# Create an MDO Scenario¶

from __future__ import annotations

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
from numpy import ones

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 - 15:35:26:
INFO - 15:35:26: *** Start MDOScenario execution ***
INFO - 15:35:26: MDOScenario
INFO - 15:35:26:    Disciplines: AnalyticDiscipline
INFO - 15:35:26:    MDO formulation: DisciplinaryOpt
INFO - 15:35:26: Optimization problem:
INFO - 15:35:26:    minimize y(x)
INFO - 15:35:26:    with respect to x
INFO - 15:35:26:    over the design space:
INFO - 15:35:26:    +------+-------------+-------+-------------+-------+
INFO - 15:35:26:    | name | lower_bound | value | upper_bound | type  |
INFO - 15:35:26:    +------+-------------+-------+-------------+-------+
INFO - 15:35:26:    | x    |      -2     |  -0.5 |      2      | float |
INFO - 15:35:26:    +------+-------------+-------+-------------+-------+
INFO - 15:35:26: Solving optimization problem with algorithm L-BFGS-B:
INFO - 15:35:26: ...   0%|          | 0/100 [00:00<?, ?it]
INFO - 15:35:26: ...   1%|          | 1/100 [00:00<00:00, 368.89 it/sec, obj=-1.09]
INFO - 15:35:26: ...   2%|▏         | 2/100 [00:00<00:00, 431.85 it/sec, obj=-1.04]
INFO - 15:35:26: ...   3%|▎         | 3/100 [00:00<00:00, 512.69 it/sec, obj=-1.24]
INFO - 15:35:26: ...   4%|▍         | 4/100 [00:00<00:00, 530.62 it/sec, obj=-1.23]
INFO - 15:35:26: ...   5%|▌         | 5/100 [00:00<00:00, 544.15 it/sec, obj=-1.24]
INFO - 15:35:26: ...   6%|▌         | 6/100 [00:00<00:00, 551.11 it/sec, obj=-1.24]
INFO - 15:35:26: ...   7%|▋         | 7/100 [00:00<00:00, 558.43 it/sec, obj=-1.24]
INFO - 15:35:26: Optimization result:
INFO - 15:35:26:    Optimizer info:
INFO - 15:35:26:       Status: 0
INFO - 15:35:26:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
INFO - 15:35:26:       Number of calls to the objective function by the optimizer: 8
INFO - 15:35:26:    Solution:
INFO - 15:35:26:       Objective: -1.236108341859242
INFO - 15:35:26:       Design space:
INFO - 15:35:26:       +------+-------------+--------------------+-------------+-------+
INFO - 15:35:26:       | name | lower_bound |       value        | upper_bound | type  |
INFO - 15:35:26:       +------+-------------+--------------------+-------------+-------+
INFO - 15:35:26:       | x    |      -2     | -1.292695718944152 |      2      | float |
INFO - 15:35:26:       +------+-------------+--------------------+-------------+-------+
INFO - 15:35:26: *** End MDOScenario execution (time: 0:00:00.023966) ***

{'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], -1.236108341859242)'


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()

['MMA', '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', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'SBO']


## Available post-processing¶

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

get_available_post_processings()

['Animation', 'BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', '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:

Total running time of the script: ( 0 minutes 0.045 seconds)

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