This package contains the OpenMDAO Standard Library. It’s intended to contain all of the plugins that are officially supported and released as part of openmdao.
Bases: openmdao.main.arch.Architecture
Bi-Level Integrated Systems Synthesis architecture
Implementation of the BLISS2000 optimization architecture based on the work described in the following journal article:
J. Sobieszczanski-Sobieski, T. Altus, M. Phillips, and Sandu, Bilevel Integrated System Synthesis for Concurrent and Distributed Processing, AIAA journal, vol. 41, no. 10, pp. 1996-2003, 2003.
Bases: openmdao.main.component.Component
Used to create outputs in the SubSytemOpt assembly.
Bases: openmdao.main.component.Component
Component which adds the weight factors for each output state variable for a given subsystem.
subsystem objective
Bases: openmdao.main.assembly.Assembly
Assembly which takes global inputs, coupling indeps, and weight factors as inputs and runs a local optimization on the local des vars.
Implementation of the Collaborative Optimization Architecture
Bases: openmdao.main.arch.Architecture
switch to decide between EI or PI for infill criterion
number of initial training points to use
EI or PI to use for stopping condition of optimization
number of adaptively sampled points to use
Bases: openmdao.main.arch.Architecture
Architecture that uses a single top level optimizer, enforcing consistency with equality constraints.
Script to run all Architectures in openmdao.lib.architectures against all OptProblems in openmdao.lib.optproblems.
Builds a list of architectures.
builds a list of optproblems
Runs all the architectures against all the test problems. A console script runs this function.
Runs the architectures against optproblems and records the results.
A central place to access all of the OpenMDAO case recorders, case iterators, and case filters in the standard library.
Bases: object
A CaseRecorder/CaseIterator containing Cases having the same set of input/output strings but different data. Cases are not necessarily unique.
Bases: openmdao.lib.casehandlers.caseset.CaseArray
A CaseRecorder/CaseIterator containing Cases having the same set of input/output strings but different data. All Cases in the set are unique.
Return a new CaseSet with Cases that are common to this and all others.
Return True if this CaseSet has no Cases in common with the given CaseSet.
Retrieve the values of specified variables from cases in a CaseIterator.
Returns a CaseSet containing cases with the specified varnames.
Cases in the case iterator that do not have all of the specified varnames are ignored.
A CaseRecorder and CaseIterator that store the cases in a CSV file.
Bases: object
An iterator that returns Case objects from a passed-in iterator of cases. This can be useful for runtime-generated cases from an optimizer, etc.
Quote character in the input CSV file should be ' or ". Other choices don’t seem to get identified by csv.Sniffer.
All string data must be contained inside of quotes. This includes field headers.
Bases: object
Stores cases in a csv file. Defaults to cases.csv.
We need a custom get_attributes because we aren’t using Traits to manage our changeable settings. This is unfortunate, and should be changed to something that automates this somehow.
Store the case in a csv file. The format for a line of data follows:
Field 1 - label Field 2 - [Empty] Field 3 - Input 1 ... Field i+2 - Input i Field i+3 - [Empty] Field i+4 - Output 1 ... Field i+j+4 - Output j Field i+j+5 - [Empty] Field i+j+6 - retries Field i+j+7 - max_retries Field i+j+8 - parent_uuid Field i+j+9 - msg
A CaseRecorder and CaseIterator that store the cases in a relational DB (Python’s sqlite.)
Bases: object
Pulls Cases from a relational DB (sqlite). It doesn’t support general sql queries, but it does allow for a series of boolean selectors, e.g., ‘x<=y’, that are ANDed together.
Bases: object
Records Cases to a relational DB (sqlite). Values other than floats, ints or strings are pickled and are opaque to SQL queries.
Retrieve the values of specified variables from a sqlite DB containing Case data.
Returns a dict containing a list of values for each entry, keyed on variable name.
Only data from cases containing ALL of the specified variables will be returned so that all data values with the same index will correspond to the same case.
Based on command line options, display an XY plot using data from a sqlite Case DB.
Display an XY plot using Case data from a sqlite DB.
Bases: object
Dumps cases in a “pretty” form to a file-like object called “out” (defaults to sys.stdout). If out is None, cases will be ignored.
Closes out unless it’s sys.stdout or sys.stderr. Note that a closed recorder will do nothing in record().
Case filters provide a means to select cases based on their index in the sequence of cases or the case data values.
Bases: object
Select based on a boolean Python expression of the case data or seqno. Case data is accessed by case['name']
Bases: object
Select based on an iterator of case numbers.
Bases: openmdao.lib.casehandlers.filters.IteratorCaseFilter
Select based on a sequence of case numbers.
Bases: openmdao.lib.casehandlers.filters.IteratorCaseFilter
Select based on start, stop, and step of case numbers.
A Case Iterator and CaseRecorder that stores the cases in a list.
Bases: list
An iterator that returns Case objects from a passed-in iterator of cases. This can be useful for runtime-generated cases from an optimizer, etc.
Bases: object
Stores cases in a list.
Pseudo package providing a central place to access all of the OpenMDAO components in the standard library.
Bases: openmdao.main.component.Component
Takes inputs and passes them directly to outputs to be broadcast out to other components.
Names of the variables you want to broadcast from this component.
Name/type pairs describing the variable types of each broadcast variable; ‘default’ name is used if no other type is set explicitly.
Expected Improvement calculation for one or more objectives.
Bases: openmdao.main.component.Component
CaseSet which contains a single case representing the criteria value.
Name of the variable to maximize the expected improvement around. Must be a NormalDistrubtion type.
The Normal Distribution of the predicted value for some function at some point where you wish to calculate the EI.
The expected improvement of the predicted_value.
The probability of improvement of the predicted_value.
Expected Improvement calculation for one or more objectives.
Bases: openmdao.main.component.Component
CaseIterator which contains only Pareto optimal cases according to criteria.
Switch to use either probability (PI) or expected (EI) improvement.
Names of responses to maximize expected improvement around. Must be NormalDistribution type.
Number of Monte Carlo Samples with which to calculate probability of improvement.
CaseIterator which contains NormalDistributions for each response at a location where you wish to calculate EI.
The expected improvement of the next_case.
The probability of improvement of the next_case.
Bases: openmdao.main.component_with_derivatives.ComponentWithDerivatives
Run an external code as a component. The component can be configured to run the code on a remote server. See execute().
Default stdin is the ‘null’ device, default stdout is the console, and default stderr is error.out.
Environment variables required by the command.
Delay between polling for command completion. A value of zero will use an internally computed default.
Resources required to run this component.
Maximum time to wait for command completion. A value of zero implies an infinite wait.
Return code from the command.
True if the command timed-out.
The command to be executed.
Check that all ‘specific’ input or output external files exist. If an external file path specifies a pattern, it is not checked.
Copy inputs from inputs_dir that match patterns.
This can be useful for resetting problem state.
Copy files from results_dir that match patterns.
This can be useful for workflow debugging when the external code takes a long time to execute.
Runs the specified command.
- Existing output (but not in/out) files are removed.
- Checks that all external input files exist.
- Runs the command.
- Checks that all external output files exist.
If a subclass generates outputs (such as postprocessing results), then it should set attribute check_external_outputs False and call check_files() itself.
If resources have been specified, an appropriate server is allocated and the command is run on that server. Otherwise the command is run locally.
When running remotely, the following resources are set:
Key | Value |
---|---|
job_name | self.get_pathname() |
remote_command | self.command (first item) |
args | self.command (2nd through last items) |
job_environment | self.env_vars |
input_path | self.stdin |
output_path | self.stdout |
error_path | self.stderr (if != STDOUT) |
join_files | If self.stderr == STDOUT |
wallclock_time | self.timeout (if non-zero) |
Note
Input files to be sent to the remote server are defined by FileMetadata entries in the external_files list with input True. Similarly, output files to be retrieved from the remote server are defined by entries with output True.
Warning
Any file not labeled with binary True will undergo newline translation if the local and remote machines have different newline representations. Newline translation will corrupt a file which is binary but hasn’t been labeled as such.
Don’t allow setting of ‘command’ or ‘resources’ by a remote client.
MetaModel is a class which supports generalized meta modeling capabilities. It has two slots, one for surrogate model generators and a second for the model that is being approximated. The first slot, named surrogate, must always be filled before anything else is done. This slot gets filled with a dictionary that specifies which surrogate model generator should be used for which outputs. The keys of the dictionary are the variable names, and the values are the particular surrogate model generators which adhere to the ISurrogate interface. A special key, 'default', can be used to indicate a surrogate model generator to be used if no specific one is given for a particular variable. Any specified variables will override the default. OpenMDAO provides some surrogate modelers in openmdao.lib.surrogatemodels.
from openmdao.main.api import Assembly
from openmdao.lib.components.api import MetaModel
from openmdao.lib.surrogatemodels.api import KrigingSurrogate,LogisticRegression
class Simulation(Assembly):
def configure(self):
self.add('meta_model',MetaModel())
#using KriginSurrogate for all outputs
self.meta_model.surrogate = {'default':KrigingSurrogate()}
#alternately, overiding the default for a specific variable
self.meta_model.surrogate = {'default':LogisticRegression(),
'f_xy':KrigingSurrogate()}
Once the surrogate dictionary has been specified, the model slot, called model, can be filled with a component. As soon as a component is put in the slot, MetaModel will automatically mirror the inputs and outputs of that component. In other words, MetaModel will have the same inputs and outputs as whatever component is put into the model slot.
from openmdao.main.api import Assembly
from openmdao.lib.components.api import MetaModel
from openmdao.lib.surrogatemodels.api import KrigingSurrogate
from openmdao.lib.optproblems.branin import BraninComponent
class Simulation(Assembly):
def configure(self):
self.add('meta_model',MetaModel())
self.meta_model.surrogate = {'default':KrigingSurrogate()}
#component has two inputs: x,y
self.meta_model.model = BraninComponent()
#meta_model now has two inputs: x,y
self.meta_model.x = 9
self.meta_model.y = 9
Depending on the component being approximated, you may not want to generate approximations for all the outputs. Alternatively, you may want to exclude some of the inputs from consideration when the surrogate models are generated if the inputs are going to be held constant for a given study. MetaModel provides two I/O-Traits to handle this situation: includes and excludes. Only one of these traits can be used at a time, and both inputs and outputs are specified at the same time.
If you are specifying the includes, then only the I/O-Traits in that list will be used. If you are specifying the excludes, then everything but the I/O-Traits in the list will be mirrored by MetaModel.
from openmdao.main.api import Assembly
from openmdao.lib.components.api import MetaModel
from openmdao.lib.surrogatemodels.api import KrigingSurrogate
from openmdao.lib.optproblems.branin import BraninComponent
class Simulation(Assembly):
def configure(self):
self.add('meta_model',MetaModel())
self.meta_model.surrogate = {'default':KrigingSurrogate()}
#component has two inputs: x,y
self.meta_model.model = BraninComponent()
#exclude the x input
self.meta_model.excludes=['x']
or
from openmdao.main.api import Assembly
from openmdao.lib.components.api import MetaModel
from openmdao.lib.surrogatemodels.api import KrigingSurrogate
from openmdao.lib.optproblems.branin import BraninComponent
class Simulation(Assembly):
def configure(self):
self.add('meta_model',MetaModel())
self.meta_model.surrogate = {'default': KrigingSurrogate()}
#component has two inputs: x,y
self.meta_model.model = BraninComponent()
#include only the y input
self.meta_model.includes=['y']
MetaModel treats inputs and outputs a little differently. All the inputs, regardless of which ones are being included/excluded, will be mirrored by a MetaModel. But if inputs are excluded, then MetaModel won’t pass down their values to the surrogate models as inputs to training cases.
When outputs are excluded, they no longer get mirrored by MetaModel. They won’t get surrogate models fit to them, and consequently, they won’t be available to the simulation from MetaModel.
Now you have set up your MetaModel with a specific surrogate model, and you have put a model into the model slot. The input and output inclusions/exclusions have been specified. The next step is to actually start training and executing the MetaModel in simulations.
MetaModel has two operating modes: training and prediction. When run in training mode, MetaModel passes its given inputs down to the model in the model slot and runs it. Then it stores the outputs from the model to use for generating a surrogate model later. When run in predict mode, MetaModel will check for any new training data and, if present, will generate a surrogate model for each model output with the data. Then it will make a prediction of the model outputs for the given inputs. A MetaModel instance must always be run in training mode before executing it in predict mode.
To put an instance of MetaModel into the training mode, you must set the train_next event trait before executing the component. This event trait automatically resets itself after the execution, so it must be set again before each training case. An event trait is just a trigger mechanism, and it will trigger its behavior regardless of the value you set it to.
from openmdao.main.api import Assembly
from openmdao.lib.components.api import MetaModel
from openmdao.lib.surrogatemodels.api import KrigingSurrogate
from openmdao.lib.optproblems.branin import BraninComponent
class Simulation(Assembly):
def configure(self):
self.add('meta_model',MetaModel())
self.meta_model.surrogate = {'default':KrigingSurrogate()}
#component has two inputs: x,y
self.meta_model.model = BraninComponent()
self.meta_model.train_next = True
self.meta_model.x = 2
self.meta_model.y = 3
self.meta_model.execute()
In a typical iteration hierarchy, a Driver is responsible for setting the train_next event when appropriate. This is accomplished via the IHasEvents Driver sub-interface. The train_next event is added to a Driver, which will then automatically set train_next prior to each iteration of the model. A simple code snippet is presented below, while a more detailed example can be found in the single_objective_ei example under the openmdao.examples.expected_improvement package.
from openmdao.main.api import Assembly
from openmdao.lib.drivers.api import DOEdriver
from openmdao.lib.components.api import MetaModel
from openmdao.lib.surrogatemodels.api import KrigingSurrogate
from openmdao.lib.optproblems.branin import BraninComponent
class Simulation(Assembly):
def configure(self):
self.add('meta_model',MetaModel())
self.meta_model.surrogate = {'default':KrigingSurrogate()}
#component has two inputs: x,y
self.meta_model.model = BraninComponent()
self.add('driver',DOEdriver())
self.driver.workflow.add('meta_model')
self.driver.add_event('meta_model.train_next')
When the train_next event is not set, MetaModel automatically runs in predict mode. When in predict mode, the outputs provided are the result of predicted outputs from the surrogate model inside of MetaModel.
Before being able to predict the surrogate model response for any of the outputs of MetaModel, the surrogate model must be trained with the recorded training data. This will happen automatically whenever MetaModel is run in predict mode and new training data is available. This makes MetaModel more efficient, because it is not trying to retrain the model constantly when running large sets of training cases. Instead, the actual surrogate model training is only done when a prediction is needed and new training data is available.
Metamodel provides basic Meta Modeling capability.
Bases: openmdao.main.component.Component
Slot for the Component or Assembly being encapsulated.
Records training cases
A list of names of variables to be excluded from the public interface.
A list of names of variables to be included in the public interface.
If True, metamodel will report errors reported from the component. If False, metamodel will swallow the errors but log that they happened and exclude the casefrom the training set
CaseIterator containing cases to use as initial training data. When this is set, all previous training data is cleared and replaced with data from this CaseIterator
Dictionary that provides a mapping between variables and surrogate models for each output. The “default” key must be given. It is the default surrogate model for all outputs. Any specific surrogate models can be specifed by a key with the desired variable name.
Dictionary that provides mapping between variables and arguments that should be passed to the surrogate model. Keys should match those in the surrogate dictionary. Values can be a list of ordered arguments, a dictionary of named arguments, or a two-tuple of a list and a dictionary.
Return the list of names of public inputs that correspond to model inputs.
Return the list of names of public outputs that correspond to model outputs.
called whenever the model variable is set or when includes/excludes change.
Bases: openmdao.main.component.Component
Takes one List input and splits it into n indvidual outputs. This is a logical demultiplexer.
number of items in the array to be demultiplexed
Bases: openmdao.main.component.Component
Takes in n inputs and exports a length n List with the data. It is a logical multiplexer.
number of inputs to be multiplexed
Pareto Filter – finds non-dominated cases.
Bases: openmdao.main.component.Component
Takes a set of cases and filters out the subset of cases which are pareto optimal. Assumes that smaller values for model responses are better, so all problems must be posed as minimization problems.
CaseSet with the cases to be filtered to find the pareto optimal subset.
List of outputs from the case to consider for filtering. Note that only case outputs are allowed as criteria.
Resulting collection of dominated cases.
Resulting collection of pareto optimal cases.
Differentiates a driver’s workflow using an analytic method.
Bases: openmdao.lib.differentiators.chain_rule.ChainRule
Differentiates a driver’s workflow using one of the analytic methods.
approach for assembling the problem. functional - convert all comps to functional formresidual - convert all comps to residual formhybrid - no conversion, each comps uses what it has
Choose forward or adjoint mode
Set to True for sparse storage of matrices.
Returns the derivative of output_name with respect to wrt.
Pseudo package providing a central place to access all of the OpenMDAO differentiators in the standard library.
A differentiator is a special object that can be used by a driver to calculate the first or second derivatives of a workflow. The derivatives are calculated from the parameter inputs to the objective and constraint outputs. Any driver that has been derived from the DriverUsesDerivatives base class contains a Slot called Differentiator. This slot can take a Differentiator object.
The ChainRule differentiator calculates the gradient of a Drivers’s workflow using forward automatic differentiation (i.e., successive application of the chainrule from the Parameters to the Objectives and Constraints.)
This differentiator is under construction. At present, it works for any workflow that contains Assemblies or Components for which derivatives have been specified for all connected components. Work is underway to include finite differencing of subsections of the model, and to support nested drivers. If your model requires any of these features, then you should use the FiniteDifference differentiator.
Differentiates a driver’s workflow using the Chain Rule with Numerical Derivatives (CRND) method.
Bases: openmdao.main.container.Container
Differentiates a driver’s workflow using the Chain Rule with Numerical Derivatives (CRND) method.
Default finite difference step size.
Returns the Hessian matrix for all outputs in the Driver’s workflow.
This method is not implemented yet.
Returns the 2nd derivative of output_name with respect to both vars in the tuple wrt.
Returns the Hessian matrix of the given output with respect to all parameters.
Returns the derivative of output_name with respect to wrt.
Returns the gradient of the given output with respect to all parameters.
Object that can take a subsection of a model and perform finite difference on it.
Bases: object
An object that takes a subsection of a model and performs a finite difference. The cases are run with a point distribution generator. Thus, we can take advantage of multiprocessing if it is available.
Performs finite difference of our submodel with respect to wrt. Variables are intialized with init_vals.
A differentiator is a special object that can be used by a driver to calculate the first or second derivatives of a workflow. The derivatives are calculated from the parameter inputs to the objective and constraint outputs. Any driver that has been derived from the DriverUsesDerivatives base class contains a Slot called Differentiator. This slot can take a Differentiator object.
The FiniteDifference differentiator provides the gradient vector and Hessian matrix of the workflow using the finite difference method. For first derivatives, you have a choice of forward, backward, or central differencing. Second derivatives are calculated using the standard three-point difference for both on-diagonal and off-diagonal terms.
The FiniteDifference differentiator also supports Finite Difference with Analytical Derivatives (FDAD), wherein a component’s analytical derivatives can be used to speed up that component under finite difference.
The FiniteDifference differentiator can be used with any optimizer that can usegradients, including the CONMIN, NEWSUMT, and SLSQP drivers. optimizer by plugging it into the differentiator socket.
from openmdao.main.api import Assembly
from openmdao.lib.drivers.api import NEWSUMTdriver
from openmdao.lib.differentiators.finite_difference import FiniteDifference
from openmdao.examples.simple.paraboloid import Paraboloid
class OptimizationConstrained(Assembly):
"""Constrained optimization of the Paraboloid."""
def configure(self):
# Create Paraboloid component instances
self.add('paraboloid', Paraboloid_Derivative())
# Create Optimizer instance
self.add('driver', NEWSUMTdriver())
# Driver process definition
self.driver.workflow.add('paraboloid')
# Differentiator
self.driver.differentiator = FiniteDifference()
self.driver.differentiator.form = 'central'
self.driver.differentiator.default_stepsize = .0001
# Objective
self.driver.add_objective('paraboloid.f_xy')
# Design Variables
self.driver.add_parameter('paraboloid.x', low=-50., high=50., fd_step=.01)
self.driver.add_parameter('paraboloid.y', low=-50., high=50.)
# Constraints
self.driver.add_constraint('paraboloid.x-paraboloid.y >= 15.0')
The only argument that FiniteDifference takes is the driver you are plugging into.
FiniteDifference has two additional control variables. The form parameter is used to declare which difference the first derivative will use. (The default is 'central'.) The default_stepsize parameter is used to set a default finite difference step size. Note that you can declare a separate finite difference step size for each parameter in the call to add_parameter. Here, the finite difference step size for the input 'x' to paraboloid is set to .01. If you don’t specify fd_step for a parameter, then the default step size is used.
Differentiates a driver’s workflow using the Finite Difference with Analytical Derivatives (FDAD) method.
A variety of difference types are available for both first and second order.
Bases: openmdao.main.container.Container
Differentiates a driver’s workflow using the Finite Difference with Analytical Derivatives (FDAD) method. A variety of difference types are available for both first and second order.
Default finite difference step size.
Finite difference form (central, forward, backward)
Returns the Hessian matrix for all outputs in the Driver’s workflow.
Returns the 2nd derivative of output_name with respect to both vars in the tuple wrt.
Returns the Hessian matrix of the given output with respect to all parameters.
Returns the derivative of output_name with respect to wrt.
Returns the gradient of the given output with respect to all parameters.
Evaluates a first order central difference.
Evaluates a first order forward or backward difference.
Pseudo package providing a central place to access all of the OpenMDAO doegenerators in the standard library.
DOEgenerator that performs a central composite Design of Experiments. Plugs into the DOEgenerator socket on a DOEdriver.
Bases: openmdao.main.container.Container
DOEgenerator that performs a central composite Design of Experiments. Plugs into the DOEgenerator socket on a DOEdriver.
Number of independent parameters in the DOE.
Type of central composite design
Bases: openmdao.main.container.Container
DOEgenerator that returns rows in a CSV file. Plugs into the DOEgenerator socket on a DOEdriver.
Name of CSV file.
Expected number of parameters in the DOE
The FullFactorial DOEgenerator implements a full factorial Design of Experiments; that is, it generates a set of design points that fully span the range of the parameters at the requested resolution. It plugs into the DOEgenerator socket on a DOEdriver.
Bases: openmdao.main.container.Container
DOEgenerator that performs a full-factorial Design of Experiments. Plugs into the DOEgenerator socket on a DOEdriver.
Number of levels of values for each parameter.
Number of independent parameters in the DOE.
The OptLatinHypercube component implements an algorithm that produces an optimal Latin hypercube based on an evolutionary optimization of its Morris-Mitchell sampling criterion.
Bases: object
Bases: openmdao.main.container.Container
IDOEgenerator which provides a Latin hypercube DOE sample set.
Number of parameters, or dimensions, for the DOE.
Number of sample points in the DOE sample set.
Bases: openmdao.main.container.Container
IDOEgenerator which provides a Latin hypercube DOE sample set. The Morris-Mitchell sampling criterion of the DOE is optimzied using an evolutionary algorithm.
Number of generations the optimization will evolve over.
Vector norm calculation method. ‘1-norm’ is faster, but less accurate.
Number of parameters, or dimensions, for the DOE.
Number of sample points in the DOE sample set.
Size of the population used in the evolutionary optimization.
Returns True if the given array is a Latin hypercube. The given array is assumed to be a numpy array.
Calculates a random Latin hypercube set of n points in k dimensions within [0,1]^k hypercube.
Returns an n by k numpy array.
DOEgenerator that performs a uniform space-filling Design of Experiments. Plugs into the DOEgenerator socket on a DOEdriver.
Bases: openmdao.main.container.Container
DOEgenerator that performs a space-filling Design of Experiments with uniform distributions on all design variables. Plugs into the DOEgenerator socket on a DOEdriver.
Number of independent parameters in the DOE.
Number of total samples in the DOE.
The BroydenSolver can be used to solve for the set of inputs (independents) that are needed to to make a model satisfy an equation (the dependent equation) that is a function of model outputs. BroydenSolver is based on the quasi-Newton-Raphson algorithms found in SciPy’s nonlinear solver library. As the name implies, a Broyden update is used to approximate the Jacobian matrix. In fact, no Jacobian is evaluated with these algorithms, so they are quicker than a full Newton solver, but they may not be suitable for all problems.
To see how to use the BroydenSolver, consider a problem where we’d like to solve for the intersection of a line and a parabola. We can implement this as a single component.
from openmdao.lib.datatypes.api import Float
from openmdao.main.api import Component
class MIMOSystem(Component):
""" Two equations, two unknowns """
x = Float(10.0, iotype="in", doc="Input 1")
y = Float(10.0, iotype="in", doc="Input 2")
f_xy = Float(0.0, iotype="out", doc="Output 1")
g_xy = Float(0.0, iotype="out", doc="Output 2")
def execute(self):
""" Evaluate:
f_xy = 2.0*x**2 - y + 2.0
g_xy = 2.0*x - y - 4.0
"""
x = self.x
y = self.y
self.f_xy = 2.0*x**2 - y + 2.0
self.g_xy = 2.0*x - y + 4.0
Notice that this is a two-input problem – the variables are x and y. There are also two equations that need to be satisfied: the equation for the line and the equation for the parabola. There are actually two solutions to this set of equations. The solver will return the first one that it finds. You can usually find other solutions by starting the solution from different initial points. We start at (10, 10), as designated by the default values for the variables x and y.
Next, we build a model that uses the BroydenSolver to find a root for the equations defined in MIMOSystem.
from openmdao.lib.drivers.api import BroydenSolver
from openmdao.main.api import Assembly
class SolutionAssembly(Assembly):
""" Solves for the root of MIMOSystem. """
def configure(self):
self.add('driver', BroydenSolver())
self.add('problem', MIMOSystem())
self.driver.workflow.add('problem')
self.driver.add_parameter('problem.x', low=-1.0e99, high=1.0e99)
self.driver.add_parameter('problem.y', low=-1.0e99, high=1.0e99)
self.driver.add_constraint('problem.f_xy = 0.0')
self.driver.add_constraint('problem.g_xy = 0.0')
self.driver.itmax = 20
self.driver.alpha = .4
self.driver.tol = .000000001
The parameters are the independent variables that the solver is allowed to vary. The method add_parameter is used to define these. Broyden does not utilize the low and high arguments, so they are set to some large arbitrary negative and positive values.
The equations that we want to satisfy are added as equality constraints using the add_constraint method. We want to find x and y that satisfy f_xy=0 and g_xy=0, so these two equations are added to the solver.
Both the add_parameter and add_constraint methods are presented in more detail in MDAO Architectures.
The resulting solution should yield:
>>> top = SolutionAssembly()
>>> top.run()
>>> print top.problem.x, top.problem.y
1.61... 7.23...
Five parameters control the solution process in the BroydenSolver.
broyden2: Broyden’s second method – the same as broyden1 but updates the inverse Jacobian directly
broyden3: Broyden’s third method – the same as broyden2, but instead of directly computing the inverse Jacobian, it remembers how to construct it using vectors. When computing inv(J)*F, it uses those vectors to compute this product, thus avoiding the expensive NxN matrix multiplication.
excitingmixing: The excitingmixing algorithm. J=-1/alpha
The default value for algorithm is "broyden2".
self.driver.algorithm = "broyden2"
This parameter specifies the maximum number of iterations before BroydenSolver terminates. The default value is 10.
self.driver.itmax = 10
This parameter specifies the mixing coefficient for the algorithm. The mixing coefficient is a linear scale factor applied to the update of the parameters, so increasing it can lead to quicker convergence but can also lead to instability. The default value is 0.4. If you use the excitingmixing algorithm, you should try a lower value, such as 0.1.
self.driver.alpha = 0.1
Convergence tolerance for the solution. Iteration ends when the constraint equation is satisfied within this tolerance. The default value is 0.00001.
self.driver.tol = 0.00001
This parameter is only used for the excitingmixing algorithm where the mixing coefficient is adaptively adjusted. It specifies the maximum allowable mixing coefficient for adaptation. The default value is 1.0.
self.driver.alphamax = 1.0
broyednsolver.py – Solver based on the nonlinear solvers found in Scipy.Optimize.
Bases: openmdao.main.driver.Driver
MIMO Newton-Raphson Solver with Broyden approximation to the Jacobian. Algorithms are based on those found in scipy.optimize.
Nonlinear solvers
These solvers find x for which F(x)=0. Both x and F are multidimensional.
All solvers have the parameter iter (the number of iterations to compute); some of them have other parameters of the solver. See the particular solver for details.
A collection of general-purpose nonlinear multidimensional solvers.
The broyden2 is the best. For large systems, use broyden3; excitingmixing is also very effective. The remaining nonlinear solvers from SciPy are, in their own words, of “mediocre quality,” so they were not implemented.
Algorithm to use. Choose from broyden2, broyden3, and excitingmixing.
Mixing Coefficient.
Maximum Mixing Coefficient (only used with excitingmixing.)
Maximum number of iterations before termination.
Convergence tolerance. If the norm of the independent vector is lower than this, then terminate successfully.
Adds a constraint in the form of a boolean expression string to the driver.
Parameters:
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if types is [‘eq’].
Removes all constraints.
Removes all parameters.
Returns a copy of our constraints dict.
Returns a list of tuples of the form (lhs, rhs, comparator, is_violated).
From SciPy, Broyden’s second method.
Updates inverse Jacobian by an optimal formula. There is NxN matrix multiplication in every iteration.
The best norm(F(x))=0.003 achieved in ~20 iterations.
from scipy, Broyden’s second (sic) method.
Updates inverse Jacobian by an optimal formula. The NxN matrix multiplication is avoided.
The best norm(F(x))=0.003 achieved in ~20 iterations.
from scipy, The excitingmixing method.
J=-1/alpha
The best norm(F(x))=0.005 achieved in ~140 iterations.
Note: SciPy uses 0.1 as the default value for alpha for this algorithm. Ours is set at 0.4, which is appropriate for Broyden2 and Broyden3, so adjust it accordingly if there are problems.
Returns an ordered dict of constraint objects.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
The CaseIteratorDriver provides the capability to evaluate one or more cases on a workflow. These evaluations can be performed either sequentially (the default) or concurrently (subject to computational resources available).
During sequential execution, each case is evaluated by applying the inputs to the workflow, executing the workflow, retrieving the outputs, and recording the evaluated case.
For concurrent execution, a modified form of the assembly is packaged into an egg, which is a file which can be sent to a remote server for execution. The modifications consist of replacing the assembly’s driver with a default driver, and setting that driver’s workflow to the CaseIteratorDriver’s workflow. After the egg is created, the ResourceAllocationManager (RAM) is used to allocate servers to evaluate the cases concurrently. Servers are selected based on egg requirements (Python version, installed packages, etc.).
Ordinarily, the model (modified form of the assembly) is loaded into a server prior to each evaluation. Since loading takes some time, this reloading process can be skipped if reload_model is set False. Some models require reloading (typically due to limitations of certain components used), so always reloading is the safe default. Note that during sequential execution no reloading takes place.
Bases: openmdao.main.driver.Driver
A base class for Drivers that run sets of cases in a manner similar to the ROSE framework. Concurrent evaluation is supported, with the various evaluations executed across servers obtained from the ResourceAllocationManager.
If ABORT, any error stops the evaluation of the whole set of cases.
Extra resource requirements (unusual).
If True, no distribution or orphan requirements will be included in the generated egg.
Maximum number of times to retry a failed case.
If True, reload the model between executions.
If True, evaluate cases sequentially.
Runs all cases and records results in recorder. Uses setup() and resume() with default arguments.
Resume execution.
Bases: openmdao.lib.drivers.caseiterdriver.CaseIterDriverBase
Run a set of cases provided by an ICaseIterator. Concurrent evaluation is supported, with the various evaluations executed across servers obtained from the ResourceAllocationManager.
Filter used to select cases to evaluate.
Iterator supplying Cases to evaluate.
Iterator supplying evaluated Cases.
cobyladriver.py - Contains a driver that wraps the cobyla optimizer as used in pyOpt:
Minimize a function using the Constrained Optimization BY Linear Approximation (COBYLA) method
COBYLA is gradient-free and can handle inequality constraints.
Bases: openmdao.main.driver.Driver
Minimize a function using the Constrained Optimization BY Linear Approximation (COBYLA) method.
COBYLA is gradient-free and can handle inequality constraints.
Note: constraints should be added using the OpenMDAO convention (positive = violated)
Fortran output unit. Leave this at 6 for STDOUT
Controls the frequency of output: 0 (no output),1,2,3
Maximum number of function evaluations.
Name of output file (if iout not 6).
Reasonable initial changes to the variables.
Final accuracy in the optimization (not precisely guaranteed).
Error code returned from COBYLA.
Adds a constraint in the form of a boolean expression string to the driver.
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds an objective to the driver.
Takes an iterator of objective strings and creates objectives for them in the driver.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if types is [‘ineq’].
Removes all constraints.
Removes all objectives.
Removes all parameters.
Returns a copy of our constraints dict.
Returns a list of constraint values
Returns a list of values of the evaluated objectives.
Returns a list of values of the evaluated objectives.
Returns an ordered dict of inequality constraint objects.
Returns an OrderedDict of objective expressions.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the specified objective expression. Spaces within the expression are ignored.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
CONMIN is a Fortran program written as a subroutine to solve linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. If analytic gradients of the objective or constraint functions are not available (i.e., if a Differentiator is not plugged into the differentiator socket), then the gradients are calculated by CONMIN’s internal finite difference code. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved. The conjugate direction method of Fletcher and Reeves is used for this purpose.
More information on CONMIN can be found in the CONMIN User’s Manual.
CONMIN has been included in the OpenMDAO standard library to provide users with a basic gradient-based optimization algorithm.
Basic Interface
The CONMIN code contains a number of different parameters and switches that are useful for controlling the optimization process. These can be subdivided into those parameters that will be used in a typical optimization problem and those that are more likely to be used by an expert user.
For the simplest possible unconstrained optimization problem, CONMIN just needs an objective function and one or more decision variables (parameters.) The basic interface conforms to OpenMDAO’s driver API.
The OpenMDAO CONMIN driver can be imported from openmdao.lib.drivers.api.
from openmdao.lib.drivers.api import CONMINdriver
Typically, CONMIN will be used as a driver in the top level assembly, though it also can be used in a subassembly as part of a nested driver scheme. Using the OpenMDAO script interface, a simple optimization problem can be set up as follows:
from openmdao.main.api import Assembly
from openmdao.examples.enginedesign.vehicle import Vehicle
from openmdao.lib.drivers.api import CONMINdriver
class EngineOptimization(Assembly):
""" Top level assembly for optimizing a vehicle. """
def configure(self):
# Create CONMIN Optimizer instance
self.add('driver', CONMINdriver())
# Create Vehicle instance
self.add('vehicle', Vehicle())
# add Vehicle to optimizer workflow
self.driver.workflow.add('vehicle')
# CONMIN Flags
self.driver.iprint = 0
self.driver.itmax = 30
# CONMIN Objective
self.driver.add_objective('vehicle.fuel_burn')
# CONMIN Design Variables
self.driver.add_parameter('vehicle.spark_angle', low=-50. , high=10.)
self.driver.add_parameter('vehicle.bore', low=65. , high=100.)
This first section of code defines an assembly called EngineOptimization. This assembly contains a DrivingSim component and a CONMINdriver, both of which are created and added inside the __init__ function with add. The DrivingSim component is also added to the driver’s workflow. The objective function, design variables, constraints, and any CONMIN parameters are also assigned in the __init__ function.
Controlling the Optimization
It is often necessary to control the convergence criteria for an optimization. The CONMIN driver allows control over both the number of iterations before termination as well as the convergence tolerance (both absolute and relative).
The maximum number of iterations is specified by setting the itmax parameter. The default value is 10.
self.driver.itmax = 30
The convergence tolerance is controlled with dabfun and delfun. Dabfun is the absolute change in the objective function to indicate convergence (i.e., if the objective function changes by less than dabfun, then the problem is converged). Similarly, delfun is the relative change of the objective function with respect to the value at the previous step. Note that delfun has a hard-wired minimum of 1e-10 in the Fortran code, and dabfun has a minimum of 0.0001.
self.driver.dabfun = .001
self.driver.delfun = .1
All of these convergence checks are always active during optimization. The tests are performed in the following sequence:
The number of successive iterations that the convergence tolerance should be checked before terminating the loop can also be specified with the itrm parameter, whose default value is 3.
self.driver.itrm = 3
CONMIN can calculate the gradient of both the objective functions and of the constraints using a finite difference approximation. This is the default behavior if no Differentiator is plugged into the differentiator socket. Two parameters control the step size used for numerically estimating the local gradient: fdch and fdchm. The fdchm parameter is the minimum absolute step size that the finite difference will use, and fdch is the step size relative to the design variable.
self.driver.fdch = .0001
self.driver.fdchm = .0001
Note
The default values of fdch and fdchm are set to 0.01. This may be too large for some problems and will manifest itself by converging to a value that is not the minimum. It is important to evaluate the scale of the objective function around the optimum so that these can be chosen well.
You can also replace CONMIN’s finite difference with OpenMDAO’s built-in capability by inserting a differentiator into the Differentiator slot in the driver.
For certain problems, it is desirable to scale the inputs. Several scaling options are available, as summarized here:
Value | Result |
---|---|
nscal < 0 | User-defined scaling with the vector in scal |
nscal = 0 | No scaling of the design variables |
nscal > 0 | Scale the design variables every NSCAL iteration. Please see the CONMIN User’s Manual for additional notes about using this option. |
If your problem uses linear constraints, you can improve the efficiency of the optimization process by designating those that are linear functions of the design variables as follows:
map(self.driver.add_constraint, ['vehicle.stroke < vehicle.bore',
'vehicle.stroke * vehicle.bore > 1.0'])
self.driver.cons_is_linear = [1, 0]
Here, the first constraint is linear, and the second constraint is nonlinear. If cons_is_linear is not specified, then all the constraints are assumed to be nonlinear. Note that the original CONMIN parameter for this is ISC. If your constraint includes some framework output in the equation, then it is probably not a linear function of the design variables.
Finally, the iprint parameter can be used to display diagnostic messages inside of CONMIN. These messages are currently sent to the standard output.
self.driver.iprint = 0
Higher positive values of iprint turn on the display of more levels of output, as summarized below. To make it easier to swap drivers, and iprint of -1 also suppresses all output.
Value | Result |
---|---|
iprint = 0 | All output is suppressed |
iprint = 1 | Print initial and final function information |
iprint = 2 | Debug level 1: All of the above plus control parameters |
iprint = 3 | Debug level 2: All of the above plus all constraint values, number of active/violated constraints, direction vectors, move parameters, and miscellaneous information |
iprint = 4 | Complete debug: All of the above plus objective function gradients, active and violated constraint gradients, and miscellaneous information |
iprint = 5 | All of above plus each proposed design vector, objective and constraints during the one-dimensional search |
iprint = 101 | All of above plus a dump of the arguments passed to subroutine CONMIN |
Advanced Options
The following options exercise some of the more advanced capabilities of CONMIN. The details given here briefly summarize the effects of these parameters; more information is available in the CONMIN User’s Manual.
conmindriver.py - Driver for the CONMIN optimizer.
The CONMIN driver can be a good example of how to wrap another Driver for OpenMDAO. However, there are some things to keep in mind.
1. This implementation of the CONMIN Fortran driver is interruptable, in that control is returned every time an objective or constraint evaluation is needed. Most external optimizers just expect a function to be passed for these, so they require a slightly different driver implementation than this.
2. The CONMIN driver is a direct wrap, and all inputs are passed using Numpy arrays. This means there are a lot of locally stored variables that you might not need for a pure Python optimizer.
Ultimately, if you are wrapping a new optimizer for OpenMDAO, you should endeavour to understand the purpose for each statement so that your implementation doesn’t do any unneccessary or redundant calculation.
Bases: openmdao.main.driver_uses_derivatives.DriverUsesDerivatives
Driver wrapper of Fortran version of CONMIN.
0: Initial and final state
1: Initial evaluation of objective and constraint values
2: Evalute gradients of objective and constraints (internal only)
3: Evalute gradients of objective and constraints
4: One-dimensional search on unconstrained function
5: Solve 1D search problem for unconstrained function
Array designating whether each constraint is linear.
Constraint thickness parameter.
Constraint thickness parameter for linear and side constraints.
Minimum absolute value of ctl used in optimization.
Minimum absolute value of ct used in optimization.
Absolute convergence tolerance.
Relative convergence tolerance.
Relative change in parameters when calculating finite difference gradients. (only when CONMIN calculates gradient)
Minimum absolute step in finite difference gradient calculations. (only when CONMIN calculates gradient)
Conjugate gradient restart. parameter.
Print information during CONMIN solution. Higher values are more verbose. 0 suppresses all output.
Maximum number of iterations before termination.
Number of consecutive iterations to indicate convergence (relative or absolute).
Linear objective function flag. Set to True if objective is linear.
Participation coefficient - penalty parameter that pushes designs towards the feasible region.
Mean value of the push-off factor in the method of feasible directions.
Adds a constraint in the form of a boolean expression string to the driver.
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds an objective to the driver.
Takes an iterator of objective strings and creates objectives for them in the driver.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if types is [‘ineq’].
Removes all constraints.
Removes all objectives.
Removes all parameters.
Returns a copy of our constraints dict.
Returns a list of constraint values
Returns a list of values of the evaluated objectives.
Returns a list of values of the evaluated objectives.
Returns an ordered dict of inequality constraint objects.
Returns an OrderedDict of objective expressions.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the specified objective expression. Spaces within the expression are ignored.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
Bases: openmdao.lib.drivers.caseiterdriver.CaseIterDriverBase
Driver for evaluating models at point distributions.
A list of outputs to be saved with each case.
Iterator supplying values of point distribitions.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Removes all parameters.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
Bases: openmdao.main.container.Container
Generate the input cases for finite differences.
Form of finite difference used
Number of parameters, or dimensions
Order of the finite differences
Set to True to skip running the baseline case.
The DOEdriver provides the capability to execute a DOE on a workflow. This Driver supports the IHasParameters interface. At execution time, the driver will use the list of parameters added to it by the user to create a specific DOE and then iteratively execute the DOE cases on the workflow.
Users can pick from any of the DOEgenerators provided in the standard library or provide their own custom instance of a DOEgenerator. A DOEgenerator must be plugged into the DOEgenerator socket on the DOEdriver in order to operate.
from openmdao.main.api import Assembly from openmdao.lib.drivers.api import DOEdriver from openmdao.lib.doegenerators.api import FullFactorial from openmdao.lib.optproblems.branin import BraninComponent class Analysis(Assembly): def configure(self): self.add('branin', BraninComponent()) self.add('driver', DOEdriver()) self.driver.workflow.add('branin') self.driver.add_parameter('branin.x',low=-5.,high=10.) self.driver.add_parameter('branin.y',low=0.,high=15.) #use a full factorial DOE with 2 variables, and 3 levels # for each variable self.driver.DOEgenerator = FullFactorial(num_levels=3)
The min and max metadata of the parameters are used to denote the range for each variable over which the DOE will span.
By default, the normalized parameter values are written to a CSV file in the driver’s execution directory, with a name of <driver-name>.csv. This can be used later to rerun all of the cases by using a CSVFile DOE generator. You can also select which cases should be run by filling the case_filter slot.
doedriver.py – Driver that executes a Design of Experiments.
Bases: openmdao.lib.drivers.caseiterdriver.CaseIterDriverBase
Driver for Design of Experiments.
Iterator supplying normalized DOE values.
Selects cases to be run.
A list of outputs to be saved with each case.
Name of CSV file to record to (default is <driver-name>.csv)
Record normalized DOE values to CSV file.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Removes all parameters.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
Bases: openmdao.lib.drivers.caseiterdriver.CaseIterDriverBase
Driver for Design of Experiments within a specified neighborhood around a point.
Iterator supplying normalized DOE values.
Multiplicative factor for neighborhood DOE Driver.
Another factor for neighborhood DOE Driver.
A list of outputs to be saved with each case.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Removes all parameters.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
Genetic is a driver which performs optimization using a genetic algorithm based on Pyevolve. Genetic is a global optimizer and is ideal for optimizing problems with integer or discrete design variables because it is a non-derivative based optimization method.
Genetic can be used in any simulation by importing it from openmdao.lib.drivers.api:
from openmdao.lib.drivers.api import Genetic
Design Variables
IOtraits are added to Genetic and become optimization parameters. Genetic will vary the set of parameters to search for an optimum. Genetic supports three variable types: Float, Int, and Enum. These types can be used as parameters in any optimization.
You add design variables to Genetic using the add_parameter method.
from openmdao.main.api import Assembly, Component, set_as_top
from openmdao.lib.drivers.api import Genetic
from openmdao.lib.datatypes.api import Float, Int, Enum
class SomeComp(Component):
"""Arbitrary component with a few variables, but which does not really do
any calculations
"""
w = Float(0.0, low=-10, high=10, iotype="in")
x = Float(0.0, low=0.0, high=100.0, iotype="in")
y = Int(10, low=10, high=100, iotype="in")
z = Enum([-10, -5, 0, 7], iotype="in")
class Simulation(Assembly):
"""Top Level Assembly used for simulation"""
def configure(self):
self.add('driver', Genetic())
self.add('comp', SomeComp())
# Driver process definition
self.driver.workflow.add('comp')
self.driver.add_parameter('comp.x')
self.driver.add_parameter('comp.y')
self.driver.add_parameter('comp.z')
top = set_as_top(Simulation())
In the above example, three parameters were added to the optimizer. The optimizer figures out for itself what type of variable it is and behaves appropriately. In all three cases, since no low or high arguments were provided, the optimizer will use the values from the metadata provided in the variable deceleration.
For comp.x the optimizer will try floats between 0.0 and 100.0. For comp.y the optimizer will try integers between 10 and 100. For comp.z the optimizer will pick from the list of allowed values: [-10,-5,0,7].
You can override the low and high values from the metadata if you want the optimizer to use a different range instead of the default.
top.driver.add_parameter('comp.w', low=5.0, high=7.0)
Now, for comp.x the optimizer will only try values between 5.0 and 7.0. Note that low and high are applicable only to Float and Int variables. For Enum variables, low and high are not applicable.
Configuration
When setting the objective you can specify a single variable name or a more complex function, such as
top.driver.add_objective("comp.x")
or
top.driver.clear_objectives()
top.driver.add_objective("2*comp.x + comp.y + 3*comp.z")
In the second example above, a more complex objective function was created where the overall objective was a weighted combination of comp.x, comp.y, and comp.z.
To set the optimizer to either minimize or maximize your objective, you set the opt_type variable of Genetic to "minimize" or "maximize.
top.driver.opt_type = "minimize"
You can control the size of the population in each generation and the maximum number of generations in your optimization with the population_size and generations variables.
top.driver.population_size = 80
top.driver.generations = 100
As you increase the population size, you are effectively adding diversity in to the gene pool of your optimization. A large population means that a larger number of individuals from a given generation will be chosen to provide genetic material for the next generation. So there is a better chance that weaker individuals will pass on their genes. This diversity helps to ensure that your optimization will find a true global optimum within the allowed design space. However, it also serves to slow down the optimization because of the increased number of function evaluations necessary for each generation.
Picking an appropriate value for the maximum number of generations will depend highly on the specifics of your problem. Setting this number too low will likely prevent the optimization from converging on a true optimum. Setting it too high will help you find the true optimum, but you may end up wasting the computation time on later generations where the optimum has been found.
You can further control the behavior of the genetic algorithm by setting the crossover_rate, mutation_rate, selection_method, and elitism variables. These settings will allow you to fine-tune the convergence of your optimization to achieve the desired result; however, for many optimizations the default values will work well and won’t need to be changed.
The crossover_rate controls the rate at which the crossover operator gets applied to the genome of a set of individuals who are reproducing. The allowed values are between 0.0 and 1.0. A higher rate will mean that more of the genes are swapped between parents. The result will be a more uniform population and better searching of the design space. If the rate is set too high, then it is likely that stronger individuals could be lost to churn.
top.driver.crossover_rate = 0.9
The mutation_rate controls how likely any particular gene is to experience a mutation. A low, but non-zero, mutation rate will help prevent stagnation in the gene pool by randomly moving the values of genes. If this rate is set too high, the algorithm basically degrades into a random search through the design space. The allowed values are between 0.0 and 1.0.
top.driver.mutation_rate = .02
In a pure genetic algorithm, it is possible that your best performing individual will not survive from one generation to the next due to competition, mutation, and crossover. If you want to ensure that the best individual survives intact from one generation to the next, then turn on the elitism flag for your optimization. This will ensure that the best individual is always copied to the next generation no matter what.
top.driver.elitism = True
A number of different commonly used selection algorithms are available. The default algorithm is the Roulette Wheel Algorithm, but Rank Selection, and Uniform Selection are also available. The selection_method variable allows you to select the algorithm; allowed values are: "roulette_wheel," "rank," and "uniform".
top.driver.selection_method="rank"
A simple Pyevolve-based driver for OpenMDAO.
Bases: openmdao.main.driver.Driver
Genetic algorithm for the OpenMDAO framework, based on the Pyevolve Genetic algorithm module.
The crossover rate used when two parent genomes reproduce to form a child genome.
Controls the use of elitism in the creation of new generations.
The maximum number of generations the algorithm will evolve to before stopping.
The mutation rate applied to population members.
Sets the optimization to either minimize or maximize the objective function.
The size of the population in each generation.
Random seed for the optimizer. Set to a specific value for repeatable results; otherwise leave as None for truly random seeding.
The selection method used to pick population members who will survive for breeding into the next generation.
The genome with the best score from the optimization.
Adds an objective to the driver.
Takes an iterator of objective strings and creates objectives for them in the driver.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Removes all objectives.
Removes all parameters.
Returns a list of values of the evaluated objectives.
Returns a list of values of the evaluated objectives.
Returns an OrderedDict of objective expressions.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the specified objective expression. Spaces within the expression are ignored.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
The FixedPointIterator is a simple solver that can solve a single-input single-output problem using fixed point iteration. It provides a way to iterate on a single input to match an output. In other words, fixed point iteration can be used to solve the equation x = f(x). By extension, FixedPointIterator can be used to close a loop in the data flow. The algorithm is useful for some problems, so it is included here. However, it may require more functional evaluations than the BroydenSolver.
As an example, let’s implement a component that can be run iteratively to produce the square root of a number.
from openmdao.lib.datatypes.api import Float
from openmdao.main.api import Component
class Babylonian(Component):
""" The Babylonians had a neat way of calculating square
roots using Fixed Point Iteration"""
x = Float(1.0, iotype="in", doc="Input is x")
y = Float(iotype="out", doc="Output is y")
def execute(self):
""" Iterate to find the square root of 2, the Babylonian way:
"""
x = self.x
self.y = 0.5*(2.0/x + x)
An assembly with this component and the FixedPointIterator would look like this.
from openmdao.lib.drivers.api import FixedPointIterator
from openmdao.main.api import Assembly
class SolutionAssembly(Assembly):
""" Solves for the root of MIMOSystem. """
def configure(self):
""" Creates a new Assembly with this problem
the answer should be 1.4142.....
"""
self.add('driver', FixedPointIterator())
self.add('problem', Babylonian())
self.driver.workflow.add('problem')
# Set our independent and dependent
self.driver.add_parameter('problem.x', low=-9.e99, high=9.e99)
self.driver.add_constraint('problem.y = problem.x')
The x input and the F(x) output equation are specified as string expressions using the add_parameter and add_constraint methods. The constraint contains the equation x = f(x), which we are trying to solve. Note that this is a single-input single-output method, so it is only valid to specify one constraint and one parameter.
>>> top = SolutionAssembly()
>>> top.run()
>>> print top.problem.x
1.4142...
Two additional parameters control the FixedPointIterator. The parameter tolerance sets the convergence tolerance for the comparison between value of x_out at the current iteration and the previous iteration. The default value for tolerance is 0.001. The parameter max_iteration specifies the number of iterations to run. The default value for max_iterations is 25.
A more useful example in which the FixedPointIterator is used to converge two coupled components is shown in MDAO Architectures.
A simple iteration driver. Basically runs a workflow, passing the output to the input for the next iteration. Relative change and number of iterations are used as termination criteria.
Bases: openmdao.main.driver.Driver
A simple fixed point iteration driver, which runs a workflow and passes the value from the output to the input for the next iteration. Relative change and number of iterations are used as termination criterea. This type of iteration is also known as Gauss-Seidel.
Maximum number of iterations before termination.
Absolute convergence tolerance between iterations.
For multivariable iteration, type of normto use to test convergence.
Adds a constraint in the form of a boolean expression string to the driver.
Parameters:
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if types is [‘eq’].
Removes all constraints.
Removes all parameters.
Returns a copy of our constraints dict.
Returns a list of tuples of the form (lhs, rhs, comparator, is_violated).
Returns an ordered dict of constraint objects.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
Bases: openmdao.main.driver.Driver
A simple driver to run a workflow until some stop condition is met
maximun number of iterations
If True, driver will ignore stop conditions for the first iteration, and run at least one iteration
current iteration counter
Removes all stop conditions.
Returns a list of evaluated stop conditions.
Returns a list of stop condition strings.
Removes the stop condition matching the given string.
Return True if any of the stopping conditions evaluate to True.
NEWSUMT is a Fortran subroutine for solving linear and nonlinear constrained or unconstrained function minimization problems. It has been included in the OpenMDAO standard library to provide users with a basic gradient-based optimization algorithm.
The minimization algorithm used in NEWSUMT is a sequence of unconstrained minimizations technique (SUMT) where the modified Newton’s method is used for unconstrained function minimizations.
If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference.
NEWSUMT treats inequality constraints in a way that is especially well suited to engineering design applications.
More information on NEWSUMT can be found in the NEWSUMT Users Guide.
Basic Interface
The NEWSUMT code contains a number of different parameters and switches that are useful for controlling the optimization process. These can be subdivided into those parameters that will be used in a typical optimization problem and those that are more likely to be used by an expert user.
For the simplest possible unconstrained optimization problem, NEWSUMT just needs an objective function and one or more decision variables (parameters.) The basic interface conforms to OpenMDAO’s driver API.
The OpenMDAO NEWSUMT driver can be imported from openmdao.lib.drivers.api.
from openmdao.lib.drivers.api import NEWSUMTdriver
Typically, NEWSUMT will be used as a driver in the top level assembly, though it can be also used in a subassembly as part of a nested driver scheme. Using the OpenMDAO script interface, a simple optimization problem can be set up as follows:
from openmdao.main.api import Assembly
from openmdao.examples.enginedesign.vehicle import Vehicle
from openmdao.lib.drivers.api import CONMINdriver
class EngineOptimization(Assembly):
""" Top level assembly for optimizing a vehicle. """
def configure(self):
""" Creates a new Assembly for vehicle performance optimization."""
# Create CONMIN Optimizer instance
self.add('driver', NEWSUMTdriver())
# Create Vehicle instance
self.add('vehicle', Vehicle())
# add Vehicle to optimizer workflow
self.driver.workflow.add('vehicle')
# CONMIN Flags
self.driver.iprint = 0
self.driver.itmax = 30
# CONMIN Objective
self.driver.add_objective('vehicle.fuel_burn')
# CONMIN Design Variables
self.driver.add_parameter('vehicle.spark_angle', low=-50. , high=10.)
self.driver.add_parameter('vehicle.bore', low=65. , high=100.)
This first section of code defines an assembly called EngineOptimization. This assembly contains a DrivingSim component and a NEWSUMTdriver, both of which are created and added inside the __init__ function with add. The DrivingSim component is also added to the driver’s workflow. The objective function, design variables, constraints, and any NEWSUMT parameters are also assigned in the __init__ function.
Basic Parameters
This section contains the basic parameters for NEWSUMT.
The default behavior for NEWSUMT is to calculate its own gradients and Hessians of the objective and constraints using a first-order forward finite difference. The second derivatives are approximated from the first order differences. You can replace NEWSUMT’s finite difference with OpenMDAO’s built-in capability by inserting a differentiator into the Differentiator slot in the driver.
If you want to use NEWSUMT for the finite difference calculation and want the same finite difference step size in all your variables, you can set the default_fd_stepsize parameter.
self.driver.default_fd_stepsize = .0025
The default step size will be used for all parameters for which you have not set the fd_step attribute.
When using NEWSUMT, if you have any linear constraints, it may be advantageous to specify them as such so that NEWSUMT can treat them differently. Use the integer array ilin to designate whether a constraint is linear. A value of 0 indicates that that constraint is non-linear, while a value of 1 indicates that that the constraint is linear. This parameter is optional, and when it is omitted, all constraints are assumed to be nonlinear.
map(self.driver.add_constraint, ['vehicle.stroke < vehicle.bore',
'vehicle.stroke * vehicle.bore > 1.0'])
self.driver.ilin_linear = [1, 0]
Similarly, NEWSUMT has a flag parameter to indicate whether the objective function is linear or nonlinear. Setting lobj to 1 indicates a linear objective function. Setting it to 0, which is the default value, indicates a nonlinear objective function.
self.driver.lobj = 0
The iprint parameter can be used to display diagnostic messages. These messages are currently sent to the standard output.
self.driver.iprint = 0
Higher positive values of iprint turn on the display of more levels of output, as summarized below.
Value | Result |
---|---|
iprint = 0 | All output is suppressed, including warnings |
iprint = 1 | Print initial and final designs only |
iprint = 2 | Print brief results of analysis for initial and final designs together with minimal intermediate information |
iprint = 3 | Detailed printing |
iprint = 4 | Debugging printing |
Controlling the Optimization
NEWSUMT provides a variety of parameters to control the convergence criteria for an optimization.
The maximum number of iterations is specified by setting the itmax parameter. The default value is 10.
self.driver.itmax = 30
The convergence tolerance is controlled with six parameters. The following table summarizes these parameters.
Parameter | Description | Default |
---|---|---|
epsgsn | Convergence criteria of the golden section algorithm used for the one-dimensional minimization | 0.001 |
epsodm | Convergence criteria of the unconstrained minimization | 0.001 |
epsrsf | Convergence criteria for the overall process | 0.001 |
maxgsn | Maximum allowable number of golden section iterations used for 1D minimization | 20 |
maxodm | Maximum allowable number of one-dimensional minimizations | 6 |
maxrsf | Maximum allowable number of unconstrained minimizations | 15 |
self.driver.epsgsn = .000001
self.driver.maxgsn = 40
Advanced Options
There are additional options for advanced users. More information on these parameters can be found in the NEWSUMT Users Guide. (This doc is slow to load.)
Parameter | Description | Default |
---|---|---|
mflag | Flag for penalty multiplier. If 0, initial value computed by NEWSUMT. If 1, initial value set by ra | 0 |
ra | Penalty multiplier. Required if mflag=1 | 1.0 |
racut | Penalty multiplier decrease ratio. Required if mflag=1 | 0.1 |
ramin | Lower bound of penalty multiplier. Required if mflag=1 | 1.0e-13 |
g0 | Initial value of the transition parameter | 0.1 |
newsumtdriver.py - Driver for the NEWSUMT optimizer.
Bases: openmdao.main.driver_uses_derivatives.DriverUsesDerivatives
Driver wrapper of Fortran version of NEWSUMT.
Todo
Check to see if this itmax variable is needed. NEWSUMT might handle it for us.
Default finite difference stepsize. Parameters with specified values override this.
Convergence criteria of the golden section algorithm used for the one dimensional minimization.
Convergence criteria of the unconstrained minimization.
Convergence criteria for the overall process.
Initial value of the transition parameter.
Array designating whether each constraint is linear.
Print information during NEWSUMT solution. Higher values are more verbose. If 0, print initial and final designs only.
Maximum number of iterations before termination.
Set to 1 if linear objective function.
Maximum allowable number of golden section iterations used for 1D minimization.
Maximum allowable number of one dimensional minimizations.
Maximum allowable number of unconstrained minimizations.
Flag for penalty multiplier. If 0, initial value computed by NEWSUMT. If 1, initial value set by ra.
Penalty multiplier. Required if mflag=1
Penalty multiplier decrease ratio. Required if mflag=1.
Lower bound of penalty multiplier. Required if mflag=1.
Maximum bound imposed on the initial step size of the one-dimensional minimization.
Adds a constraint in the form of a boolean expression string to the driver.
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds an objective to the driver.
Takes an iterator of objective strings and creates objectives for them in the driver.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if types is [‘ineq’].
Removes all constraints.
Removes all objectives.
Removes all parameters.
Returns a copy of our constraints dict.
Returns a list of constraint values
Returns a list of values of the evaluated objectives.
Returns a list of values of the evaluated objectives.
Returns an ordered dict of inequality constraint objects.
Returns an OrderedDict of objective expressions.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the specified objective expression. Spaces within the expression are ignored.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
sensitivity.py – Driver to calculate the gradient of a workflow and return it as a driver output.
SensitivityDriver includes a differentiator slot where the differentiation method can be plugged. Fake finite difference is supported.
Bases: openmdao.main.driver_uses_derivatives.DriverUsesDerivatives
Driver to calculate the gradient of a workflow and return it as a driver output. The gradient is calculated from all inputs (Parameters) to all outputs (Objectives and Constraints).
SensitivityDriver includes a differentiator slot where the differentiation method can be plugged. Fake finite difference is supported.
Objective baseline values where sensitivity is evaluated.
Constraint baseline values where sensitivity is evaluated.
Sensitivity of the objectives with respect to the parameters. Index 1 is the objective output, while index 2 is the parameter input.
Objective names that correspond to our array indices.
Sensitivity of the constraints with respect to the parameters. Index 1 is the constraint output, while index 2 is the parameter input.
Constraint names that correspond to our array indices.
Parameter names that correspond to our array indices.
Parameter baseline values where sensitivity is evaluated.
Adds a constraint in the form of a boolean expression string to the driver.
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds an objective to the driver.
Takes an iterator of objective strings and creates objectives for them in the driver.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if this Driver supports constraints of the given types.
Removes all constraints.
Removes all objectives.
Removes all parameters.
Returns a list of tuples of the form (lhs, rhs, comparator, is_violated) from evalution of equality constraints.
Returns a list of tuples of the form (lhs, rhs, comparator, is_violated) from evalution of inequality constraints.
Returns a list of values of the evaluated objectives.
Return a list of constraint objects
Returns an ordered dict of equality constraint objects.
Returns an ordered dict of inequality constraint objects.
Returns an OrderedDict of objective expressions.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the specified objective expression. Spaces within the expression are ignored.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
A simple driver that runs cases from a CaseIterator and records them with a CaseRecorder.
Bases: openmdao.main.driver.Driver
A Driver that sequentially runs a set of cases provided by an ICaseIterator and optionally records the results in a CaseRecorder. This is intended for test cases or very simple models only. For a more full-featured Driver with similar functionality, see CaseIteratorDriver.
For each case coming from the iterator, the workflow will be executed once.
Source of Cases.
slsqpdriver.py - Contains a driver that wraps the SLSQP optimizer as used in pyOpt:
Minimize a function using Sequential Least SQuares Programming.
SLSQP is a gradient optimizer that can handle both equality and inequality constraints.
Bases: openmdao.main.driver_uses_derivatives.DriverUsesDerivatives
Minimize a function using the Sequential Least SQuares Programming (SLSQP) method.
SLSQP is a gradient optimizer that can handle both equality and inequality constraints.
Note: Constraints should be added using the OpenMDAO convention (positive = violated).
Convergence accuracy
Fortran output unit. Leave this at 6 for STDOUT.
Controls the frequency of output: 0 (no output),1,2,3.
Maximum number of iterations.
Name of output file (if iout not 6).
Error code returned from SLSQP.
Adds a constraint in the form of a boolean expression string to the driver.
Adds an existing Constraint object to the driver.
cnst: Constraint object
Adds an objective to the driver.
Takes an iterator of objective strings and creates objectives for them in the driver.
Adds a parameter or group of parameters to the driver.
If neither “low” nor “high” is specified, the min and max will default to the values in the metadata of the variable being referenced. If they are not specified in the metadata and not provided as arguments, a ValueError is raised.
Returns True if this Driver supports constraints of the given types.
Removes all constraints.
Removes all objectives.
Removes all parameters.
Returns a list of tuples of the form (lhs, rhs, comparator, is_violated) from evalution of equality constraints.
Returns a list of tuples of the form (lhs, rhs, comparator, is_violated) from evalution of inequality constraints.
Returns a list of values of the evaluated objectives.
Returns a list of values of the evaluated objectives.
Return a list of constraint objects
Returns an ordered dict of equality constraint objects.
Returns an ordered dict of inequality constraint objects.
Returns an OrderedDict of objective expressions.
Returns an ordered dict of parameter objects.
Sets all parameters to their start value, if a start value is given
Return a list of strings containing constraint expressions.
Returns a list of parameter targets. Note that this list may contain more entries than the list of Parameter and ParameterGroup objects since ParameterGroups have multiple targets.
Removes the constraint with the given string.
Removes the specified objective expression. Spaces within the expression are ignored.
Removes the parameter with the given name.
Sets a single parameter by its name attribute.
Pushes the values in the iterator ‘values’ into the corresponding variables in the model. If the ‘case’ arg is supplied, the values will be set into the case and not into the model.
Bases: openmdao.main.component.Component
Bases: openmdao.main.problem_formulation.OptProblem
Branin Test Problem Definition
Scalable Test Optimization test problem proposed by Martins and Marriage.
J. R. R. A. Martins and C. Marriage, “An Object-Oriented Framework for Multidisciplinary Design Optimization,” 3rd AIAA Multidisciplinary Design Optimization Specialist Conference, 2007.
Bases: openmdao.main.component.Component
coefficient for the output variables
Two discipline components. From Sellar’s analytic problem.
Sellar, R. S., Batill, S. M., and Renaud, J. E., “Response Surface Based, Concurrent Subspace Optimization for Multidisciplinary System Design,” Proceedings References 79 of the 34th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 1996.
Bases: openmdao.main.component.Component
Component containing Discipline 1.
Local Design Variable.
Disciplinary Coupling.
Global Design Variable.
Global Design Variable.
Output of this Discipline.
Bases: openmdao.main.component_with_derivatives.ComponentWithDerivatives
Component containing Discipline 1.
Local Design Variable.
Disciplinary Coupling.
Global Design Variable.
Global Design Variable.
Output of this Discipline.
Bases: openmdao.main.component.Component
Component containing Discipline 2.
Disciplinary Coupling.
Global Design Variable.
Global Design Variable.
Output of this Discipline.
Bases: openmdao.main.component_with_derivatives.ComponentWithDerivatives
Component containing Discipline 2.
Disciplinary Coupling.
Global Design Variable.
Global Design Variable.
Output of this Discipline.
Bases: openmdao.main.problem_formulation.OptProblem
Sellar test problem definition.
Bases: openmdao.main.problem_formulation.OptProblem
Sellar test problem definition using components analytical derivatives.
Pseudo package providing a central place to access all of the OpenMDAO surrogatemodels in the standard library.
Surrogate model based on Kriging.
Bases: object
Returns a NormalDistribution centered around the value, with a standard deviation of 0.
Surrogate Model based on a logistic regression model, with regularization to adjust for overfitting. Based on work from Python logistic regression.
Bases: openmdao.main.container.Container
L2 regularization strength
Returns the value iself. Logistic regressions don’t have uncertainty.
Surrogate Model based on second order response surface equations.
Bases: openmdao.main.container.Container
Returns the value iself. Response surface equations don’t have uncertainty.
Pseudo package providing a central place to access all of the OpenMDAO datatypes in the standard library.
Bases: object
A DomainObj represents a (possibly multi-zoned) mesh and data related to that mesh.
Add zones from other to self, retaining names where possible.
Add a Zone. Returns the added zone.
Construct a new DomainObj from zones extended according to zone_args. Existing zone names are used for the new domain’s zones.
Construct a new DomainObj from grid and flow data extracted from the specified regions of each zone. Existing zone names are used for the new domain’s zones.
Test if self and other are equivalent.
Convert to Cartesian coordinate system.
Convert to cylindrical coordinate system.
Remove a zone. Returns the removed zone.
Rename a zone.
Translate coordinates.
Bases: object
Contains solution variables for a Zone. All variables have the same shape and grid location.
Add a numpy.ndarray of scalar data and bind to name. Returns the added array.
Add a Vector and bind to name. Returns the added vector.
Construct a new FlowSolution by replication. The existing ghosts/rind planes specification is retained.
Construct a new FlowSolution from data extracted from the specified region.
Test if self and other are equivalent.
Convert to Cartesian coordinate system.
Convert to cylindrical coordinate system.
Number of ghost cells for each index direction.
Position at which data is located, must be one of (‘Vertex’, ‘CellCenter’)
Bases: openmdao.lib.datatypes.domain.vector.Vector
Coordinate data for a Zone. Currently limited to structured grids. 1D spatial data must set ‘x’. 2D spatial data must set ‘x’, and ‘y’ or ‘r’ and ‘t’. 3D spatial data must set ‘x’, ‘y’, and ‘z’ or ‘r’, ‘t’, and ‘z’. Note that index dimension is not the same as spatial dimension. For example, a curve in 3D space is represented by 1D ‘x’, ‘y’, and ‘z’ arrays. It can also be represented by 2D or 3D arrays where only one index dimension varies.
Construct a new GridCoordinates by linear extrapolation. The existing ghosts/rind planes specification is retained.
Construct a new GridCoordinates from data extracted from the specified region.
Test if self and other are equivalent.
Convert to Cartesian coordinate system.
Convert to cylindrical coordinate system.
Predefined classes used by mesh_probe(). Some typical fluid flow metric calculation classes are included here. Others may be added via register_metric(). A list of available metrics is returned by list_metrics(). Note that the name a metric is registered under need not match its class name.
Metrics may be used with 1D, 2D, or 3D Cartesian coordinates. They may also be used with polar (2D) or cylindrical (3D) coordinates. calculate() should be prepared for this.
Bases: object
Computes area of mesh surface.
Bases: object
Computes corrected mass flow across a mesh surface.
Bases: object
Computes length of mesh curve.
Bases: object
Computes mass flow across a mesh surface.
Bases: object
Computes weighted static pressure for a mesh region.
Bases: object
Computes weighted static temperature for a mesh region.
Bases: object
Computes weighted total pressure for a mesh region.
Bases: object
Computes weighted total temperature for a mesh region.
Bases: object
Computes volume of mesh volume.
Creates a minimal metric calculation class for var_name and registers it. This can be used for averaging scalar flow variables without having to statically create a class and register it. The created class does not support dimensionalization.
Register a metric calculation class.
Functions to read and write a DomainObj in Plot3D format. Many function arguments are common:
Default argument values are set for a typical 3D multiblock single-precision Fortran unformatted file. When writing, zones are assumed in Cartesian coordinates with data located at the vertices.
Returns a DomainObj initialized from Plot3D grid_file and f_file. Variables are assigned to names of the form f_N.
Returns a DomainObj initialized from Plot3D grid_file.
Returns a DomainObj initialized from Plot3D grid_file and q_file. Q variables are assigned to ‘density’, ‘momentum’, and ‘energy_stagnation_density’. Scalars are assigned to ‘mach’, ‘alpha’, ‘reynolds’, and ‘time’.
Returns a list of zone dimensions from Plot3D grid_file.
Writes domain to grid_file and f_file in Plot3D format. If varnames is None, then all arrays and then all vectors are written. Ghost data is not written.
Writes domain to grid_file in Plot3D format. Ghost data is not written.
Writes domain to grid_file and q_file in Plot3D format. Requires ‘density’, ‘momentum’, and ‘energy_stagnation_density’ variables as well as ‘mach’, ‘alpha’, ‘reynolds’, and ‘time’ scalars. Ghost data is not written.
Support for calculating one or more scalar averages across one or more regions in a domain.
Calculate metrics on mesh regions. Currently only supports structured grids.
Returns a list of metric values in the order of the variables list.
Note
The per-item averaging scheme is simplistic. For instance, all four vertices of a face get equal weight, or the two cells sharing a face get equal weight. This will lead to inaccuracies for highly irregular grids.
Bases: object
Vector data for a FlowSolution, also the base for GridCoordinates. In Cartesian coordinates, array indexing order is x,y,z; so an ‘i-face’ is a y,z surface. In cylindrical coordinates, array indexing order is z,r,t; so an ‘i-face’ is an r,t surface.
Construct a new Vector by replication.
Construct a new Vector from data extracted from the specified region.
Test if self and other are equivalent.
Convert to Cartesian coordinate system.
Convert to cylindrical coordinate system.
Number of ghost/rind planes for each index direction.
Bases: object
One zone in a possibly multi-zone DomainObj.
Construct a new Zone by linearly extending the grid and replicating the flow. Symmetry data is copied.
Construct a new Zone from grid and flow data extracted from the specified region. Symmetry data is copied.
Test if self and other are equivalent.
Convert to Cartesian coordinate system.
Convert to cylindrical coordinate system.
Translate coordinates.
Coordinate system in use.