gemseo / problems / scalable


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.


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.


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.


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.