Merging multiple objectives to a scalar target for single-target BO

import matplotlib.pyplot as plt
import numpy as np
import torch

import bofire.strategies.api as strategies
from bofire.benchmarks.api import DTLZ2
from bofire.data_models.objectives import api as objectives_data_model
from bofire.data_models.strategies import api as strategies_data_model

Benchmark Problem

Only used for domain definition

bench = DTLZ2(dim=2, num_objectives=2)
experiments = bench.f(bench.domain.inputs.sample(10), return_complete=True)

domain = bench.domain

Change the objectives: Multiplication, only reasonable for objectives > 0

outputs = domain.outputs.get_by_objective()

outputs[0].objective = objectives_data_model.MaximizeObjective(w=1.0, bounds=(0.0, 5.0))
outputs[1].objective = objectives_data_model.MaximizeObjective(w=1.0, bounds=(0.0, 2.0))
# outputs[1].objective = objectives_data_model.MaximizeSigmoidObjective(w = 0.5, tp=2.5, steepness=3.)

Select Strategies

We will use pure multiplicative and additive Sobo strategies, as well as a mixed one for this example: - Multiplicative: $f = f_0^{w_0} \cdot f_1^{w_1}$ - Additive: $f = f_0 \cdot w_0 + f_1 \cdot w_1$ - Mixed (with f1 being the additive objective): $f = f_0^{w_0} \cdot (1 + w_1 \cdot f_1)$

strategy_data_model = {
    "multiplicative": strategies_data_model.MultiplicativeSoboStrategy(domain=domain),
    "additive": strategies_data_model.AdditiveSoboStrategy(domain=domain),
    "mixed": strategies_data_model.MultiplicativeAdditiveSoboStrategy(
        domain=domain, additive_features=["f_1"]
    ),
}

We will now create the strategies and evaluate them on a grid to visualize the objectives.

We see the following: - Multiplicative: The objective is a product of the objectives: If either $f_0$ or $f_1$ is low, the objective is low. - Additive: The objective is a sum of the objectives: We see a linear increase in the objective with increasing $f_0$ and $f_1$. This is useful for complementary objectives. - Mixed: The objective is more strict w.r.t. $f_0$ than the additive objective $f_1$. The overall desirability can also be high, if $f_1$ is low.

Changing the weights $w_i$ in the objectives above will further change the preference of $f_0$ and $f_1$.

# map from the strategy data-model to the actual strategy object instances
strategy = {
    key: strategies.map(strategy_data_model)
    for (key, strategy_data_model) in strategy_data_model.items()
}

# tell the strategies about the experiments. This is required to set up the models, but not for the objective evaluation
for _, strat in strategy.items():
    strat.tell(experiments)

# get the objectives for evaluation as a torch executable
objectives = {
    key: strategy._get_objective_and_constraints()[0]
    for (key, strategy) in strategy.items()
}

# f_0 / f_1 coordinates for objctive evaluation
mesh = np.meshgrid(np.linspace(0, 2, 100), np.linspace(0, 5, 100))
# transform to matrix-form torch tensor
mesh_tensor = torch.tensor([m.flatten() for m in mesh]).T

/tmp/ipykernel_4005/1215888523.py:4: UserWarning:

Creating a tensor from a list of numpy.ndarrays is extremely slow. Please consider converting the list to a single numpy.ndarray with numpy.array() before converting to a tensor. (Triggered internally at /pytorch/torch/csrc/utils/tensor_new.cpp:253.)

# evaluate objectives
objectives_eval = {
    key: obj(mesh_tensor).detach().numpy().reshape(mesh[0].shape)
    for (key, obj) in objectives.items()
}

# plot the objectives as contour plots
for key, obj in objectives_eval.items():
    plt.figure()
    plt.contour(*mesh, obj, label=key)
    plt.title(key)
    plt.xlabel("f_0")
    plt.ylabel("f_1")
    plt.grid(True)
    plt.colorbar()

plt.show()

/tmp/ipykernel_4005/261754645.py:4: UserWarning:

The following kwargs were not used by contour: 'label'

--- title: Merging multiple objectives to a scalar target for single-target BO jupyter: python3 --- ```{python} import matplotlib.pyplot as plt import numpy as np import torch import bofire.strategies.api as strategies from bofire.benchmarks.api import DTLZ2 from bofire.data_models.objectives import api as objectives_data_model from bofire.data_models.strategies import api as strategies_data_model ``` ## Benchmark Problem Only used for domain definition ```{python} bench = DTLZ2(dim=2, num_objectives=2) experiments = bench.f(bench.domain.inputs.sample(10), return_complete=True) domain = bench.domain ``` ### Change the objectives: Multiplication, only reasonable for objectives > 0 ```{python} outputs = domain.outputs.get_by_objective() outputs[0].objective = objectives_data_model.MaximizeObjective(w=1.0, bounds=(0.0, 5.0)) outputs[1].objective = objectives_data_model.MaximizeObjective(w=1.0, bounds=(0.0, 2.0)) # outputs[1].objective = objectives_data_model.MaximizeSigmoidObjective(w = 0.5, tp=2.5, steepness=3.) ``` ## Select Strategies We will use pure multiplicative and additive Sobo strategies, as well as a mixed one for this example: - Multiplicative: $f = f_0^{w_0} \cdot f_1^{w_1}$ - Additive: $f = f_0 \cdot w_0 + f_1 \cdot w_1$ - Mixed (with f1 being the additive objective): $f = f_0^{w_0} \cdot (1 + w_1 \cdot f_1)$ ```{python} strategy_data_model = { "multiplicative": strategies_data_model.MultiplicativeSoboStrategy(domain=domain), "additive": strategies_data_model.AdditiveSoboStrategy(domain=domain), "mixed": strategies_data_model.MultiplicativeAdditiveSoboStrategy( domain=domain, additive_features=["f_1"] ), } ``` ### We will now create the strategies and evaluate them on a grid to visualize the objectives. We see the following: - Multiplicative: The objective is a product of the objectives: If either $f_0$ or $f_1$ is low, the objective is low. - Additive: The objective is a sum of the objectives: We see a linear increase in the objective with increasing $f_0$ and $f_1$. This is useful for complementary objectives. - Mixed: The objective is more strict w.r.t. $f_0$ than the additive objective $f_1$. The overall desirability can also be high, if $f_1$ is low. Changing the weights $w_i$ in the objectives above will further change the preference of $f_0$ and $f_1$. ```{python} # map from the strategy data-model to the actual strategy object instances strategy = { key: strategies.map(strategy_data_model) for (key, strategy_data_model) in strategy_data_model.items() } ``` ```{python} # tell the strategies about the experiments. This is required to set up the models, but not for the objective evaluation for _, strat in strategy.items(): strat.tell(experiments) ``` ```{python} # get the objectives for evaluation as a torch executable objectives = { key: strategy._get_objective_and_constraints()[0] for (key, strategy) in strategy.items() } ``` ```{python} # f_0 / f_1 coordinates for objctive evaluation mesh = np.meshgrid(np.linspace(0, 2, 100), np.linspace(0, 5, 100)) # transform to matrix-form torch tensor mesh_tensor = torch.tensor([m.flatten() for m in mesh]).T ``` ```{python} # evaluate objectives objectives_eval = { key: obj(mesh_tensor).detach().numpy().reshape(mesh[0].shape) for (key, obj) in objectives.items() } ``` ```{python} # plot the objectives as contour plots for key, obj in objectives_eval.items(): plt.figure() plt.contour(*mesh, obj, label=key) plt.title(key) plt.xlabel("f_0") plt.ylabel("f_1") plt.grid(True) plt.colorbar() plt.show() ```