differential_evolution_driver.py

Driver for a differential evolution genetic algorithm.

TODO: add better references than: https://en.wikipedia.org/wiki/Differential_evolution

Most of this driver (except execute_ga) is based on SimpleGA, so the following may still apply:

The following reference is only for the penalty function: Smith, A. E., Coit, D. W. (1995) Penalty functions. In: Handbook of Evolutionary Computation, 97(1).

The following reference is only for weighted sum multi-objective optimization: Sobieszczanski-Sobieski, J., Morris, A. J., van Tooren, M. J. L. (2015) Multidisciplinary Design Optimization Supported by Knowledge Based Engineering. John Wiley & Sons, Ltd.

class openmdao.drivers.differential_evolution_driver.DifferentialEvolution(objfun, comm=None, model_mpi=None)

Bases: object

Differential Evolution Genetic Algorithm.

TODO : add better references than: https://en.wikipedia.org/wiki/Differential_evolution

Parameters:

objfunfunction

Objective callback function.

commMPI communicator or None

The MPI communicator that will be used objective evaluation for each generation.

model_mpiNone or tuple

If the model in objfun is also parallel, then this will contain a tuple with the the total number of population points to evaluate concurrently, and the color of the point to evaluate on this rank.

Attributes:

commMPI communicator or None

The MPI communicator that will be used objective evaluation for each generation.

lchromint

Chromosome length.

model_mpiNone or tuple

If the model in objfun is also parallel, then this will contain a tuple with the the total number of population points to evaluate concurrently, and the color of the point to evaluate on this rank.

npopint

Population size.

objfunfunction

Objective function callback.

__init__(objfun, comm=None, model_mpi=None)

Initialize genetic algorithm object.

execute_ga(x0, vlb, vub, pop_size, max_gen, random_state, F=0.5, Pc=0.5)

Perform the genetic algorithm.

Parameters:

x0ndarray

Initial design values.

vlbndarray

Lower bounds array.

vubndarray

Upper bounds array.

pop_sizeint

Number of points in the population.

max_genint

Number of generations to run the GA.

random_stateint

Seed-number which controls the random draws.

Ffloat

Differential rate.

Pcfloat

Crossover rate.

Returns:

ndarray

Best design point.

float

Objective value at best design point.

int

Number of successful function evaluations.

class openmdao.drivers.differential_evolution_driver.DifferentialEvolutionDriver(**kwargs)

Bases: Driver

Driver for a differential evolution genetic algorithm.

This algorithm requires that inputs are floating point numbers.

Parameters:

**kwargsdict of keyword arguments

Keyword arguments that will be mapped into the Driver options.

Attributes:

_problem_commMPI.Comm or None

The MPI communicator for the Problem.

_concurrent_pop_sizeint

Number of points to run concurrently when model is a parallel one.

_concurrent_colorint

Color of current rank when running a parallel model.

_desvar_idxdict

Keeps track of the indices for each desvar, since DifferentialEvolution sees an array of design variables.

_ga<DifferentialEvolution>

Main genetic algorithm lies here.

_nfitint

Number of successful function evaluations.

_randomstateint

Seed-number which controls the random draws.

__init__(**kwargs)

Initialize the DifferentialEvolutionDriver driver.

add_recorder(recorder)

Add a recorder to the driver.

Parameters:

recorderCaseRecorder

A recorder instance.

check_relevance()

Check if there are constraints that don’t depend on any design vars.

This usually indicates something is wrong with the problem formulation.

cleanup()

Clean up resources prior to exit.

declare_coloring(num_full_jacs=3, tol=1e-25, orders=None, perturb_size=1e-09, min_improve_pct=5.0, show_summary=True, show_sparsity=False, use_scaling=False, randomize_subjacs=True, randomize_seeds=False, direct=True)

Set options for total deriv coloring.

Parameters:

num_full_jacsint

Number of times to repeat partial jacobian computation when computing sparsity.

tolfloat

Tolerance used to determine if an array entry is nonzero during sparsity determination.

ordersint

Number of orders above and below the tolerance to check during the tolerance sweep.

perturb_sizefloat

Size of input/output perturbation during generation of sparsity.

min_improve_pctfloat

If coloring does not improve (decrease) the number of solves more than the given percentage, coloring will not be used.

show_summarybool

If True, display summary information after generating coloring.

show_sparsitybool

If True, display sparsity with coloring info after generating coloring.

use_scalingbool

If True, use driver scaling when generating the sparsity.

randomize_subjacsbool

If True, use random subjacobians corresponding to their declared sparsity patterns.

randomize_seedsbool

If True, use random seeds when computing the sparsity.

directbool

If using bidirectional coloring, use the direct method when computing the column adjacency matrix instead of the substitution method.

get_constraint_values(ctype='all', lintype='all', driver_scaling=True)

Return constraint values.

Parameters:

ctypestr

Default is ‘all’. Optionally return just the inequality constraints with ‘ineq’ or the equality constraints with ‘eq’.

lintypestr

Default is ‘all’. Optionally return just the linear constraints with ‘linear’ or the nonlinear constraints with ‘nonlinear’.

driver_scalingbool

When True, return values that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is True.

Returns:

dict

Dictionary containing values of each constraint.

get_design_var_values(get_remote=True, driver_scaling=True)

Return the design variable values.

Parameters:

get_remotebool or None

If True, retrieve the value even if it is on a remote process. Note that if the variable is remote on ANY process, this function must be called on EVERY process in the Problem’s MPI communicator. If False, only retrieve the value if it is on the current process, or only the part of the value that’s on the current process for a distributed variable.

driver_scalingbool

When True, return values that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is True.

Returns:

dict

Dictionary containing values of each design variable.

get_driver_derivative_calls()

Return number of derivative evaluations made during a driver run.

Returns:

int

Number of derivative evaluations made during a driver run.

get_driver_objective_calls()

Return number of objective evaluations made during a driver run.

Returns:

int

Number of objective evaluations made during a driver run.

get_exit_status()

Return exit status of driver run.

Returns:

str

String indicating result of driver run.

get_objective_values(driver_scaling=True)

Return objective values.

Parameters:

driver_scalingbool

When True, return values that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is True.

Returns:

dict

Dictionary containing values of each objective.

get_reports_dir()

Get the path to the directory where the report files should go.

If it doesn’t exist, it will be created.

Returns:

str

The path to the directory where reports should be written.

property msginfo

Return info to prepend to messages.

Returns:

str

Info to prepend to messages.

objective_callback(x, icase)

Evaluate problem objective at the requested point.

In case of multi-objective optimization, a simple weighted sum method is used:

\[f = (\sum_{k=1}^{N_f} w_k \cdot f_k)^a\]

where \(N_f\) is the number of objectives and \(a>0\) is an exponential weight. Choosing \(a=1\) is equivalent to the conventional weighted sum method.

The weights given in the options are normalized, so:

\[\sum_{k=1}^{N_f} w_k = 1\]

If one of the objectives \(f_k\) is not a scalar, its elements will have the same weights, and it will be normed with length of the vector.

Takes into account constraints with a penalty function.

All constraints are converted to the form of \(g_i(x) \leq 0\) for inequality constraints and \(h_i(x) = 0\) for equality constraints. The constraint vector for inequality constraints is the following:

\[ \begin{align}\begin{aligned}g = [g_1, g_2 \dots g_N], g_i \in R^{N_{g_i}}\\h = [h_1, h_2 \dots h_N], h_i \in R^{N_{h_i}}\end{aligned}\end{align} \]

The number of all constraints:

\[N_g = \sum_{i=1}^N N_{g_i}, N_h = \sum_{i=1}^N N_{h_i}\]

The fitness function is constructed with the penalty parameter \(p\) and the exponent \(\kappa\):

\[\Phi(x) = f(x) + p \cdot \sum_{k=1}^{N^g}(\delta_k \cdot g_k)^{\kappa} + p \cdot \sum_{k=1}^{N^h}|h_k|^{\kappa}\]

where \(\delta_k = 0\) if \(g_k\) is satisfied, 1 otherwise

Note

The values of \(\kappa\) and \(p\) can be defined as driver options.

Parameters:

xndarray

Value of design variables.

icaseint

Case number, used for identification when run in parallel.

Returns:

float

Objective value.

bool

Success flag, True if successful.

int

Case number, used for identification when run in parallel.

record_derivatives()

Record the current total jacobian.

record_iteration()

Record an iteration of the current Driver.

run()

Execute the genetic algorithm.

Returns:

bool

Failure flag; True if failed to converge, False is successful.

scaling_report(outfile='driver_scaling_report.html', title=None, show_browser=True, jac=True)

Generate a self-contained html file containing a detailed connection viewer.

Optionally pops up a web browser to view the file.

Parameters:

outfilestr, optional

The name of the output html file. Defaults to ‘driver_scaling_report.html’.

titlestr, optional

Sets the title of the web page.

show_browserbool, optional

If True, pop up a browser to view the generated html file. Defaults to True.

jacbool

If True, show jacobian information.

Returns:

dict

Data used to create html file.

set_design_var(name, value, set_remote=True)

Set the value of a design variable.

‘name’ can be a promoted output name or an alias.

Parameters:

namestr

Global pathname of the design variable.

valuefloat or ndarray

Value for the design variable.

set_remotebool

If True, set the global value of the variable (value must be of the global size). If False, set the local value of the variable (value must be of the local size).

use_fixed_coloring(coloring=<object object>)

Tell the driver to use a precomputed coloring.

Parameters:

coloringstr or Coloring

A coloring filename or a Coloring object. If no arg is passed, filename will be determined automatically.