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¶

In [ ]:

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

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¶

In [ ]:

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)

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¶

In [ ]:

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

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

Out[ ]:

'a + {a**2} + b + c + d + a:b + a:c + a:d + b:c + b:d + c:d'

Find D-optimal Design¶

In [ ]:

data_model = DoEStrategy(
    domain=domain,
    criterion=DOptimalityCriterion(formula=model_type),
    ipopt_options={"maxiter": 100, "disp": 0},
)
strategy = strategies.map(data_model=data_model)
design = strategy.ask(17)
design

data_model = DoEStrategy( domain=domain, criterion=DOptimalityCriterion(formula=model_type), ipopt_options={"maxiter": 100, "disp": 0}, ) strategy = strategies.map(data_model=data_model) design = strategy.ask(17) design

Out[ ]:

	a	b	c	d
0	5.000000e+00	40.000000	180.000002	199.999998
1	2.047832e+00	40.000000	180.000002	800.000008
2	5.000000e+00	40.000000	180.000002	800.000008
3	5.000000e+00	800.000008	79.999999	199.999998
4	5.000000e+00	800.000008	79.999999	800.000008
5	-9.973772e-09	40.000000	180.000002	199.999998
6	5.000000e+00	800.000008	180.000002	199.999998
7	-9.973772e-09	800.000008	180.000002	800.000008
8	-8.091201e-09	40.000000	79.999999	199.999998
9	5.000000e+00	40.000000	79.999999	199.999998
10	-9.981833e-09	40.000000	79.999999	800.000008
11	2.907832e+00	40.000000	79.999999	800.000008
12	-9.976118e-09	800.000008	180.000002	199.999998
13	-9.906825e-09	800.000008	79.999999	199.999998
14	-9.981833e-09	40.000000	79.999999	800.000008
15	-8.091050e-09	800.000008	79.999999	800.000008
16	5.000000e+00	800.000008	180.000002	800.000008

Analyze Confounding¶

In [ ]:

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()

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()