Design with explicit Formula

This tutorial notebook shows how to setup a D-optimal design with BoFire while providing an explicit formula and not just one of the four available keywords linear, linear-and-interaction, linear-and-quadratic, fully-quadratic.

Make sure that cyipoptis installed. The recommend way is the installation via conda conda install -c conda-forge cyipopt.

Imports

import bofire.strategies.api as strategies
from bofire.data_models.api import Domain, Inputs
from bofire.data_models.features.api import ContinuousInput
from bofire.data_models.strategies.api import DoEStrategy
from bofire.data_models.strategies.doe import DOptimalityCriterion
from bofire.utils.doe import get_confounding_matrix

Setup of the problem

input_features = Inputs(
    features=[
        ContinuousInput(key="a", bounds=(0, 5)),
        ContinuousInput(key="b", bounds=(40, 800)),
        ContinuousInput(key="c", bounds=(80, 180)),
        ContinuousInput(key="d", bounds=(200, 800)),
    ],
)
domain = Domain(inputs=input_features)

Definition of the formula for which the optimal points should be found

model_type = "a + {a**2} + b + c + d + a:b + a:c + a:d + b:c + b:d + c:d"
model_type
'a + {a**2} + b + c + d + a:b + a:c + a:d + b:c + b:d + c:d'

Find D-optimal Design

data_model = DoEStrategy(
    domain=domain,
    criterion=DOptimalityCriterion(formula=model_type),
    ipopt_options={"max_iter": 100, "print_level": 0},
)
strategy = strategies.map(data_model=data_model)
design = strategy.ask(17)
design
a b c d
0 5.000000 40.000000 180.0 200.000000
1 0.000000 99.440742 80.0 393.854501
2 0.000000 800.000000 80.0 200.000000
3 5.000000 800.000000 80.0 791.836164
4 0.000000 800.000000 180.0 800.000000
5 0.000000 800.000000 80.0 800.000000
6 5.000000 40.000000 180.0 800.000000
7 2.835284 196.954398 80.0 465.644657
8 5.000000 354.402908 80.0 200.000000
9 0.000000 661.237803 80.0 352.660140
10 5.000000 800.000000 80.0 605.990034
11 5.000000 40.000000 80.0 800.000000
12 0.000000 272.971940 180.0 200.000000
13 5.000000 800.000000 180.0 200.000000
14 5.000000 676.257397 180.0 754.742127
15 0.000000 40.000000 180.0 800.000000
16 0.000000 40.000000 80.0 377.392833

Analyze Confounding

import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns


matplotlib.rcParams["figure.dpi"] = 120

m = get_confounding_matrix(
    domain.inputs,
    design=design,
    interactions=[2, 3],
    powers=[2],
)

sns.heatmap(m, annot=True, annot_kws={"fontsize": 7}, fmt="2.1f")
plt.show()