gemseo / algos / pareto

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pareto_front module

Pareto front.

class gemseo.algos.pareto.pareto_front.ParetoFront(distance_from_utopia, f_anchors, f_anti_utopia, f_optima, f_utopia, f_utopia_neighbors, x_anchors, x_optima, x_utopia_neighbors)[source]

Bases: object

A Pareto front.

The design and objective vectors are noted x and f respectively.

Parameters:
  • distance_from_utopia (float)

  • f_anchors (RealArray)

  • f_anti_utopia (RealArray)

  • f_optima (RealArray)

  • f_utopia (RealArray)

  • f_utopia_neighbors (RealArray)

  • x_anchors (RealArray)

  • x_optima (RealArray)

  • x_utopia_neighbors (RealArray)

classmethod from_optimization_problem(problem)[source]

Create a ParetoFront from an OptimizationProblem.

Parameters:

problem – The optimization problem.

Returns:

The Pareto front.

Return type:

ParetoFront

distance_from_utopia: float

The shortest Euclidean distance from the Pareto front to the f_utopia.

f_anchors: RealArray

The values of the objectives of all anchor points.

At those points, each objective is minimized one at a time.

Its shape is (n_anchors, f_dimension).

f_anti_utopia: RealArray

The anti-utopia point, i.e. the maximum objective vector.

Its shape is (f_dimension,).

f_optima: RealArray

The objective values of the Pareto optima.

Its shape is (n_optima, f_dimension).

f_utopia: RealArray

The utopia point, i.e. the minimum objective vector.

In most Pareto fronts, there is no design value for which the objective is equal to the utopia.

Its shape is (f_dimension,).

f_utopia_neighbors: RealArray

The objectives value of the closest point(s) to the f_utopia.

The distance separating them from f_utopia is distance_from_utopia.

Its shape is (n_neighbors, f_dimension).

x_anchors: RealArray

The values of the design variables values of all anchor points.

At those points, each objective is minimized one at a time.

Its shape is (n_anchors, x_dimension).

x_optima: RealArray

The values of the design variables of the Pareto optima.

Its shape is (n_optima, x_dimension).

x_utopia_neighbors: RealArray

The design variables value of the closest point(s) to the f_utopia.

The distance separating them from f_utopia is distance_from_utopia.

Its shape is (n_neighbors, x_dimension).