User manual

The goal is to formulate and solve robust optimization problem.

A robust optimization problem consists of a parametric objective objective J(x, \theta) and/or a parametric inequality constraint G(x, \theta) where x is a design variable and \theta a parameter.

\begin{aligned} & \underset{x \in \Rset^n}{\text{minimize~}} & & J(x, \theta) \\ & \text{subject to} & & G(x, \theta) \geq 0\\ \end{aligned}

The problem is made robust by:

  • modelling the parameter \theta by the the random vector \Theta with given distribution \cD.

  • choosing measure functions \rho_{J, \cD} and \lambda_{G, \cD} for the objective and constraint functions.

The the robust optimization problem reads:

\begin{aligned} & \underset{x \in \Rset^n}{\text{minimize~}} & & \rho_{J, \cD}(x) \ \\ & \text{subject to} & & \lambda_{G, \cD}(x) \geq 0\\ \end{aligned}

The definition of the measure functions is associated to the concept of MeasureEvaluation.

A measure evaluation can be used through MeasureFunction to expose generic function services.

A robust optimization problem can be defined with RobustOptimizationProblem, and then solved using a RobustOptimizationAlgorithm.

Note that this measure evaluation can be discretized over \theta so as to define a deterministic optimization problem using MeasureFactory.

Measure function

MeasureFunction(*args)

Measure function.

Measure evaluation

MeasureEvaluation(*args)

Measure evaluation base class.

MeanMeasure(*args)

Mean measure function.

MeanStandardDeviationTradeoffMeasure(*args)

Mean/variance tradeoff measure function.

QuantileMeasure(*args)

Quantile measure function.

WorstCaseMeasure(*args)

Worst case measure function.

VarianceMeasure(*args)

Variance measure function.

JointChanceMeasure(*args)

Joint chance measure function.

IndividualChanceMeasure(*args)

Individual chance measure function.

AggregatedMeasure(*args)

Aggregated measure function.

Define a robust optimization problem

RobustOptimizationProblem(*args)

Robust optimization problem.

Discretize a measure function

MeasureFactory(*args)

Discretize a measure function.

Solve a robust optimization problem

RobustOptimizationAlgorithm(*args)

Robust optimization algorithm base class.

SequentialMonteCarloRobustAlgorithm(*args)

Sequential Monte Carlo robust optimization algorithm.

Solve an inverse reliability problem

SubsetInverseSampling(*args)

Subset inverse simulation.

SubsetInverseSamplingResult(*args)

Result for inverse subset simulation.

InverseFORM(*args)

Inverse FORM.

InverseFORMResult(*args)

Result of Inverse FORM.