Desirability Optimization

This example demonstrates how to set up a multi-target optimization problem using the desirability approach. The focus lies on defining the target objects with the necessary transformations enabling the desirability computation, and the creation of the corresponding optimization objective.

Imports

import pandas as pd

from baybe import Campaign
from baybe.objectives import DesirabilityObjective
from baybe.parameters.numerical import NumericalContinuousParameter
from baybe.targets import NumericalTarget

Defining the Search Space

Because the search space is of secondary importance in this example, we keep it simple and consider only a single parameter, without loss of generality:

searchspace = NumericalContinuousParameter("parameter", (0, 1)).to_searchspace()

Defining the Targets

Next, we define our optimization targets. Because desirability computation relies on averaging target values, it is required that all targets are properly normalized. This can be achieved by applying appropriate target transformations, for which BayBE offers several built-in choices and also offers full customization for advanced use cases.

Target Normalization

If you know what you are doing, you can also disable the normalization check via the require_normalization flag, with the consequence that the selected averaging method is executed on the target values no matter if they are normalized or not.

For our example, we consider three simple targets reflecting different optimization goals. The first target takes values in the interval [0, 100] and is to be maximized. The normalized_ramp() constructor helps us achieve this by applying an affine transformation whose output is clamped to the unit interval:

target_max = NumericalTarget.normalized_ramp("target_max", cutoffs=(0, 100))

The second target takes values in the interval [-10, 0] and is to be minimized:

target_min = NumericalTarget.normalized_ramp(
    "target_min", cutoffs=(-10, 0), descending=True
)

For the third target, we like to match a certain value. To do so, we apply a target transformation that penalizes the distance to this value using a bell-shaped curve centered around it:

target_match = NumericalTarget.match_bell("target_match", match_value=50, sigma=5)

Customization

Note that you can easily change the specifics of the applied transformations by resorting to other target constructors or specifying custom transformation logic. For more details, see our target userguide.

Creating the Objective

The targets are collected in a DesirabilityObjective, which takes care of the averaging process. The specifics of the averaging can be configured by specifying optional weights for the targets and the type of averaging to be used:

targets = [target_max, target_min, target_match]
objective = DesirabilityObjective(targets, weights=[20, 20, 60], scalarizer="MEAN")

Getting Recommendations

We can now use the objective, like any other, to query recommendations, e.g. by setting up a Campaign:

campaign = Campaign(searchspace, objective)
recommendations = campaign.recommend(batch_size=3)
print(recommendations)

   parameter
0   0.137022
1   0.254427
2   0.695105

Accessing Desirability Values

Once the target measurements are available, …

recommendations[target_max.name] = [65, 35, 87]
recommendations[target_min.name] = [-8, -3, -5]
recommendations[target_match.name] = [55, 25, 48]

… we can access the corresponding desirability values via the objective:

campaign.add_measurements(recommendations)
desirability = objective.transform(recommendations, allow_extra=True)
print(pd.concat([recommendations, desirability], axis=1))

   parameter  target_max  target_min  target_match  Desirability
0   0.137022          65          -8            55      0.653918
1   0.254427          35          -3            25      0.130002
2   0.695105          87          -5            48      0.827870