RobustOptimizationProblem¶

class otrobopt.RobustOptimizationProblem(*args)¶

Robust optimization problem.

Must consist at least of one MeasureEvaluation, either on the objective or the constraint.

Available constructors:

RobustOptimizationProblem(robustnessMeasure, reliabilityMeasure)

RobustOptimizationProblem(objective, reliabilityMeasure)

RobustOptimizationProblem(robustnessMeasure, inequalityConstraint)

Parameters:

robustnessMeasureMeasureEvaluation: Measure function on the objective.
reliabilityMeasureMeasureEvaluation: Mesure function on the constraints
objectiveopenturns.Function: Objective function
inequalityConstraintopenturns.Function: Inequality constraint

Examples

>>> import openturns as ot
>>> import otrobopt

Pure robustness problem:

>>> thetaDist = ot.Normal(2.0, 0.1)
>>> f_base = ot.SymbolicFunction(['x1', 'theta'], ['x1*theta+cos(x1+theta)'])
>>> f = ot.ParametricFunction(f_base, [1], [1.0])
>>> robustnessMeasure = otrobopt.VarianceMeasure(f, thetaDist) 
>>> problem = otrobopt.RobustOptimizationProblem(robustnessMeasure, ot.Function())
>>> algo = ot.Cobyla(problem)
>>> algo.setStartingPoint([0.0]*robustnessMeasure.getInputDimension())
>>> algo.run()
>>> x_et = algo.getResult().getOptimalPoint()
>>> print(x_et)
[0.55...]
>>> J_et = algo.getResult().getOptimalValue()
>>> print(J_et)
[3.42...e-05]

Robustness problem with deterministic constraint:

>>> thetaDist = ot.Normal(2.0, 0.1)
>>> f_base = ot.SymbolicFunction(['x1', 'theta'], ['x1*theta'])
>>> f = ot.ParametricFunction(f_base, [1], [1.0])
>>> robustnessMeasure = otrobopt.MeanMeasure(f, thetaDist)
>>> g = ot.SymbolicFunction(['x1'], ['x1 - 5.0'])
>>> problem = otrobopt.RobustOptimizationProblem(robustnessMeasure, g)
>>> algo = ot.Cobyla(problem)
>>> algo.setStartingPoint([0.0]*robustnessMeasure.getInputDimension())
>>> algo.run()
>>> x_et = algo.getResult().getOptimalPoint()
>>> J_et = algo.getResult().getOptimalValue()

Pure reliability problem:

>>> thetaDist = ot.Normal(2.0, 0.1)
>>> f = ot.SymbolicFunction(['x1'], ['x1+1'])
>>> g_base = ot.SymbolicFunction(['x1', 'theta'], ['x1+theta'])
>>> g = ot.ParametricFunction(g_base, [1], [1.0])
>>> reliabilityMeasure = otrobopt.JointChanceMeasure(g, thetaDist, ot.Greater(), 0.95)
>>> problem = otrobopt.RobustOptimizationProblem(f, reliabilityMeasure)
>>> algo = ot.Cobyla(problem)
>>> algo.setStartingPoint([0.0]*robustnessMeasure.getInputDimension())
>>> algo.run()
>>> x_et = algo.getResult().getOptimalPoint()
>>> print(x_et)
[-1.83...]
>>> J_et = algo.getResult().getOptimalValue()
>>> print(J_et)
[-0.83...]

Robustness & reliability problem:

>>> thetaDist = ot.Normal(2.0, 0.1)
>>> f_base = ot.SymbolicFunction(['x1', 'theta'], ['x1*theta'])
>>> f = ot.ParametricFunction(f_base, [1], [1.0])
>>> robustnessMeasure = otrobopt.MeanMeasure(f, thetaDist)
>>> g_base = ot.SymbolicFunction(['x1', 'theta'], ['x1+theta'])
>>> g = ot.ParametricFunction(g_base, [1], [1.0])
>>> reliabilityMeasure = otrobopt.JointChanceMeasure(g, thetaDist, ot.Greater(), 0.95)
>>> problem = otrobopt.RobustOptimizationProblem(robustnessMeasure, reliabilityMeasure)
>>> algo = ot.Cobyla(problem)
>>> algo.setStartingPoint([0.0]*robustnessMeasure.getInputDimension())
>>> algo.run()
>>> x_et = algo.getResult().getOptimalPoint()
>>> print(x_et)
[-1.83...]
>>> J_et = algo.getResult().getOptimalValue()
>>> print(J_et)
[-3.67...]

Methods

`getBounds`()	Accessor to bounds.
`getClassName`()	Accessor to the object's name.
`getDimension`()	Accessor to input dimension.
`getDistribution`()	Distribution accessor.
`getEqualityConstraint`()	Accessor to equality constraints.
`getInequalityConstraint`()	Accessor to inequality constraints.
`getLevelFunction`()	Accessor to level function.
`getLevelValue`()	Accessor to level value.
`getName`()	Accessor to the object's name.
`getObjective`()	Accessor to objective function.
`getReliabilityMeasure`()	Reliability measure accessor.
`getResidualFunction`()	Accessor to level function.
`getRobustnessMeasure`()	Robustness measure accessor.
`getVariablesType`()	Accessor to the variables type.
`hasBounds`()	Test whether bounds had been specified.
`hasEqualityConstraint`()	Test whether equality constraints had been specified.
`hasInequalityConstraint`()	Test whether inequality constraints had been specified.
`hasLevelFunction`()	Test whether level function had been specified.
`hasMultipleObjective`()	Test whether objective function is a scalar or vector function.
`hasName`()	Test if the object is named.
`hasReliabilityMeasure`()	Reliability measure flag accessor.
`hasResidualFunction`()	Test whether a least-square problem is defined.
`hasRobustnessMeasure`()	Robustness measure flag accessor.
`isContinuous`()	Check if the problem is continuous.
`isMinimization`([marginalIndex])	Test whether this is a minimization or maximization problem.
`setBounds`(bounds)	Accessor to bounds.
`setEqualityConstraint`(equalityConstraint)	Accessor to equality constraints.
`setInequalityConstraint`(inequalityConstraint)	Accessor to inequality constraints.
`setLevelFunction`(levelFunction)	Accessor to level function.
`setLevelValue`(levelValue)	Accessor to level value.
`setMinimization`(minimization[, marginalIndex])	Tell whether this is a minimization or maximization problem.
`setName`(name)	Accessor to the object's name.
`setObjective`(objective)	Accessor to objective function.
`setReliabilityMeasure`(reliabilityMeasure)	Reliability measure accessor.
`setResidualFunction`(residualFunction)	Accessor to level function.
`setRobustnessMeasure`(robustnessMeasure)	Robustness measure accessor.
`setVariablesType`(variableType)	Accessor to the variables type.

__init__(*args)¶

getBounds()¶

Accessor to bounds.

Returns:

boundsInterval: Problem bounds.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getDimension()¶

Accessor to input dimension.

Returns:

dimensionint: Input dimension of objective function.

getDistribution()¶

Distribution accessor.

Returns:

distributionopenturns.Distribution: Parameter distribution

getEqualityConstraint()¶

Accessor to equality constraints.

Returns:

equalityFunction: Describe equality constraints.

getInequalityConstraint()¶

Accessor to inequality constraints.

Returns:

inequalityFunction: Describe inequality constraints.

getLevelFunction()¶

Accessor to level function.

Returns:

levelFunction: Level function.

getLevelValue()¶

Accessor to level value.

Returns:

valuefloat: Level value.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getObjective()¶

Accessor to objective function.

Returns:

objectiveFunction: Objective function.

getReliabilityMeasure()¶

Reliability measure accessor.

The measure on associated to the constraint

Returns:

reliabilityMeasureMeasureEvaluation: Mesure function on the constraints

getResidualFunction()¶

Accessor to level function.

Returns:

levelFunction: Level function.

getRobustnessMeasure()¶

Robustness measure accessor.

The measure on associated to the objective function

Returns:

robustnessMeasureMeasureEvaluation: Measure function on the objective.

getVariablesType()¶

Accessor to the variables type.

Returns:

variablesTypeIndices: Types of the variables.

Notes

Possible values for each variable are ot.OptimizationProblemImplementation.CONTINUOUS, ot.OptimizationProblemImplementation.INTEGER and ot.OptimizationProblemImplementation.`BINARY`.

hasBounds()¶

Test whether bounds had been specified.

Returns:

valuebool: True if bounds had been set for this problem, False otherwise.

hasEqualityConstraint()¶

Test whether equality constraints had been specified.

Returns:

valuebool: True if equality constraints had been set for this problem, False otherwise.

hasInequalityConstraint()¶

Test whether inequality constraints had been specified.

Returns:

valuebool: True if inequality constraints had been set for this problem, False otherwise.

hasLevelFunction()¶

Test whether level function had been specified.

Returns:

valuebool: True if level function had been set for this problem, False otherwise.

hasMultipleObjective()¶

Test whether objective function is a scalar or vector function.

Returns:

valuebool: False if objective function is scalar, True otherwise.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasReliabilityMeasure()¶

Reliability measure flag accessor.

If no reliability measure was set, the problem should have a robustness measure. The constraints are deduced from the reliability measure.

Returns:

hasReliabilityMeasurebool: Whether a reliability measure was set

hasResidualFunction()¶

Test whether a least-square problem is defined.

Returns:

valuebool: True if this is a least-squares problem, False otherwise.

hasRobustnessMeasure()¶

Robustness measure flag accessor.

If no robustness measure was set, the problem should have a reliability measure. The objective is deduced from the robustness measure.

Returns:

hasReliabilityMeasurebool: Whether a robustness measure was set

isContinuous()¶

Check if the problem is continuous.

Returns:

isContinuousbool: Returns True if all variables are continuous.

isMinimization(marginalIndex=0)¶

Test whether this is a minimization or maximization problem.

Parameters:

marginal_indexint, default=0: Index of the output marginal (for multi-objective only)

Returns:

valuebool: True if this is a minimization problem (default), False otherwise.

setBounds(bounds)¶

Accessor to bounds.

Parameters:

boundsInterval: Problem bounds.

setEqualityConstraint(equalityConstraint)¶

Accessor to equality constraints.

Parameters:

equalityConstraintFunction: Equality constraints.

setInequalityConstraint(inequalityConstraint)¶

Accessor to inequality constraints.

Parameters:

inequalityConstraintFunction: Inequality constraints.

setLevelFunction(levelFunction)¶

Accessor to level function.

Parameters:

levelFunctionFunction: Level function.

setLevelValue(levelValue)¶

Accessor to level value.

Parameters:

levelValuefloat: Level value.

setMinimization(minimization, marginalIndex=0)¶

Tell whether this is a minimization or maximization problem.

Parameters:

minimizationbool: True if this is a minimization problem, False otherwise.
marginal_indexint, default=0: Index of the output marginal (for multi-objective only)

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setObjective(objective)¶

Accessor to objective function.

Parameters:

objectiveFunctionFunction: Objective function.

Notes

Constraints and bounds are cleared if the objective has a different input dimension in order to keep the problem valid at all time.

setReliabilityMeasure(reliabilityMeasure)¶

Reliability measure accessor.

The measure on associated to the constraint

Parameters:

reliabilityMeasureMeasureEvaluation: Mesure function on the constraints

setResidualFunction(residualFunction)¶

Accessor to level function.

Parameters:

levelFunctionFunction: Level function.

setRobustnessMeasure(robustnessMeasure)¶

Robustness measure accessor.

The measure on associated to the objective function

Parameters:

robustnessMeasureMeasureEvaluation: Measure function on the objective.

setVariablesType(variableType)¶

Accessor to the variables type.

Parameters:

variablesTypeIndices: Types of the variables.

Notes

Possible values for each variable are ot.OptimizationProblemImplementation.CONTINUOUS, ot.OptimizationProblemImplementation.INTEGER and ot.OptimizationProblemImplementation.BINARY.

RobustOptimizationProblem¶

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