gemseo_fmu / problems / disciplines

# gemseo_fmu.problems.disciplines.sellar¶

FMU disciplines of the Sellar use case.

Use case proposed by Sellar et al. in

Sellar, R., Batill, S., & Renaud, J. (1996). Response surface based, concurrent subspace optimization for multidisciplinary system design. In 34th aerospace sciences meeting and exhibit (p. 714).

The MDO problem is written as follows:

\begin{split}\begin{aligned} \text{minimize the objective function }&obj=x_{local}^2 + x_{shared,2} +y_1^2+e^{-y_2} \\ \text{with respect to the design variables }&x_{shared},\,x_{local} \\ \text{subject to the general constraints } & c_1 \leq 0\\ & c_2 \leq 0\\ \text{subject to the bound constraints } & -10 \leq x_{shared,1} \leq 10\\ & 0 \leq x_{shared,2} \leq 10\\ & 0 \leq x_{local} \leq 10. \end{aligned}\end{split}

where the coupling variables are

$\text{Discipline 1: } y_1 = \sqrt{x_{shared,1}^2 + x_{shared,2} + x_{local} - 0.2\,y_2},$

and

$\text{Discipline 2: }y_2 = |y_1| + x_{shared,1} + x_{shared,2}.$

and where the general constraints are

\begin{align}\begin{aligned}c_1 = 3.16 - y_1^2\\c_2 = y_2 - 24\end{aligned}\end{align}

This package implements three disciplines to compute the different coupling variables, constraints and objective: