Scalable models¶

Benchmark MDO formulations based on scalable disciplines¶

The api implements several classes to benchmark MDO formulations based on scalable disciplines.

The ScalabilityStudy class implements the concept of scalability study:

By instantiating a ScalabilityStudy, the user defines the MDO problem in terms of design parameters, objective function and constraints.
For each discipline, the user adds a dataset stored in a AbstractFullCache and select a type of ScalableModel to build the ScalableDiscipline associated with this discipline.
The user adds different optimization strategies, defined in terms of both optimization algorithms and MDO formulation.
The user adds different scaling strategies, in terms of sizes of design parameters, coupling variables and equality and inequality constraints. The user can also define a scaling strategies according to particular parameters rather than groups of parameters.
Lastly, the user executes the ScalabilityStudy and the results are written in several files and stored into directories in a hierarchical way, where names depends on both MDO formulation, scaling strategy and replications when it is necessary. Different kinds of files are stored: optimization graphs, dependency matrix plots and of course, scalability results by means of a dedicated class: ScalabilityResult.

The PostScalabilityStudy class implements the way as the set of ScalabilityResult-based result files contained in the study directory are graphically post-processed. This class provides several methods to easily change graphical properties, notably the plot labels. It also makes it possible to define a cost function per MDO formulation, converting the numbers of executions and linearizations of the different disciplines required by a MDO process in an estimation of the computational cost associated with what would be a scaled version of the true problem.

Warning

Comparing MDO formulations in terms of estimated true computational time rather than CPU time of the ScalabilityStudy is highly recommended. Indeed, time is often an obviousness criterion to distinguish between MDO formulations having the same performance in terms of distance to the optimum: look at our calculation budget and choose the best formulation that satisfies this budget, or even saves us time. Thus, it is important to carefully define these cost functions.

Scalable MDO problem¶

This module implements the concept of scalable problem by means of the ScalableProblem class.

Given

a MDO scenario based on a set of sampled disciplines with a particular problem dimension,
a new problem dimension (= number of inputs and outputs),

a scalable problem:

makes each discipline scalable based on the new problem dimension,
creates the corresponding MDO scenario.

Then, this MDO scenario can be executed and post-processed.

We can repeat this tasks for different sizes of variables and compare the scalability, which is the dependence of the scenario results on the problem dimension.

Scalable discipline¶

The discipline implements the concept of scalable discipline. This is a particular discipline built from a input-output learning dataset associated with a function and generalizing its behavior to a new user-defined problem dimension, that is to say new used-defined input and output dimensions.

Alone or in interaction with other objects of the same type, a scalable discipline can be used to compare the efficiency of an algorithm applying to disciplines with respect to the problem dimension, e.g. optimization algorithm, surrogate model, MDO formulation, MDA, …

The ScalableDiscipline class implements this concept. It inherits from the MDODiscipline class in such a way that it can easily be used in a Scenario. It is composed of a ScalableModel.

The user only needs to provide:

the name of a class overloading ScalableModel,
a dataset as an AbstractFullCache
variables sizes as a dictionary whose keys are the names of inputs and outputs and values are their new sizes. If a variable is missing, its original size is considered.

The ScalableModel parameters can also be filled in, otherwise the model uses default values.

Scalable model factory¶

This module contains the ScalableModelFactory which is a factory to create a ScalableModel from its class name by means of the ScalableModelFactory.create() method. It is also possible to get a list of available scalable models (see ScalableModelFactory.scalable_models method) and to check is a type of scalable model is available (see ScalableModelFactory.is_available() method)

Scalable model¶

This module implements the abstract concept of scalable model which is used by scalable disciplines. A scalable model is built from a input-output learning dataset associated with a function and generalizing its behavior to a new user-defined problem dimension, that is to say new used-defined input and output dimensions.

The concept of scalable model is implemented through ScalableModel, an abstract class which is instantiated from:

data provided as an AbstractFullCache
variables sizes provided as a dictionary whose keys are the names of inputs and outputs and values are their new sizes. If a variable is missing, its original size is considered.

Scalable model parameters can also be filled in. Otherwise the model uses default values.

Scalable diagonal model¶

This module implements the concept of scalable diagonal model, which is a particular scalable model built from an input-output dataset relying on a diagonal design of experiments (DOE) where inputs vary proportionally from their lower bounds to their upper bounds, following the diagonal of the input space.

So for every output, the dataset catches its evolution with respect to this proportion, which makes it a monodimensional behavior. Then, for a new user-defined problem dimension, the scalable model extrapolates this monodimensional behavior to the different input directions.

The concept of scalable diagonal model is implemented through the ScalableDiagonalModel class which is composed of a ScalableDiagonalApproximation. With regard to the diagonal DOE, GEMSEO proposes the DiagonalDOE class.