gemseo / problems / scalable

# gemseo.problems.scalable.parametric¶

## Scalable module from Tedford and Martins (2010)¶

The modules located in the scalable_tm directory offer a set of classes relative to the scalable problem introduced in the paper:

Tedford NP, Martins JRRA (2010), Benchmarking multidisciplinary design optimization algorithms, Optimization and Engineering, 11(1):159-183.

### Overview¶

This scalable problem aims to minimize an objective function quadratically depending on shared design parameters and coupling variables, under inequality constraints linearly depending on these coupling variables.

#### System discipline¶

A system discipline computes the constraints and the objective in function of the shared design parameters and coupling variables.

#### Strongly coupled disciplines¶

The coupling variables are the outputs of strongly coupled disciplines.

Each strongly coupled discipline computes a set of coupling variables linearly depending on local design parameters, shared design parameters, coupling variables from other strongly coupled disciplines, and belonging to the unit hypercube.

#### Scalability¶

This problem is said “scalable” because several sizing features can be chosen by the user:

• the number of local design parameters for each discipline,

• the number of shared design parameters,

• the number of coupling variables for each discipline,

• the number of disciplines.

A given sizing configuration is called “scaling strategy” and this scalable module is particularly useful to compare different MDO formulations with respect to the scaling strategy.

### Implementation¶

#### The scalable problem¶

The TMScalableProblem class instantiates the disciplines of the problem, that are TMMainDiscipline and several TMSubDiscipline, as well as the DesignSpace. These instantiated objects can be used in a Scenario, e.g. MDOScenario or DOEScenario.

#### The scalable study¶

The TMScalableStudy class instantiates a TMScalableProblem for a particular scaling strategy where the number of local design parameters is the same for all disciplines as well as the number of coupling variables. It provides a method to run MDO formulations and graphical capabilities to analyze the results.

#### The parametric scalable study¶

The TMParamSS class instantiates several TMScalableStudy associated with different scaling strategies, e.g. different numbers of local design parameters or different numbers of coupling variables. It provides a method to run MDO formulations and save results on the disk. The TMParamSSPost provides graphical capabilities to post-process these saved results.