gemseo.algos.pareto.pareto_front module#

Pareto front.

class 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).