Constraints

Constraints need to be satisfied for a result to be acceptable. Limits on displacement, frequency, or pressure drop, are common examples.

Constraint Categories

All constraints in an optimization problem can be placed into the following distinct categories:

Inequality Constraint: One sided condition that must be satisfied.
$\begin{matrix} g_{j} (x) \leq 0 & j = 1, ..., m \end{matrix}$
Equality Constraint: Precise condition that must be satisfied.
$\begin{matrix} h_{k} (x) = 0 & k = 1, ..., m_{h} \end{matrix}$
Side Constraint: Bounds on the input variables that limit the region of search for the optimum.
$x_{i}^{L} \leq x_{i} \leq x_{i}^{U}$

Constraint Types

Constraints can be defined as type Deterministic or Random (probabilistic) when settings up an Optimization in HyperStudy, depending on the design requirements.

Deterministic: Deterministic constraints enable you to manually define a Bound Type, Bound Value, and evaluation source for the output response(s).
Random: Random problem formulations take into account the variability in the design and study the corresponding variability in the performances. This aspect is studied under reliability and robustness.; Random constraints require you to modify the CFD Limit if the reliability requirement is different than the default value of 99.00%. The CFD Limit is the reliability requirement on the constraint; that is the probability of (Output Response >= 0) > 99.00%.