Contents - Index

Find Optimal Targets Dialog Box





The Find Optimal Targets dialog box is used to find the set of targets optimizing an objective function or a characteristic of an output variable.  The optimal targets for the continuous input variables are found for the current tolerances and selected categories of the category input variables.  If these tolerances are later changed, the optimization should be repeated.  The optimization is performed over the region bounded by the Minimum Target and Maximum Target entered in the Continuous Input Variable dialog box for those inputs whose Use for Optimization check box is checked.  Constrained optimizations can be performed by specifying the constraints as part of the equations for the output variable and objective function.  See the hints at the bottom for speeding up the optimization.

The Find Optimal Targets dialog box is displayed by selecting the Find Optimal Targets menu item on the Analysis menu or by clicking on the    button on the toolbar.
The dialog controls are:
Output list box:
Used to select the output variable or objective function to optimize.  If there are multiple output variables with specifications, one can also select "All Included Output Variables".  This will result is the simultaneous optimization of all output variables with specifications that have the Include in Optimization check box in the Output Variable dialog box checked. 
Characteristic list box:
Used to select the characteristic to optimize.  Only the applicable characteristics are displayed.  For example, Cpk is only displayed when at least one specification limit has been entered for the output variable and if statistical or process tolerances are specified.
For an output variable, the following characteristics can be optimized: Percent Defective, Cpk, Distance Inside Spec, Distance From Target, Lower End of Interval for Values and Upper End of Interval for Values.
For an objective function, the value can either be maximized or minimized.
If "All Included Output Variables" is selected in the Output list box, one can either minimize the total percent defective, maximize the worst Cpk, maximize the worst relative distance inside spec.  Total percent defective and worst Cpk requires that all included output have statistical or process tolerances and at least one spec limit.  Relative distance inside spec requires that each included output have a 2-sided spec or 1 spec with a target.
If the desired characteristic to optimize does not appear, it is either because it is not appropriate for the method of tolerancing specified or because a required value has not been entered.  For example, Cpk is not appropriate if worst-case tolerancing is used and cannot be calculated if at least one spec limit has not been entered.
Simplex Optimize button:
Performs optimization using simplex method.  The simplex method is generally the faster method.  The simplex method starts at a randomly generated point and then travels downhill (minimum) or uphill (maximum) until it finds a local optimum.  When several local optimums exist, it can miss the global optimum.  By examining plots using the Plots dialog box one can determine if multiple local optimums exist.  If so, the simplex method should be repeated multiple times or the interval optimization routine used instead.  If the simplex optimization is performed multiple times, the targets of the inputs end up being set to the best result obtained.
The error message "Cannot find starting values for inputs where function is valid." means the function produces divide by zero, square root of a negative number or other calculation errors at the randomly generated starting points.  The program generated 100 random starting points trying to find one which the function could be evaluated at. 
Interval Optimize button:
Performs optimization using interval analysis.  Optimization using interval analysis is the safest approach.  Interval analysis optimization is guaranteed to converge to the global optimum regardless of the existence of local optimums.  It bounds the optimum each step of the way.  However, it can be slow.
The error message "Function not valid over entire domain" means the function produces divides by zero, square root of a negative number or other calculation errors over the entire region of optimization. 
When the optimization begins, the bottom four buttons are hidden and a Halt button displayed instead.  Clicking the Halt button stops the optimization.  The optimization will display its progress until completed.  When done, it will display a message indicating whether a better point has been found.  If a better point is found, the targets for the inputs are updated.  If no better point is found, the targets of the inputs are not changed.
You can adjust the stopping criteria of both optimization routines by clicking the Options button.  This displays the Optimization Options dialog box.  The current settings typically give 2 to 3 significant digits of accuracy.  The Precision button performs an additional simplex optimization beginning at the current set of targets but using more stringent stopping criteria.  This optimization is designed to improve the precision of the previous result to 5 or more digits of accuracy.
To close the dialog box, click the Close button.  For help, click the Help button or press the F1 key.

HINTS FOR SPEEDING UP THE OPTIMIZATION:
  • For output variables, select first order Taylor-series or first order Curve-Fit in the Output Variable dialog box  before doing the optimization.  This will greatly simplify the functions being optimized and generally does not effect the results of the optimization.
  • When worst-case tolerancing is performed, convert all tolerances to statistical tolerances (use Variables menu), perform the optimization and then convert all tolerances back to worst-case tolerances.  Optimizing a statistical tolerances takes much less time than a worst-case tolerance because evaluating a worst-case tolerance in itself takes two optimizations which must be nested within the optimization of the targets.  The method of tolerancing used has a minor effect of the results of the optimization.
  • For process tolerances, so long as the operating windows are proportional to the standard deviations, such as +/- 1.5 SD, convert all tolerances to statistical tolerances (use Variables menu), perform the optimization and then convert all tolerances back to process tolerances.    Optimizing a statistical tolerances takes much less time than a process tolerance because evaluating a process tolerance in itself takes three optimizations (minimum average, maximum average, maximum standard deviation) which must be nested within the optimization of the targets.  The method of tolerancing used has a minor effect of the results of the optimization.