What is a normalized constraint?

Consider the following stress constraint

-15000 < σ_axial < 20000

If σ_axial is equal to 35000, then the normalized constraint for the upper bound is

(35000 - 20000) / |20000| = 0.750

0.0 < .750 => Violated constraint

The normalized constraint for the lower bound is

(-15000 - 35000) / |-15000| = -3.333

-3.333 < 0.0 => Satisfied constraint

When reviewing constraint values after an optimization, know the following:

1. Normalized constraint values are unitless.
2. The result files (.f06, .log) will report 'constraint' values, but are actually 'normalized constraint' values.
3. A normalized constraint that is positive, or greater than zero, indicates a violated constraint. A normalized constraint that is negative, or less than zero, indicates a satisfied constraint.
4. Each design cycle may have a different dominating constraint. For example, one design cycle might show a stress constraint is dominating, but the next design cycle shows a displacement constraint is dominating. The Responses App can be used to determine the exact constraint values.
5. Instead of using zero to distinguish between violated and satisfied constraints, the optimizer by default will use a value of .005 or 0.5%. As a result, some optimization solutions will show final values that slightly exceed the bounds. The threshold is controlled by GMAX on the DOPTPRM entry and has a default value of .005.

For more information, refer to the MSC Nastran Design Sensitivity and Optimization User's Guide, sections: Constraint Screening and Normalized Constraints.