Multi-objective minimization

The objective is to learn the Pareto front of multiple minimization objectives. A vector of objective values \(\mathbf{y}\in \mathbb{R}^q\) lies at the Pareto front if the improvement (decrease) if it is not dominated by any other possible vector of outcomes. A vector \(\mathbf{y}_1\) is dominated by a vector \(\mathbf{y}_2\) if all entries of \(\mathbf{y}_2\) are smaller or equal the entries of \(\mathbf{y}_1\).

The strategy to find samples close or at the Pareto front is to maximize the hypervolume enclosed by all non-dominated sampling points and the upper reference point \(\mathbf{y}_{\rm upper}\). The progress is defined in terms of the decreasing hypervolume between the lower reference point \(\mathbf{y}_{\rm lower}\) and the non-dominated sampling points.

name (str)

The name of the objective.

Default: "objective"

variables (cell{str})

A list with the names of the variables that specify the objective.

Default: A list with the first two variables in the list of all variables.

lower_reference (cell{float})

Specifies the reference point \(\mathbf{y}_{\rm lower}\) of the hypervolume. The entries should be at maximum slightly smaller than the minimal possible value of each objective.

Default: This value has no default and must be provided

upper_reference (cell{float})

Specifies the reference point \(\mathbf{y}_{\rm upper}\) of the hypervolume. The entries should be at least slightly larger than the maximal possible value of each objective.

Default: This value has no default and must be provided

partitioning_tolerance (float)

The parameter can be increased to obtain an approximate partitioning faster. The tolerance is a fraction of the total hypervolume. When a hypercell’s volume divided by the total hypervolume is less than the tolerance, it is disregarded.

Default: 0.0

localize (bool)

If true, a local search is performed, i.e. samples are not drawn in regions with large uncertainty.

Default: false

min_acq_val (float)

The study is stopped if the maximum acquisition value (usually expected hypervolume improvement) of the last 5 iterations is below min_acq_val.

Default: 1e-16