex models. Using either overlaid contour plots or sets of PO predictions, we can compare the options and select a suitable compromise.…”