Optimality criteria

In [ ]:

import matplotlib.pyplot as plt

import bofire.strategies.api as strategies
from bofire.data_models.constraints.api import LinearEqualityConstraint
from bofire.data_models.domain.api import Domain
from bofire.data_models.features.api import ContinuousInput, ContinuousOutput
from bofire.data_models.strategies.api import DoEStrategy
from bofire.data_models.strategies.doe import (
    AOptimalityCriterion,
    DOptimalityCriterion,
    EOptimalityCriterion,
    IOptimalityCriterion,
    KOptimalityCriterion,
    SpaceFillingCriterion,
)
from bofire.strategies.doe.objective import get_objective_function

import matplotlib.pyplot as plt import bofire.strategies.api as strategies from bofire.data_models.constraints.api import LinearEqualityConstraint from bofire.data_models.domain.api import Domain from bofire.data_models.features.api import ContinuousInput, ContinuousOutput from bofire.data_models.strategies.api import DoEStrategy from bofire.data_models.strategies.doe import ( AOptimalityCriterion, DOptimalityCriterion, EOptimalityCriterion, IOptimalityCriterion, KOptimalityCriterion, SpaceFillingCriterion, ) from bofire.strategies.doe.objective import get_objective_function

/home/linznedd/miniforge3/envs/bofire/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

Designs for different optimality criteria¶

In [ ]:

# Optimal designs for a quadratic model on the unit square
domain = Domain(
    inputs=[ContinuousInput(key=f"x{i+1}", bounds=(0, 1)) for i in range(2)],
    outputs=[ContinuousOutput(key="y")],
)
model_type = "fully-quadratic"
n_experiments = 13

designs = {}
for crit in [
    DOptimalityCriterion,
    AOptimalityCriterion,
    KOptimalityCriterion,
    EOptimalityCriterion,
    IOptimalityCriterion,
]:
    criterion = crit(formula=model_type)
    data_model = DoEStrategy(
        domain=domain,
        criterion=criterion,
        ipopt_options={"maxiter": 300},
    )
    strategy = strategies.map(data_model=data_model)
    design = strategy.ask(candidate_count=n_experiments)
    obj_value = get_objective_function(
        criterion=criterion, domain=domain, n_experiments=n_experiments
    ).evaluate(design.to_numpy().flatten())
    designs[obj_value] = design.to_numpy()

fig = plt.figure(figsize=((8, 8)))
ax = fig.add_subplot(111)
ax.set_title("Designs with different optimality criteria")
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
for obj, X in designs.items():
    ax.scatter(X[:, 0], X[:, 1], s=40, label=obj)
ax.grid(alpha=0.3)
ax.legend();

# Optimal designs for a quadratic model on the unit square domain = Domain( inputs=[ContinuousInput(key=f"x{i+1}", bounds=(0, 1)) for i in range(2)], outputs=[ContinuousOutput(key="y")], ) model_type = "fully-quadratic" n_experiments = 13 designs = {} for crit in [ DOptimalityCriterion, AOptimalityCriterion, KOptimalityCriterion, EOptimalityCriterion, IOptimalityCriterion, ]: criterion = crit(formula=model_type) data_model = DoEStrategy( domain=domain, criterion=criterion, ipopt_options={"maxiter": 300}, ) strategy = strategies.map(data_model=data_model) design = strategy.ask(candidate_count=n_experiments) obj_value = get_objective_function( criterion=criterion, domain=domain, n_experiments=n_experiments ).evaluate(design.to_numpy().flatten()) designs[obj_value] = design.to_numpy() fig = plt.figure(figsize=((8, 8))) ax = fig.add_subplot(111) ax.set_title("Designs with different optimality criteria") ax.set_xlabel("$x_1$") ax.set_ylabel("$x_2$") for obj, X in designs.items(): ax.scatter(X[:, 0], X[:, 1], s=40, label=obj) ax.grid(alpha=0.3) ax.legend();

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit https://github.com/coin-or/Ipopt
******************************************************************************

Space filling design¶

In [ ]:

# Space filling design on the unit 2-simplex
domain = Domain(
    inputs=[ContinuousInput(key=f"x{i+1}", bounds=(0, 1)) for i in range(3)],
    outputs=[ContinuousOutput(key="y")],
    constraints=[
        LinearEqualityConstraint(
            features=["x1", "x2", "x3"],
            coefficients=[1, 1, 1],
            rhs=1,
        ),
    ],
)
data_model = DoEStrategy(
    domain=domain, criterion=SpaceFillingCriterion(), ipopt_options={"maxiter": 500}
)
strategy = strategies.map(data_model=data_model)
X = strategy.ask(candidate_count=40).to_numpy()

fig = plt.figure(figsize=((10, 8)))
ax = fig.add_subplot(111, projection="3d")
ax.view_init(45, 20)
ax.set_title("Space filling design")
ax.set_xlabel("$x_1$")
ax.set_ylabel("$x_2$")
ax.set_zlabel("$x_3$")

# plot feasible polytope
ax.plot(xs=[0, 0, 1, 0], ys=[0, 1, 0, 0], zs=[1, 0, 0, 1], linewidth=2)

# plot design points
ax.scatter(xs=X[:, 0], ys=X[:, 1], zs=X[:, 2], s=40)

# Space filling design on the unit 2-simplex domain = Domain( inputs=[ContinuousInput(key=f"x{i+1}", bounds=(0, 1)) for i in range(3)], outputs=[ContinuousOutput(key="y")], constraints=[ LinearEqualityConstraint( features=["x1", "x2", "x3"], coefficients=[1, 1, 1], rhs=1, ), ], ) data_model = DoEStrategy( domain=domain, criterion=SpaceFillingCriterion(), ipopt_options={"maxiter": 500} ) strategy = strategies.map(data_model=data_model) X = strategy.ask(candidate_count=40).to_numpy() fig = plt.figure(figsize=((10, 8))) ax = fig.add_subplot(111, projection="3d") ax.view_init(45, 20) ax.set_title("Space filling design") ax.set_xlabel("$x_1$") ax.set_ylabel("$x_2$") ax.set_zlabel("$x_3$") # plot feasible polytope ax.plot(xs=[0, 0, 1, 0], ys=[0, 1, 0, 0], zs=[1, 0, 0, 1], linewidth=2) # plot design points ax.scatter(xs=X[:, 0], ys=X[:, 1], zs=X[:, 2], s=40)

Out[ ]:

<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7cf598509510>