Constrained space filling - Reasonable Design Space

In this part, we’ll look deeper into how the space filling point sampling algorithm works. Also, the definition of sampling constraints will be explained.

It’s not uncommon to have optimization problems where simply providing individual bounds for every variable is insufficient, for example geometrical problems where a sum of thicknesses may not exceed a given value. Such infeasible experiments can be avoided in the sampling (DOE), while maintaining a good space filling design.

Consider an LS-OPT project with the following variable design:

setup_x_y

And let’s say we constantly need the variable X to be larger than Y for the experiment to be feasible. In order to do this, we need an Expression to help us. This is created by selecting the Create Sampling Constraint button in the Constraints tab of the Sampling dialog. The Sampling constraint wizard opens up, where we can specify the expression, called VarConstr1 and a lower or upper bound, respectively.

sampling_composites

Selecting Create will generate a Composite expression and a Constraint, and add the Constraint to the list of Sampling Constraints.This makes LS-OPT take the constraint into account while doing point sampling.

This is the point sampling we get after running LS-OPT with these settings:

Here’s a more involved example with two constraints, sin(x*90)-y < 0 and
x*x-y > 0. (Did you know that LS-OPT uses degrees instead of radians for trig functions?)