Only one property or measure seldom defines the production process or the quality of a
manufactured product. In most practical optimization situations more than one response
variable must be considered simultaneously.
There is no simple procedure for combining the different response variables into one
general performance measure, because:
- The response variables are measured with different scales.
- The relative significance of different response variables differs.
- For some response variables the objective is maximization, but for others it is
minimization or a specific target.
It is also difficult to define the optimization objectives in a "black and
white" fashion, where a response of 100 is "good" but 99 is
"bad". Usually the description of the optimization objectives has a substantial
degree of vagueness and uncertainty, such as "high enough", "as low as
possible" or "close to the target".
MultiSimplex uses the approach of fuzzy set theory, with membership functions, to form
a realistic description of the optimization objectives. (Others call almost the same
approach "desirability functions"). Different response variables, with separate
scales and optimization objectives, can then be combined into a joint response measure
called the aggregated value of membership.
