# Desirability Optimization

This example demonstrates how to set up a multi-target optimization problem using the
{class}`desirability approach <baybe.objectives.desirability.DesirabilityObjective>`.
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


```python
import pandas as pd
```


```python
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:


```python
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.

```{admonition} Target Normalization
:class: note
If you know what you are doing, you can also disable the normalization check
via the
{paramref}`~baybe.objectives.desirability.DesirabilityObjective.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 {meth}`~baybe.targets.numerical.NumericalTarget.normalized_ramp` constructor helps
us achieve this by applying an affine transformation whose output is clamped to the
unit interval:


```python
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:


```python
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
{meth}`bell-shaped curve <baybe.targets.numerical.NumericalTarget.match_bell>`
centered around it:


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

```{admonition} Customization
:class: note
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
{ref}`target userguide <userguide/targets:NumericalTarget>`.
```

## Creating the Objective

The targets are collected in a
{class}`~baybe.objectives.desirability.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:


```python
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
{doc}`query recommendations </userguide/getting_recommendations>`, e.g. by setting
up a {class}`~baybe.campaign.Campaign`:


```python
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, ...


```python
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:


```python
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