Rockwell Automation Arena OptQuest Users Guide - Manual (Page 27)

3 • U NDERSTANDING THE T ERMINOLOGY
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For example, suppose that in a job-shop problem a foreman insists on finding an optimal
configuration with the following constraints:
drills + grinders <= 4
drills + grinders >= 5
where “drills” is a control that indicates the number of drills in the shop and “grinders” is
a control that indicates the number of grinders in the shop. Clearly, there is no combina-
tion that will make the sum of the drills and grinders no more than 4 and at the same time
greater than or equal to 5.
Or, for this same example, suppose the bounds for another control were:
3 <= saws <= 5
and that the following constraint was added:
saws <= 2
This also results in an infeasible problem.
You can make infeasible problems feasible by fixing the inconsistencies of the relation-
ships modeled by the constraints.
OptQuest’s highest priority is to find a solution that is constraint feasible. Once OptQuest
has found a solution that is constraint feasible, it concentrates on finding solutions that
improve the value of the objective function.
Objective
Each optimization model has one objective function that mathematically represents the
model’s goal (in terms of the assumptions and controls); the objective is either to
minimize or maximize this quantity. OptQuest’s job is to find the optimal value of the
objective by selecting and improving different values for the controls.
When model data is uncertain and can only be described using probability distributions,
the objective itself will have some probability distribution for any set of values for the
controls. You can find an empirical approximation of this probability distribution by
performing statistical analysis on a given response. The optimization model, however, is
typically defined using a desired statistic (e.g., the mean) associated with a response as the
objective to be maximized or minimized.