Create an MDO Scenario

from __future__ import annotations

from numpy import ones

from gemseo import configure_logger
from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import get_available_opt_algorithms
from gemseo import get_available_post_processings

configure_logger()

<RootLogger root (INFO)>

Let \((P)\) be a simple optimization problem:

\[\begin{split}(P) = \left\{ \begin{aligned} & \underset{x}{\text{minimize}} & & f(x) = \sin(x) - \exp(x) \\ & \text{subject to} & & -2 \leq x \leq 2 \end{aligned} \right.\end{split}\]

In this subsection, we will see how to use GEMSEO to solve this problem \((P)\) by means of an optimization algorithm.

Define the discipline

Firstly, by means of the high-level function create_discipline(), we create an MDODiscipline of AnalyticDiscipline type from a Python function:

expressions = {"y": "sin(x)-exp(x)"}
discipline = create_discipline("AnalyticDiscipline", expressions=expressions)

We can quickly access the most relevant information of any discipline (name, inputs, and outputs) with their string representations. Moreover, we can get the default input values of a discipline with the attribute MDODiscipline.default_inputs

discipline, discipline.default_inputs

(AnalyticDiscipline
   Inputs: x
   Outputs: y, {'x': array([0.])})

Now, we can to minimize this MDODiscipline over a design space, by means of a quasi-Newton method from the initial point \(0.5\).

Define the design space

For that, by means of the high-level function create_design_space(), we define the DesignSpace \([-2, 2]\) with initial value \(0.5\) by using its DesignSpace.add_variable() method.

design_space = create_design_space()
design_space.add_variable("x", l_b=-2.0, u_b=2.0, value=-0.5 * ones(1))

Define the MDO scenario

Then, by means of the create_scenario() API function, we define an MDOScenario from the MDODiscipline and the DesignSpace defined above:

scenario = create_scenario(discipline, "DisciplinaryOpt", "y", design_space)

What about the differentiation method?

The AnalyticDiscipline automatically differentiates the expressions to obtain the Jacobian matrices. Therefore, there is no need to define a differentiation method in this case. Keep in mind that for a generic discipline with no defined Jacobian function, you can use the Scenario.set_differentiation_method() method to define a numerical approximation of the gradients.

scenario.set_differentiation_method("finite_differences")

Execute the MDO scenario

Lastly, we solve the OptimizationProblem included in the MDOScenario defined above by minimizing the objective function over the DesignSpace. Precisely, we choose the L-BFGS-B algorithm implemented in the function scipy.optimize.fmin_l_bfgs_b.

scenario.execute({"algo": "L-BFGS-B", "max_iter": 100})

    INFO - 08:59:10:
    INFO - 08:59:10: *** Start MDOScenario execution ***
    INFO - 08:59:10: MDOScenario
    INFO - 08:59:10:    Disciplines: AnalyticDiscipline
    INFO - 08:59:10:    MDO formulation: DisciplinaryOpt
    INFO - 08:59:10: Optimization problem:
    INFO - 08:59:10:    minimize y(x)
    INFO - 08:59:10:    with respect to x
    INFO - 08:59:10:    over the design space:
    INFO - 08:59:10:       +------+-------------+-------+-------------+-------+
    INFO - 08:59:10:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 08:59:10:       +------+-------------+-------+-------------+-------+
    INFO - 08:59:10:       | x    |      -2     |  -0.5 |      2      | float |
    INFO - 08:59:10:       +------+-------------+-------+-------------+-------+
    INFO - 08:59:10: Solving optimization problem with algorithm L-BFGS-B:
    INFO - 08:59:10:      1%|          | 1/100 [00:00<00:00, 387.32 it/sec, obj=-1.09]
    INFO - 08:59:10:      2%|▏         | 2/100 [00:00<00:00, 455.19 it/sec, obj=-1.04]
    INFO - 08:59:10:      3%|▎         | 3/100 [00:00<00:00, 517.11 it/sec, obj=-1.24]
    INFO - 08:59:10:      4%|▍         | 4/100 [00:00<00:00, 535.11 it/sec, obj=-1.23]
    INFO - 08:59:10:      5%|▌         | 5/100 [00:00<00:00, 554.03 it/sec, obj=-1.24]
    INFO - 08:59:10:      6%|▌         | 6/100 [00:00<00:00, 566.48 it/sec, obj=-1.24]
    INFO - 08:59:10:      7%|▋         | 7/100 [00:00<00:00, 577.61 it/sec, obj=-1.24]
    INFO - 08:59:10: Optimization result:
    INFO - 08:59:10:    Optimizer info:
    INFO - 08:59:10:       Status: 0
    INFO - 08:59:10:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
    INFO - 08:59:10:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:59:10:    Solution:
    INFO - 08:59:10:       Objective: -1.2361083418592416
    INFO - 08:59:10:       Design space:
    INFO - 08:59:10:          +------+-------------+--------------------+-------------+-------+
    INFO - 08:59:10:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 08:59:10:          +------+-------------+--------------------+-------------+-------+
    INFO - 08:59:10:          | x    |      -2     | -1.292695718944152 |      2      | float |
    INFO - 08:59:10:          +------+-------------+--------------------+-------------+-------+
    INFO - 08:59:10: *** End MDOScenario execution (time: 0:00:00.026314) ***

{'max_iter': 100, 'algo': 'L-BFGS-B'}

The optimum results can be found in the execution log. It is also possible to access them with Scenario.optimization_result:

optimization_result = scenario.optimization_result
f"The solution of P is (x*, f(x*)) = ({optimization_result.x_opt}, {optimization_result.f_opt})"

'The solution of P is (x*, f(x*)) = ([-1.29269572], -1.2361083418592416)'

See also

You can find the SciPy implementation of the L-BFGS-B algorithm algorithm by clicking here. # noqa

Available algorithms

In order to get the list of available optimization algorithms, use:

get_available_opt_algorithms()

['Augmented_Lagrangian_order_0', 'Augmented_Lagrangian_order_1', 'MMA', 'MNBI', 'NLOPT_MMA', 'NLOPT_COBYLA', 'NLOPT_SLSQP', 'NLOPT_BOBYQA', 'NLOPT_BFGS', 'NLOPT_NEWUOA', 'PDFO_COBYLA', 'PDFO_BOBYQA', 'PDFO_NEWUOA', 'PSEVEN', 'PSEVEN_FD', 'PSEVEN_MOM', 'PSEVEN_NCG', 'PSEVEN_NLS', 'PSEVEN_POWELL', 'PSEVEN_QP', 'PSEVEN_SQP', 'PSEVEN_SQ2P', 'PYMOO_GA', 'PYMOO_NSGA2', 'PYMOO_NSGA3', 'PYMOO_UNSGA3', 'PYMOO_RNSGA3', 'DUAL_ANNEALING', 'SHGO', 'DIFFERENTIAL_EVOLUTION', 'LINEAR_INTERIOR_POINT', 'REVISED_SIMPLEX', 'SIMPLEX', 'HIGHS_INTERIOR_POINT', 'HIGHS_DUAL_SIMPLEX', 'HIGHS', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'NELDER-MEAD']

Available post-processing

In order to get the list of available post-processing algorithms, use:

get_available_post_processings()

['Animation', 'BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', 'DataVersusModel', 'GradientSensitivity', 'HighTradeOff', 'MultiObjectiveDiagram', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'Petal', 'QuadApprox', 'Radar', 'RadarChart', 'Robustness', 'SOM', 'ScatterPareto', 'ScatterPlotMatrix', 'TopologyView', 'VariableInfluence']

Exporting the problem data.

After the execution of the scenario, you may want to export your data to use it elsewhere. The Scenario.to_dataset() will allow you to export your results to a Dataset, the basic GEMSEO class to store data.

dataset = scenario.to_dataset("a_name_for_my_dataset")

You can also look at the examples:

Examples