genetic_algorithm_driver.py¶
Driver for a simple genetic algorithm.
This is the Simple Genetic Algorithm implementation based on 2009 AAE550: MDO Lecture notes of Prof. William A. Crossley.
This basic GA algorithm is compartmentalized into the GeneticAlgorithm class so that it can be used in more complicated driver.
The following reference is only for the automatic population sizing: Williams E.A., Crossley W.A. (1998) EmpiricallyDerived Population Size and Mutation Rate Guidelines for a Genetic Algorithm with Uniform Crossover. In: Chawdhry P.K., Roy R., Pant R.K. (eds) Soft Computing in Engineering Design and Manufacturing. Springer, London.
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 multiobjective optimization: SobieszczanskiSobieski, 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.genetic_algorithm_driver.
GeneticAlgorithm
(objfun, comm=None, model_mpi=None)[source]¶ Bases:
object
Simple Genetic Algorithm.
This is the Simple Genetic Algorithm implementation based on 2009 AAE550: MDO Lecture notes of Prof. William A. Crossley. It can be used standalone or as part of the OpenMDAO Driver.
Attributes
comm
(MPI communicator or None) The MPI communicator that will be used objective evaluation for each generation.
elite
(bool) Elitism flag.
gray_code
(bool) Gray code binary representation flag.
cross_bits
(bool) Crossover swaps bits instead of tails flag. Swapping bits is similar to mutation, so when used Pc should be increased and Pm reduced.
lchrom
(int) Chromosome length.
model_mpi
(None 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.
nobj
(int) Number of objectives.
npop
(int) Population size.
objfun
(function) Objective function callback.

__init__
(objfun, comm=None, model_mpi=None)[source]¶ Initialize genetic algorithm object.
 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.

crossover
(old_gen, Pc)[source]¶ Apply crossover to the current generation.
Crossover swaps tails (kpoint crossover) of two adjacent genes.
 Parameters
 old_genndarray
Points in current generation
 Pcfloat
Probability of crossover.
 Returns
 ndarray
Current generation with crossovers applied.

decode
(gen, vlb, vub, bits)[source]¶ Decode from binary array to real value array.
 Parameters
 genndarray
Population of points, encoded.
 vlbndarray
Lower bound array.
 vubndarray
Upper bound array.
 bitsndarray(dtype=np.int)
Number of bits for decoding.
 Returns
 ndarray
Decoded design variable values.

encode
(x, vlb, vub, bits)[source]¶ Encode array of real values to array of binary arrays.
The array of arrays represents a single population member.
 Parameters
 xndarray
Design variable values.
 vlbndarray
Lower bound array.
 vubndarray
Upper bound array.
 bitsndarray(dtype=np.int)
Number of bits for decoding.
 Returns
 ndarray
Single population member, encoded.

eval_pareto
(x, obj, x_nd, obj_nd)[source]¶ Produce a set of non dominated designs.
 Parameters
 xndarray
Design points from new generation.
 objndarray
Objective values from new generation.
 x_ndndarray
Non dominated design points from previous pareto evaluation.
 obj_ndndarray
Non dominated objective values from previous pareto evaluation.
 Returns
 ndarray
Nondominated design points.
 ndarray
Objective at nondominated design points.

execute_ga
(x0, vlb, vub, vob, bits, pop_size, max_gen, random_state, Pm=None, Pc=0.5)[source]¶ Perform the genetic algorithm.
 Parameters
 x0ndarray
Initial design values
 vlbndarray
Lower bounds array.
 vubndarray
Upper bounds array. This includes overallocation so that every point falls on an integer value.
 vobndarray
Outer bounds array. This is purely for bounds check.
 bitsndarray
Number of bits to encode the design space for each element of the design vector.
 pop_sizeint
Number of points in the population.
 max_genint
Number of generations to run the GA.
 random_statenp.random.RandomState, int
Random state (or seednumber) which controls the seed and random draws.
 Pmfloat or None
Mutation rate
 Pcfloat
Crossover rate
 Returns
 ndarray
Best design point
 float
Objective value at best design point.
 int
Number of successful function evaluations.

static
from_gray
(g)[source]¶ Convert a Gray coded binary array to normal binary coding.
The input and output arrays represent a single population member.
 Parameters
 gbinary array
Gray coded binary array, e.g. np.array([0, 0, 1, 1]).
 Returns
 ndarray
Binary array using normal coding, e.g. np.array([0, 0, 1, 0]).

mutate
(current_gen, Pm)[source]¶ Apply mutations to the current generation.
A mutation flips the state of the gene from 0 to 1 or 1 to 0.
 Parameters
 current_genndarray
Points in current generation
 Pmfloat
Probability of mutation.
 Returns
 ndarray
Current generation with mutations applied.

shuffle
(old_gen)[source]¶ Shuffle (reorder) the points in the population.
Used in tournament selection.
 Parameters
 old_genndarray
Old population.
 Returns
 ndarray
New shuffled population.
 ndarray(dtype=np.int)
Index array that maps the shuffle from old to new.

static
to_gray
(g)[source]¶ Convert a binary array representing a single population member to Gray code.
 Parameters
 gbinary array
Normal binary array, e.g. np.array([0, 0, 1, 0]).
 Returns
 ndarray
Binary array using Gray code, e.g. np.array([0, 0, 1, 1]).

tournament
(old_gen, fitness)[source]¶ Apply tournament selection and keep the best points.
 Parameters
 old_genndarray
Points in current generation
 fitnessndarray
Objective value of each point.
 Returns
 ndarray
New generation with best points.

tournament_multi_obj
(old_gen, obj_val)[source]¶ Apply tournament selection and keep the best points.
This method is used if there are multiple objectives and the nondominated set is being kept.
 Parameters
 old_genndarray
Points in current generation
 obj_valndarray
Objective value of each point.
 Returns
 ndarray
New generation with best points.
 ndarray
Corresponding objective values.


class
openmdao.drivers.genetic_algorithm_driver.
SimpleGADriver
(**kwargs)[source]¶ Bases:
openmdao.core.driver.Driver
Driver for a simple genetic algorithm.

__init__
(**kwargs)[source]¶ Initialize the SimpleGADriver driver.
 Parameters
 **kwargsdict of keyword arguments
Keyword arguments that will be mapped into the Driver options.

add_recorder
(recorder)¶ Add a recorder to the driver.
 Parameters
 recorderCaseRecorder
A recorder instance.

cleanup
()¶ Clean up resources prior to exit.

declare_coloring
(num_full_jacs=3, tol=1e25, orders=None, perturb_size=1e09, min_improve_pct=5.0, show_summary=True, show_sparsity=False)¶ 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.

get_constraint_values
(ctype='all', lintype='all', driver_scaling=True)¶ Return constraint values.
 Parameters
 ctypestring
Default is ‘all’. Optionally return just the inequality constraints with ‘ineq’ or the equality constraints with ‘eq’.
 lintypestring
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)¶ 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.
 Returns
 dict
Dictionary containing values of each design variable.

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.

property
msginfo
¶ Return info to prepend to messages.
 Returns
 str
Info to prepend to messages.

objective_callback
(x, icase)[source]¶ Evaluate problem objective at the requested point.
In case of multiobjective 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_iteration
()¶ Record an iteration of the current Driver.

run
()[source]¶ Execute the genetic algorithm.
 Returns
 boolean
Failure flag; True if failed to converge, False is successful.

set_design_var
(name, value, set_remote=True)¶ Set the value of a design variable.
 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
A coloring filename. If no arg is passed, filename will be determined automatically.
