Change the seed of a DOE

Latin hypercube sampling is an example of stochastic DOE algorithm: given an input dimension and a number of samples, running the algorithm twice will give two different DOEs.

For the sake of reproducibility, GEMSEO uses a random seed: given an input dimension, a number of samples and a random seed, running the algorithm twice will give the same DOE.

In this example, we will see how GEMSEO uses the random seed and how the user can change its value.

from __future__ import annotations

from gemseo.algos.doe.lib_openturns import OpenTURNS
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.api import create_design_space
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.api import execute_algo
from gemseo.core.mdofunctions.mdo_function import MDOFunction

At the scenario level

First, we illustrate the use of the random seed at the DOEScenario level which is the appropriate level for most users. Then, we will illustrate this use at the OptimizationProblem level which can be useful for developers.

Let us consider a MDODiscipline representing the function \(y=x^2\):

discipline = create_discipline("AnalyticDiscipline", expressions={"y": "x**2"})

This function is defined over the unit interval \(x\in[0,1]\):

design_space = create_design_space()
design_space.add_variable("x", l_b=-1, u_b=1)

We want to sample this discipline over this design space. For that, we express the sampling problem as a DOEScenario:

scenario = create_scenario(
    [discipline], "DisciplinaryOpt", "y", design_space, scenario_type="DOE"
)

and solve it:

scenario.execute({"algo": "OT_OPT_LHS", "n_samples": 2})
print(scenario.formulation.opt_problem.database.get_last_n_x(2))

[array([-0.89534931]), array([0.73475608])]

You can get the value of the random seed that has been used:

print(scenario.seed)

1

Each call to execute() increments this attribute value and the underlying DOELibrary uses this seed if the user does not pass a custom value. Then, solving again this problem with the same configuration leads to a new result:

scenario.execute({"algo": "OT_OPT_LHS", "n_samples": 2})
print(scenario.formulation.opt_problem.database.get_last_n_x(2))

[array([0.04982439]), array([-0.48653892])]

and we can check that the value of the seed was incremented:

print(scenario.seed)

2

You can also pass a custom seed with the key "algo_options" of the input_data passed to DOEScenario.execute():

scenario.execute({"algo": "OT_OPT_LHS", "n_samples": 2, "algo_options": {"seed": 123}})
print(scenario.formulation.opt_problem.database.get_last_n_x(2))

[array([-0.09505332]), array([0.98400738])]

At the problem level

Basic

Let us consider a MDOFunction representing the function \(y=x^2\):

function = MDOFunction(lambda x: x**2, "f", args=["x"], outvars=["y"])

and defined over the unit interval \(x\in[0,1]\):

design_space = create_design_space()
design_space.add_variable("x", l_b=-1, u_b=1)

We want to sample this function over this design space. For that, we express the sampling problem as an OptimizationProblem:

problem = OptimizationProblem(design_space)
problem.objective = function

and solve it:

execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2)
print(problem.database.get_last_n_x(2))

[array([-0.89534931]), array([0.73475608])]

Note:

We use the function execute_algo() as the OptimizationProblem does not have a method execute() unlike the Scenario.

Solving again this problem with the same configuration leads to the same result:

execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2)
print(problem.database.get_last_n_x(2))

[array([-0.89534931]), array([0.73475608])]

and the result is still the same if we take 1 as random seed, as 1 is the default value of this seed:

execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2, seed=1)
print(problem.database.get_last_n_x(2))

[array([-0.89534931]), array([0.73475608])]

If you want to use a different random seed, you only have to change the value of seed:

execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2, seed=3)
print(problem.database.get_last_n_x(2))

[array([0.93088508]), array([-0.81399054])]

Advanced

You can also solve your problem with a lower level API by directly instantiating the DOELibrary of interest:

library = OpenTURNS()
library.algo_name = "OT_OPT_LHS"
library.execute(problem, n_samples=2)
print(problem.database.get_last_n_x(2))

[array([0.93088508]), array([-0.81399054])]

In that case, solving again the problem will give different samples as the DOELibrary.seed increments at each execution:

library.execute(problem, n_samples=2)
print(problem.database.get_last_n_x(2))

[array([0.04982439]), array([-0.48653892])]